Quantum Physics

Commuting phase terms in quantum electronic design automation (QEDA) placement circuits are logically invariant under reordering, yet their routed cost varies substantially after hardware mapping, since term order affects CNOT cancellation, interaction locality, and routing pressure. We cast parity/support phase-term ordering within a QEDA phase component as a shielded reinforcement-learning problem: a feasibility shield restricts each step to unemitted terms, so every trajectory is a valid permutation by construction, and an elite (cross-entropy-method) policy is trained against a route-charged proxy combining support-transition size and heavy-hex topology-distance features. We validate by direct Qiskit routing of logically equivalent circuits to a synthetic IBM-style heavy-hex map. On 36-term parity-walk components (50 term seeds x 2 transpiler seeds, statistics at the term-seed level), the per-instance learned ordering reduces mean routed CX to 336.0, a 5.7-12.2% paired reduction over 2-opt and simulated-annealing search at equal or greater proxy budget and 22.3% over the default construction order; routed-CX and routed-depth gains are significant after Bonferroni correction. Honest transfer audits show the proxy is predictive for the parity-walk component but not for extraction-heavy or token/permutation circuits, which require architecture-aware rewards, scoping the contribution accordingly.

We present a variational algorithm for learning an unknown quantum unitary from time-series observable measurements, with no structural assumption about the target. The core separation: a hardware-efficient parametrised circuit learns the evolution operator U via observable matching; Hamiltonian identification follows as classical post-processing via matrix logarithm, when the target happens to be exp(-iH*tau). Three experiments establish the method's generality. First, a noiseless proof of correctness with exact gradients (L-BFGS-B) achieves MSE 1.61e-14 and recovers all Hamiltonian coefficients to six decimal places. Second, a gate-learning experiment fits CNOT, iSWAP, and a Haar-random SU(4) element -- none generated by any fixed Hamiltonian -- all to process fidelity 1.000000, confirming the method does not rely on Trotterisation structure. Third, quantum deployment via SPSA-Adam under Qiskit Aer depolarising noise (p1=0.001, p2=0.01, Nshots=1024) recovers all three Ising Hamiltonian terms with errors below 8%. The optimiser, SPSA-Adam, combines SPSA's hardware-efficient two-point gradient estimation with Adam's adaptive moment updates. A four-stage moment-warm curriculum progressively extends the training horizon, converting a global non-convex problem into a sequence of well-posed local ones.

Current implementations of quantum batteries are constrained by limited energy density and short retention times associated with the electronic or molecular excitations. Here we propose a nuclear quantum battery based on collective excitation of the $^{57}$Fe nuclei of density $n$ embedded in a planar hard X-ray waveguide. Using a Green function waveguide-QED description, we study charging via excitation beyond linear response, where saturation and drive back-action reshape the incident pulse. We introduce a self-consistent waveform-engineering protocol that inhibits local radiative decay in the waveguide thus promoting absorption into high-lying collective nuclear excitation manifolds. We show an enhanced excitation cross section of the nuclear ensemble which yields superlinear charging, with maximum studied energy density scaling approximately like $n \sqrt{n}$. Our results provide a route to high-energy-density quantum charging at hard X-ray energies using contemporary X-ray sources and waveguide architectures by identifying nonlinear, collectively enhanced absorption as a key mechanism for nuclear quantum battery operation.

Li and Boyle showed that the Penrose tiling defines a quantum error-correcting code: superpositions of tilings over isometry orbits protect quantum information against erasure of any bounded region. We extend the construction to the aperiodic monotiles discovered by Smith, Myers, Kaplan and Goodman-Strauss. For the Hat, we prove strong local indistinguishability for all Hat tilings, and we prove local recoverability unconditionally for all nonsingular Hat tilings via the torus parametrization of the underlying cut-and-project scheme. The remaining singular case reduces to one sharply posed geometric question -- can a region that is a union of hats be retiled a second way? -- which we verify computationally has no counterexample up to a substantial scale: a certified $2490$-tile patch admits precisely one tiling by hats, so all $2^{2490}$ of its tile-subregions retile uniquely. Unlike the Penrose, Ammann-Beenker and Fibonacci tilings, both monotiles form two local-indistinguishability classes, so their code spaces split into two erasure-correcting sectors carrying a superselected classical label. Whether the label survives depends on which isometries are gauged: the Spectre's classes are exchanged by a $30^{\circ}$ rotation and merge once all proper isometries are gauged, whereas the Hat's are exchanged only by reflections. Under the physically natural gauge group $SE(2)$, the Hat code therefore stores one robust classical bit -- the handedness of its long-range order, readable in any bounded window with separation $\Delta = |K|\sqrt{5}/3$ -- alongside its protected quantum sectors. It is the reflexible monotile, not the chiral one, that carries the chirality bit. We give the exact Perron-Frobenius data of both codes, including the per-class reflected-Hat frequencies $(3\mp\sqrt{5})/6$ and the Spectre orientation-class frequencies $(5\pm\sqrt{15})/10$.

Non-Hermitian systems offer new opportunities for quantum optimization and computation. Here, we show that non-Hermitian quantum adiabatic algorithms require not only a real, gapped spectrum, but also a stable pseudospectrum. We propose a novel framework by mapping non-unitary quantum circuits to local Hamiltonian paths, thereby preserving their optimization advantages and shallow depth. While a direct non-Hermitian extension of the Feynman-Kitaev construction suffers severe pseudospectral instability, our history-decoupled construction yields both a controlled pseudospectrum and a real, gapped spectrum. Using the CK benchmark family of maximum independent set problems, we demonstrate polynomial-evolution-time non-Hermitian adiabatic computation that remains robust against perturbations. We further discuss a feasible optical implementation using coupled waveguides with an auxiliary lossy channel. Our work establishes pseudospectral stability, alongside real, gapped spectra, as key principles and a practical route for non-Hermitian quantum adiabatic computation.

In Hamiltonian systems, the only basis-independent quantity is the spectrum. Given a spectrum, quantum mereology seeks preferred tensor-product decompositions into local subsystems, leading to the emergence of locality. Causal order, however, remains fixed by the Hamiltonian time evolution. In contrast, higher-order quantum theory permits more general processes that need not possess a definite global causal order. In the process-matrix framework, specifying a process requires a choice of subsystems corresponding to the input and output Hilbert spaces of each agent. A change of basis redefines both the agents and the corresponding decompositions into subsystems, while leaving the spectrum of the process matrix invariant. Here, we study how causality arises from this spectrum. First, we derive spectral constraints on processes compatible with definite causal order. Second, we show that, in the thermodynamic limit, generic quantum processes admit a preferred decomposition with a definite causal order. This suggests a mechanism for the emergence of classical causality only from algebraic ingredients.

The Paradox of the Third Particle arises when particles are described relative to one of them serving as a reference frame. Although it is typically attributed to quantum superpositions, we show that the paradox and its ramifications$\unicode{x2014}$such as the relativity of subsystems$\unicode{x2014}$already occur classically. In light of this insight, we establish a no-go theorem that holds whenever physical subsystems, whether classical or quantum, are used as reference frames: if one demands that frame transformations be information-preserving, then it is impossible to meaningfully partition the world into subsystems, like individual particles, from the perspective of each frame.

We demonstrate an asymptotic gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis by employing the sum-of-squares spectral gap amplification protocol. The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost. This is achieved by using a sum-of-squares operator generated by the total charge density operator resulting in a block encoding normalization improvement of $\lambda = \mathcal{O}\left(\eta\Delta^{-1.5}+\eta^{1.5}\Delta^{-1} \right)$ compared to prior work $\lambda = \mathcal{O}(\eta\Delta^{-2}+\eta^2\Delta^{-1})$ where $\eta$ is the number of electrons and $\Delta$ is the simulation grid spacing. The asymptotic reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44\times$ corresponding to the lowest cost estimates for ab initio materials simulation.

Thermodynamics imposes fundamental constraints on the evolution of quantum systems. These constraints and their dynamical consequences have been formulated within distinct paradigms, including axiomatic approaches based on quantum master equations, microscopic descriptions of open-system dynamics, and operational formulations rooted in resource theories. While each perspective has yielded important insights into thermodynamically consistent quantum dynamics, their precise relationship has remained unresolved. Here we establish the exact equivalence of these three paradigms in the Markovian regime. We prove that thermal Lindbladians satisfying Markovianity, time-translation symmetry, and quantum detailed balance are precisely those admitting a microscopic realisation as an energy-conserving thermal collision model and, equivalently, those generating Markovian thermal operations. This unifies the existing approaches to Markovian quantum thermodynamics and identifies its dynamical underpinnings. We further provide an explicit microscopic protocol for simulating thermal Markovian processes with controlled finite-time simulation errors. We illustrate its applicability by providing faithful thermal collision-model implementations of a qubit thermalising in a bosonic environment and of a three-level autonomous thermal machine. In the latter case, the protocol gives rise to a finite-stroke thermal engine that not only reproduces the continuous-time dynamics but also its steady-state thermodynamic performance. As a whole, these results establish a unified foundation for Markovian quantum thermodynamics, showing that its axiomatic, microscopic, and operational formulations are exactly equivalent and providing a universal protocol for implementing thermal processes and machines.

The Bayesian Nagaoka--Hayashi (NH) bound is a semidefinite lower bound on the Bayes risk of multiparameter estimation, tighter than the Bayesian symmertic logarithmic derivative (SLD) Cramér--Rao bounds, and whether it can be attained is an open problem. We study the single-shot estimation of a qubit rotation, all three parameters at once, under depolarizing noise and a uniform prior, with $k$ parallel uses of the channel. Rotational covariance reduces the joint optimization of probe, measurement, and estimator, and the NH bound itself, to small semidefinite programs, solvable through $k=4$. At every number of uses and noise strength the optimized strategy reaches the NH bound within the numerical precision of the calculation, numerical evidence that the bound is attained for this channel family, while the SLD bound lies strictly below and is never attained. As the noise grows the optimal probe collapses to the tensored Bell state.

Preserving quantum resources in dissipative environments is a fundamental challenge in quantum information processing. While environmental interactions usually degrade quantum resources, we theoretically show that in a Quantum Brownian Motion (QBM) channel, continuous-variable state discrimination can be improved by increasing, rather than minimizing, the initial thermal noise. Specifically, without suppressing the inherent environmental dissipation, when combined with squeezing, this initial noise induces a coherence preservation mechanism driven by the transient non-thermalization of the probe with the bath. This preservation translates into a pronounced reduction in error probabilities for state discrimination between orthogonal squeezing directions. Furthermore, we also show that quadrature homodyne detection achieves near-optimal performance, approaching the Helstrom limit. These results highlight the advantage of exploiting thermal-squeezed states, offering a robust physical architecture for quantum communication in high-temperature environments.

Hybrid quantum-classical workflows are expected to underpin practical quantum computing applications, yet the quantum and HPC communities lack a shared framework for reasoning about where and when their integration requirements matter most. Such a framework must separate two distinct levels of analysis: the application level, where communication overhead affects runtime performance, and the real-time level, where it determines feasibility. To address this, we introduce a runtime model that decomposes workflow execution into quantum compute, classical compute, and communication costs. At the application level, a communication-to-computation ratio from this decomposition quantifies whether a workflow is communication-bound or compute-bound; at the real-time level, a feasibility constraint determines whether timing requirements can be met at all, with the reaction time setting the logical clock speed of fault-tolerant computation once they are. Application of this model to representative workflows demonstrates that co-location of quantum processors with HPC infrastructure offers negligible performance benefit for compute-intensive applications today, while tight integration remains crucial for real-time tasks such as quantum error correction needed for large scale quantum computations. However, we discuss how even at the application level these assessments may shift with hardware evolution, illustrating how the model can identify specific crossover conditions, and how, under fault tolerance, the reaction time can set application-level performance.

The ability to generate and detect quantum states of light on a single integrated photonic device is essential to scale quantum photonics into useful quantum technologies. Integrating the required capabilities into complementary-metal-oxide-semiconductor compatible monolithic chips can reduce cost and unlock new functionality through miniaturisation. In this work we demonstrate a single silicon-on-insulator photonic integrated circuit for the monolithic generation and detection of quantum light on a commercially available platform that operates entirely at room temperature. Specifically, we leverage spontaneous four-wave mixing in silicon waveguides to produce squeezed light which is subsequently detected by photodiodes operating in a pulsed homodyne detector configuration on the same chip as the source. We directly measure $0.25(1)$ dB of squeezing, including contributions from waveguide propagation loss and detection inefficiency, and include a detailed analysis of the impact of nonlinear loss on the squeezing levels achievable using this platform.

As practical quantum networks approach large-scale deployment, the need for efficient user-to-user frequency allocation is increasing, yet current approaches only provide partial solutions to the routing and spectrum allocation problem for an arbitrary quantum network. We address this challenge for repeater-less flex-grid quantum networks based on hyperentangled photons using an efficient three-stage pipeline combining leading tools in classical networking with recent advances in numerical optimization. First, double instantiations of Yen's algorithm obtain low-loss route candidates between each pair of users and the entanglement sources. Second, the advanced process optimizer (APOPT) obtains frequency channel allocations that maximize distribution rates under fidelity constraints. Finally, the constraint programming solver using satisfiability methods (CP-SAT) assigns specific frequency bins to each link, ensuring that there is no contention between frequencies from different sources. We numerically demonstrate this approach on a representative ring network and a Manhattan incumbent local exchange carrier topology, realizing significant improvements over prior genetic algorithm approaches in speed, accuracy, and scalability. Overall, this pipeline provides an efficient heuristic workflow for optimizing broadband entanglement distribution, applicable to arbitrarily connected quantum networks integrated within the existing lightwave infrastructure.

Quantum platforms can realize many-body dynamics beyond classical simulation yet complete readout remains intractable: the cost of extracting accessible information scales exponentially with system size. Classical shadows and Bell sampling offer scalable, multi-observable estimation from randomized or entanglement-assisted measurements. Here we aim to push these ideas beyond static snapshots to dynamical correlators, including out-of-time-ordered correlators (OTOCs) and two-point functions. In particular, we introduce the notion of the shadow of an operator, defined as the classical shadow of the vectorized time-evolved operator. Pauli operator-shadows enable simultaneous estimation of all local OTOCs, while Clifford operator-shadows enable efficient simultaneous estimation of all two-point correlators. Alternatively, Bell sampling allows one to simultaneously compute all diagonal OTOCs. We also prove information-theoretic lower bounds for learning OTOCs, fully characterizing their query complexities in many cases, and yielding exponential separations that formalize when the vectorized approach provides measurement-efficiency advantages.

In the Hayden--Preskill protocol, the decoder is usually assumed to know the microscopic identity of the collected output qubits. We study what happens when these labels are unavailable and only the relative order of the received qubits is preserved. The resulting order-preserving deletion channel maps an $n$-qubit scrambled register to a subsequence of length $\ell$. For a diary of fixed size $k$, we prove that the optimal entanglement fidelity converges to the no-output value $4^{-k}$ when $\ell=o(n^{2/3})$, uniformly over the scrambling unitary. For a Haar-random scrambling unitary, it converges to one when $\ell=\omega(n^{2/3})$ and $\ell=o(n)$. Monotonicity then gives the fixed-error recovery scale $\ell_{\mathrm{rec}}=\Theta(n^{2/3})$. We also consider partial position information obtained by dividing the register into $B$ consecutive blocks and revealing the block of origin of each received qubit. The recovery scale becomes $\ell_{\mathrm{rec}}(n,B)\asymp n^{2/3}B^{-1/3}$ for $B\leq\sqrt n$ and $\ell_{\mathrm{rec}}(n,B)\asymp n/B$ for $B\geq\sqrt n$. The exponent $2/3$ is traced to rank-aligned coincidences between random subsequences, which control both the converse and the recovery argument. Thus, even purely classical information about the origin of the received subsystems can change the amount of quantum output required for Hayden--Preskill recovery.

Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.

In this work, we establish a structural correspondence between quantum states and matroid theory. This connection demonstrates that key properties of quantum states, including entanglement and measurement, can be characterized in purely combinatorial terms via matroids, despite the apparent conceptual distance between these two fields. Using this framework, we show that a matroid-supported state is genuinely entangled when its underlying matroid is connected. Moreover, a uniform superposition over all bases of a matroid is genuinely entangled if and only if the matroid is connected. We also demonstrate that a local measurement in the $Z$-basis on such a state yields another matroid-supported state, whose underlying matroid is a minor of the original one. Inspired by matroid duality, we further propose a notion of quantum state duality, uncovering a deep structural symmetry in state transformations.

Learning a classical description of a quantum state is a fundamental task in quantum computation. Among the most important classes of quantum states are stabilizer states, which play a central role in quantum error correction and fault-tolerant computation. To mitigate the effects of realistic noise, agnostic learning of stabilizer states has emerged as a natural and well-motivated problem. Recently, Chen \textit{et al.} [STOC'25, p. 429-438] resolved this problem for qubit systems by using a stabilizer bootstrapping framework. However, the agnostic learning of qudit stabilizer states remains largely unexplored, since the qudit setting introduces fundamental structural differences that prevent a direct generalization of existing qubit techniques. In this paper, we successfully generalize the stabilizer bootstrapping framework to qudit systems and present the first efficient quantum algorithm for agnostic learning of qudit stabilizer states. Specifically, given copies of an unknown $n$-qudit pure state $|\psi\rangle$ that has fidelity $\tau$ with some stabilizer state, our algorithm outputs a stabilizer state $|\phi\rangle$ such that $\left| \braket{\phi|\psi} \right|^2 \geq \tau - \varepsilon$ with high probability. The algorithm uses only single-copy and four-copy measurements, and its sample and time complexity scale as $(d/\tau)^{O(d^2 \log(1/\tau))} \cdot \mathrm{poly}(n, 1/\varepsilon)$, where the dimension $d$ is an odd prime. As a direct corollary, our algorithm enables efficient estimation of the magic of a quantum state, as quantified by its stabilizer fidelity. Completing the picture, we also present a streamlined algorithm for the high-fidelity regime $\tau > \cos^2(\pi/8)$, establishing a qudit analogue of the threshold-based approach in prior qubit work.

Neutral-atom arrays and trapped-ion crystals offer complementary strengths for fault-tolerant quantum computing but lack a fast way to deterministically interact. Here we propose a controlled-$Z$ gate generated by the charge-induced-dipole ($C_4$) force between a Rydberg-excited atom and a trapped ion, balanced by a spin-dependent optical Magnus force on the ion that closes phase-space trajectories within a few microseconds. Toggling the Rydberg state extends the scheme to multi-ion crystals at negligible overhead. The resulting ${\sim}5\,$kHz atom shuttle accelerates short-distance QCCD links and enables hybrid qLDPC memories in which atom logical qubits are written onto an ion block treated as a passive storage zone. We perform circuit-level Monte Carlo simulations and find that the hybrid architecture supports orders of magnitude more operations than atom-only or ion-only architectures at fixed code distance and logical error rate.

We consider whether every quantum random access code (QRAC) with density-operator encodings and arbitrary decoding measurements obeys the conjectured bound $p\leq(1+\sqrt{m/n})/2$, where $n$ classical bits are encoded into $m$ qubits and $p$ is the worst-case success probability. We find that classical random access codes with private randomness, which form a subclass of this QRAC model, violate the bound. We embed these classical codes as QRACs with diagonal encoding states and commuting decoding measurements, and construct pure-state realizations with identical decoding statistics. The achievability theorem of Ambainis, Nayak, Ta-Shma, and Vazirani then yields violations for every fixed $p\in(1/2,1)$ at sufficiently large input length. The counterexamples span the full open interval between the conjectured and Nayak bounds at each fixed compression rate. A finite-blocklength analysis further yields order-optimal logarithmic qubit scaling for a recovery bias scaling as $\sqrt{\log_2 n/n}$ with a sufficiently large prefactor. These results identify the classical coding rate as the source of the separation and motivate restricted bounds based on quantitative spectral properties of decoding measurements.

Previous investigations of dynamical quantum phase transition (DQPT) have predominantly focused on sudden quench protocols. In this work, we systematically explore the fate of DQPT from the sudden to the slow quench regime. We establish that DQPT remains robust under slow quenching when the protocol crosses an equilibrium quantum phase transition. Conversely, we show that accidental DQPTs,which occur when the pre and post quench Hamiltonians reside in the same equilibrium phase, can be filtered out in the slow quench limit. This demonstrates that slow quenches can reveal the intrinsic connection between DQPT and equilibrium quantum phase transitions, thereby enabling DQPT to serve as a dynamical probe for identifying equilibrium quantum critical points. We illustrate these findings with examples from the XY chain, the Aubry-André model, and the trimer Su-Schrieffer-Heeger model.

Continuous-variable quantum key distribution (CVQKD) has attracted extensive attention due to its compatibility and low costs. However, bandwidth mismatch exists to varying degrees between the transmitter and receiver. This may prevent frequency components carrying modulation information from being fully perceived by the legitimate party. In this paper, we identify a practical security loophole caused by bandwidth mismatch and propose a corresponding spectral attack scheme. Different from previous approaches that exploit security loopholes to conceal the excess noise introduced by intercept-resend attacks, this scheme can directly obtain raw-key information without introducing additional disturbances. A proof-of-principle attack on a CVQKD system with filtering operation is constructed to verify the feasibility. Experimental results indicate that Eve can obtain enough information to render the system insecure if this practical security loophole is ignored. Based on the identified security loophole, corresponding defense strategies are proposed. This work helps bridge the gap between theoretical models and practical implementations, providing a reference for defense design in practical quantum communication systems.

Motion-mediated trapped-ion gates typically apply synchronized state-dependent forces to both target ions. We consider the complementary setting in which one addressing channel alternates between the targets, so their force windows do not overlap. In a complex-amplitude near-resonant description, each window generates a displacement vector, and ordered symplectic products of vectors on different ions produce the ZZ phase. For fixed envelopes and timings, relative rotations of the window displacement vectors redirect the sign and magnitude of this phase, whereas a common rotation of all displacement vectors leaves the pair phase invariant. Motivated by experimental alternating-addressing protocols, we design matched-envelope phase and contrast controls that distinguish the boundary-phase response from closure error and residual force in dark gaps. Waveform synthesis suppresses differential motion, while a reduced-spin map that is exact within the linear spin-dependent-force model accounts for projector-common motion, deterministic local-Z phases, spectator coupling, and control-parameter drift. A conditional-Ramsey protocol predicts continuous and reset contrasts of 0.998 and 0.996, with the reset rule redirecting the extracted pair phase by 0.581 rad relative to the continuous rule, modulo pi/2. In the representative comparison, sequential control uses only one active target channel at a time, but requires 1.826 times the normalized squared-force action of independently calibrated simultaneous control. For representative experimental parameters and within the stated approximations, the inter-window force-quadrature reference therefore provides an experimentally testable control resource for sequential trapped-ion interactions.

Non-Gaussianity is an essential resource for genuine quantum advantages in continuous-variable quantum systems and is regarded as a counterpart of the magic resource in discrete-variable systems. Recently, an exact correspondence between non-Gaussianity (NG) and the magic resource was identified within the Gottesman--Kitaev--Preskill (GKP) encoding framework. Whether such a relation persists beyond GKP encoding, however, remains unclear. Here, we address this question in the cat-code setting. By comparing the Wigner logarithmic negativity (WLN) and a magic measure defined from a phase-operator basis, we analyze the resource geometry of non-degenerate $d$-peaked cat states. We find that cat codes do not inherit the global value-preserving GKP magic--NG equivalence, but their asymptotic WLN geometry allows a constructive local alignment with the magic-measure geometry. Specifically, under a distinguished SU($d$) asymptotic cat code, we establish a sector-dependent alignment between WLN level sets and magic-measure level sets based on their intrinsic local geometries. These results identify both the global incompatibility and the locally constructive relation between magic and non-Gaussian resources in cat codes, suggesting a geometry-based approach to resource correspondences beyond the GKP framework.

Grover's algorithm is one of the most significant quantum algorithms, enabling the search for a marked element in an unsorted database quadratically faster than classical search algorithms. We utilize Groves's algorithm to detect the edges of a digital image faster than any classical edge detection methods. The high success probability of our method in detecting image edges, compared to most existing quantum edge detection methods, makes it a more suitable candidate for use in the presence of noise on current quantum devices. We implemented our model for the $2\times 2$ blocks of the image using a two-qubit Qiskit circuit with the QASM simulator and the noisy IBM Sydney(fake) device, making it suitable for most of the current NISQ devices.

Measurement provides access to exploring and understanding nature and finds widespread applications. It is generally believed that the weak external driving used in measurement introduces negligible disturbance to the intrinsic output of the probed system. Here, we reveal that dissipation in a non-Hermitian quantum coupled system induces interference between self-excitation and coupling-excitation spectral functions, giving rise to non-intrinsic outputs. These non-intrinsic outputs can be effectively manipulated by the ratio of weak external driving strengths applied to two channels, leading to significant phenomena: extreme suppression of dissipation by convergence effect of high-loss mode towards low-loss mode, and giant shift of resonant frequency instead of original spectral Rabi splitting. Crucially, we discover the Pythagorean relation linking eigenlevel splitting, spectral Rabi splitting and average total decay rate, enabling precise measurement of the eigenlevel splitting and coupling strength. Numerical simulations confirm that the interference outputs also exist in classical coupled systems. Our work provides a profound insight into measurement and non-Hermitian physics.

Across public tabular benchmarks, quantum machine-learning (QML) models usually lose to carefully tuned classical baselines. We argue that this is a structural property of the datasets rather than merely a limitation of current models. Because an angle-encoded quantum neural network is a partial Fourier series, a genuine advantage can arise only when the target spectrum is simultaneously off-grid, of interaction order at least three, high-frequency, supported by near-independent features, and dense beyond practical enumeration. We call the failure to satisfy these conditions the Fourier wall. We operationalize the conditions as SPECTRA, a two-tier certificate: a simulator-free structural screen followed by a decisive comparison between a matched quantum model and five tuned classical twins using paired-bootstrap confidence bounds. On industrial smart-meter data, SPECTRA correctly refuses the real peak-load target, for which gradient-boosted trees reach a held-out ROC-AUC of 0.999. On the same real energy phases with labels generated by an interacting quantum process, the dynamics-matched quantum model reaches 0.994 versus 0.699 for the best generic classical baseline, and collapses to chance when its interaction couplings are ablated. An exact classical simulator ties the quantum model at small width but incurs measured exponential evaluation cost, with an estimated hardware crossover near 13-19 sites. These results provide a practical recipe for identifying, engineering, and deploying quantum-advantage candidates in tabular data.

Maximal quantum leakage quantifies privacy against adversaries with arbitrary intentions. In this work, we prove that computing this leakage is equivalent to minimum-error quantum state discrimination with equal priors. This establishes a computable operational interpretation, addressing the previous difficulty in computing maximal quantum leakage. We further analyze the impact of collective measurements on multiple copies of a state, demonstrating that leakage increases monotonically with the number of copies, which leads to explicitly characterizing the maximal leakage in the asymptotic limit. Extending this framework to quantum channels, we develop an iterative algorithm for the jointly designing of input states and measurements. Numerical examples involving collective measurements and the maximal channel leakage demonstrate our theoretical findings.

Quantifying the disturbance caused by a quantum measurement typically requires detailed knowledge of the underlying measurement channel. In this work, we introduce a statistical disturbance bound, which connects the statistical properties of a quantum measurement to the state disturbance induced by any compatible measurement channel. Specifically, we show that the average fidelity between input and output with respect to an arbitrary ensemble of pure input states is fundamentally bounded in terms of the measurement, described as a positive operator-valued measure (POVM). We further develop the weighted state exclusion technique, which enables an experimental determination of the statistical disturbance bound without requiring explicit knowledge of the measurement effects. To see the advantages of our approach over existing information-disturbance relations, we show that our bound distinguishes between measurements with equivalent informativeness. Furthermore, we demonstrate that the weighted state exclusion technique can detect and quantify measurement-induced disturbance using state preparations that are insufficient for tomographic reconstruction of the measurement operators. Finally, we illustrate how disturbance bounds defined with respect to specific input ensembles can be used to bound an eavesdropper's guessing probability in a simple protocol for quantum randomness generation.

The Variational Quantum Eigensolver (VQE) and its adaptive variants, such as ADAPT-VQE, are central to the study of strongly correlated quantum systems. However, the classical simulation of the ansatz growth process remains constrained by the exponential scaling of operator space and the associated computational cost of unitary evolution. We introduce the Greedy Operator Commutativity Partitioning (GOCP) framework, an analytical methodology designed to optimize both operator selection and state evolution. By reformulating complex unitary rotations as a chained sequence of fifth-order O(5) Taylor series expansions, GOCP bypasses the need for explicit matrix exponentiation, reducing the computational task to a sequence of sparse matrix-vector operations. We evaluate the performance of this framework across diverse molecular systems, including BeH2 and strongly correlated H2O geometries, utilizing both Jordan-Wigner and Bravyi-Kitaev mappings. Our results demonstrate that the GOCP framework maintains exceptional numerical fidelity-exceeding 1 - 10^-6 in state fidelity-while achieving sub-chemical accuracy in ground-state energy calculations. By enabling the simulation of operator manifolds exceeding 2.68 x 10^8 elements with high efficiency, this approach provides a scalable and rigorous pathway for exploring deep variational circuits in complex quantum many-body systems.

A significant challenge in the field of large-scale fault-tolerant quantum computation is the influence of noise. In addition to the influence of noise on individual qubits, the smaller additional effect of noise correlations is also of high significance because correlated errors pose a challenge for quantum error correction. We describe the dynamics of two cavity-coupled qubits that are subject to correlated noise, assuming that the qubits are affected by longitudinal noise and not coupled directly. We find that the cavity emission enables the characterization of the noise correlations and describe the cases of white noise, quasi-static noise, and Ornstein-Uhlenbeck noise. For a known frequency spectrum, the reconstruction of the noise correlation spectral density from the cavity emission is possible by averaging over many different noise realizations. We demonstrate that, in the case of white noise, the noise correlation effects scale with the fifth order of the cavity-qubit coupling constant and are thus strongly suppressed compared with the case of quasi-static noise, where they scale with the third order. Furthermore, we present a method for extracting the noise correlation spectral density from the cavity emission in the case where the underlying noise type remains unidentified. This can be achieved by applying the convolution theorem.

We propose a pulse-shaping method for improving population transfer in multistate stimulated Raman adiabatic passage (STIRAP) with nearest-neighbour couplings only. The method extends the quasiparallel-eigenenergy approach, previously used for two- and three-state systems, to multistate chains without introducing additional shortcut fields. The pump and Stokes fields are shaped so that the eigenenergies closest to the dark state remain nearly parallel to it during the central part of the interaction, where nonadiabatic transitions are most likely to occur. We derive analytic prescriptions for the required pulse shapes and apply them to five-, seven-, and nine-state chains formed by magnetic sublevels of degenerate manifolds with angular momenta $J_g\rightarrow J_e=J_g$ and $J_g\rightarrow J_e=J_g-1$ driven by a pair of right- and left-circularly polarized pulses. Numerical simulations show that the optimized pulses can reduce the population transfer error by several orders of magnitude compared to standard Gaussian pulses. The same shapes also improve robustness against variations of the peak Rabi frequency, the single-photon detuning, and the multiphoton detuning. The comparison between the two angular-momentum families shows that the $J_g\rightarrow J_g$ chains are generally more favourable, because their Clebsch-Gordan coefficients keep the relevant bright-state gap larger in the region where the dark state changes most rapidly. Finally, simulations with spontaneous emission show that the optimized resonant pulses remain advantageous in the lossy regime as well.

Entanglement swapping is a fundamental operation in quantum repeaters for establishing entanglement between distant parties. The positive partial transpose (PPT) squared conjecture asks whether two PPT entangled links can generate terminal entanglement through entanglement swapping, or equivalently, whether the composition of two PPT maps is always entanglement breaking. Motivated by this conjecture, we investigate the map-composition problem beyond the PPT setting. For qutrit completely positive (CP) maps, we prove that the composition of any CP map whose Choi matrix is $1$-undistillable with any CP map whose Choi matrix has Schmidt number at most two is entanglement breaking in either order. Moreover, we show that the cone of $1$-undistillable CP maps is exactly the largest qutrit cone of CP maps whose composition with every CP map whose Choi matrix has Schmidt number at most two is entanglement breaking in both orders. Finally, although map composition captures only the standard maximally entangled outcome in entanglement swapping, we prove that any $1$-undistillable two-qutrit state and any state of Schmidt number at most two cannot generate terminal entanglement under an arbitrary selective measurement on the intermediate systems.

Euclidean Monte Carlo methods are effective when the path-integral weight is real and nonnegative, but finite-density fermion systems often produce sign-changing or complex scalar weights after the fermionic sector is traced out. Hamiltonian formulations avoid this complex-weight sampling problem but face rapid Hilbert-space growth. This paper studies a conditional Euclidean-Hamiltonian (CEH) reduction that combines these two descriptions. The calculation is organized around a Monte Carlo-tractable reference problem and a residual active sector. Instead of tracing the active sector into a determinant or scalar weight, CEH keeps it operator-valued and uses the reference calculation to determine projected correlation or transfer matrices. These matrices define a finite effective Hamiltonian, with the remaining finite-density dependence introduced after projection. At finite rank, the result is an effective model whose accuracy must be tested through basis enlargement, metric conditioning, stochastic matrix-element errors, and number-sector diagnostics. The construction is examined in three finite benchmarks. A two-channel oscillator tests conditional basis compression; a positive-measure stochastic calculation tests correlation-matrix harvesting and GEVP extraction, including a comparison with a PDMS-style estimator; and a four-site Hubbard ring combines a finite-budget determinant-sign stress test with finite-density continuation in non-target active spaces. The benchmarks support the proposed trade from scalar sign reweighting to a monitored active-space approximation in structured finite models, but they do not provide an end-to-end stochastic CEH treatment of the Hubbard sign problem or establish favorable scaling. Usefulness requires both low-rank approximability and efficient extraction of the required projected matrix data.

Continuous monitoring is a powerful tool for analyzing quantum systems and is increasingly used as a non-demolition technique in quantum metrology. In this context, noisy data acquired through continuous monitoring can be used to precisely pinpoint unknown parameters of the system. However, extending the theoretical framework that connects these data to the underlying parameters beyond Markovian dynamics is notoriously difficult, primarily because such dynamics cannot be expressed as completely positive divisible maps. To overcome this, we propose a method based on the reaction coordinate mapping to extend these parameter-estimation techniques beyond the Markovian regime. Our approach specifically targets linear systems with non-Markovian dynamics undergoing Gaussian continuous measurements, such as homodyne detection. Within this framework, we analyze Bayesian estimation and provide an analytical expression for the Fisher information, alongside the asymptotic scaling of the estimation precision for arbitrary parameters. Finally, we demonstrate the efficacy of our method through the example of thermometry of a bosonic bath.

We give a closed-form construction of the $n$-qubit Elegant Joint Measurement (EJM) proposed in [PRL \textbf{136}, 190201 (2026)] and show that it is part of a tunable family of measurements with tetrahedrally arranged Bloch vectors. The construction is based on the interference pattern implied by a single phase polynomial built from the elementary symmetric functions. It realises a regular tetrahedral measurement for every $n$, and the corresponding measurement unitary lies at level $n{+}1$ of the Clifford hierarchy. Starting from this measurement, we ask whether the size of the local tetrahedron -- and hence the entanglement of the basis -- can be varied while preserving its symmetry. For every even $n$ the answer is yes, and remarkably the size follows the same one-parameter law that governs the known two-qubit family, interpolating down to a $1$-uniform basis. For $n=3$ the EJM is locally isolated, while for odd $n\ge5$ we do not know an analogous closed-form family. We also give an analogous construction, valid for every $n \geq3$, with square local geometry.

We continue our study of quantum dynamics on a Lie group $G$, initiated in arXiv:2512.19840, by building the path integral that governs transition amplitudes in the Hilbert space $L^2(G)$. This relies on the proper handling of both a noncommutative momentum space and the presence of compact directions in $G$. We show that compactness can be handled through a sum over winding numbers in maximal tori of $G$, generalizing the similar sum commonly encountered for path integrals on a circle. As applications, we compute semiclassical approximations of propagators and partition functions of Euler-Arnold systems, up to (and including) two-loop order.

Quantum continual learning aims to train quantum models on sequential tasks without losing previously learned knowledge. However, variational quantum classifiers (VQCs) are prone to catastrophic forgetting under nonstationary task distributions. We propose quantum elastic weight consolidation (QEWC), a quantum Fisher information (QFI)-informed regularization method for mitigating forgetting. Unlike conventional elastic weight consolidation based on classical Fisher information (CFI), which measures parameter importance through measurement-dependent output statistics, QEWC uses QFI to quantify the intrinsic sensitivity of the parameterized quantum state. This gives an information-geometric view in which important parameters are identified by the local response of the quantum state manifold. We evaluate QEWC on VQCs trained on sequential binary classification tasks, including classical image-classification and quantum phase-classification tasks. Simulations show that sequential training without regularization causes severe forgetting, while both CFI-based EWC and QFI-based QEWC improve retention of previous tasks. Mechanistic analyses further show that the two methods impose different regularization geometries: CFI acts selectively on measurement-sensitive directions, whereas QFI imposes a denser state-geometric constraint over parameter space. Under depolarizing noise, CFI values are strongly suppressed by degraded measurement statistics, while QFI preserves a more stable sensitivity structure of the noisy parameterized quantum state. These results establish QEWC as a physically motivated approach for studying and mitigating forgetting in quantum continual learning through quantum-state geometry.

Characterizing the Hamiltonian that a quantum processor actually implements is central to calibrating and validating current quantum hardware. Many devices, however, operate with generators that are time dependent by design. Here we develop a rigorous and experimentally friendly protocol for learning time-dependent many-body Hamiltonians from continuous weak measurement records. The key observation is that interaction sparsity reduces the global reconstruction to a set of local inverse problems, whose number is controlled by the interaction connectivity rather than by the system size. Pure separable probe states suffice to drive these inversions, and a graph-coloring construction embeds them into a small number of global product-state preparations. We derive explicit reconstruction-error bounds and a sample-complexity theorem that cleanly separates the finite-sampling statistical noise from the deterministic bias of the iterative state update, and we validate the protocol on time-dependent spin chains with up to $n=8$ qubits. Beyond these results, our analysis provides a rigorous foundation for time-dependent Hamiltonian learning from continuous monitoring in many-body systems, establishing a framework that extends naturally to many platforms and probe ensembles.

We review the framework of operator Hilbert space and introduce the one- and two-particle super reduced density matrices (1-SRDMs and 2-SRDMs), as well as the super mutual information (SMI). The eigenvectors of the 1-SRDMs define what we term natural single particle operator bases, and provide a way to compress vibrational and vibronic Hamiltonians with controlled error. The SMI is defined from the operator entanglement entropy of the 1-SRDMs and 2-SRDMs, and captures the correlation between operators acting on different one-mode subspaces, which may be used to reveal and quantify both direct and indirect couplings that might otherwise be difficult to extract. Efficient numerical approaches for the calculation of SRDMs and the SMI are developed and applied to a set of prototypical vibrational and vibronic Hamiltonians, as well as approximations to the corresponding time-evolution operators. Through this, we demonstrate that: (i) commonly used vibronic Hamiltonians are amenable to extremely high levels of compression without compromising accuracy, and; (ii) SMI analysis can be used to systematically and quantitatively reveal both direct and indirect couplings that might otherwise be difficult to extract, including indirect couplings of vibrational modes via intermediary electronic-vibrational interactions.

This work explores whether localized electromagnetic interactions can be modeled in terms of an effective object-relative ultraviolet weighting of internal modes. The proposal is motivated heuristically by two considerations: a weak-field self-backreaction estimate for sufficiently localized energy-carrying modes and a three-dimensional overlap argument for localized interactions. In the resulting ansatz, the infrared sector remains unchanged up to a characteristic scale the at angular wavenumber $k_c$, while ultraviolet contributions are suppressed asymptotically by a factor of order $k_c^3/k^3$ with the angular wavenumber $k$. Because a crossover based solely on $k^\mu k_\mu$ is not well suited to the intended mode-based interpretation, the weighting is formulated in terms of the object-relative covariant mode variable $u_{\mu} k^{\mu}$ with the four-velocity $u^{\mu}$, i.e. the mode frequency measured in the rest frame of the localized interaction object. Within this restricted framework, selected one-loop QED contributions considered here become ultraviolet finite, and a restricted one-loop Ward-consistency check is preserved when the same scalar weighting is assigned consistently to the same internal photon mode in self-energy and vertex corrections. Four initial test cases are discussed: the anomalous magnetic moment, a Bethe-type low-energy Lamb-shift estimate, the Casimir effect, and a compact ultraviolet one-loop test. In the first three cases, the weighting leads to physically sensible characteristic scales associated with the electron Compton scale, an atomic bound-state scale, and plate distance, respectively. The results suggest that different observables may probe different effective localization scales. Action-level derivation, spectral consistency, and extension beyond one loop remain open problems.

It is well-known that combinatorial circuits are modeled mathematically by string diagrams in monoidal categories. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category generated by $\Sigma$. In this model, circuit semantics are then given by monoidal functors out of this free category. For quantum circuits, this functor is often valued in the category of unitary matrices. This model suffices for concrete quantum circuits, but fails to describe parameterized families of quantum circuits, such as those which arise in the analysis of ansatz circuits. In this paper, we introduce an approach to parameterized circuit semantics, which is based on enriched category theory. We first introduce an abstract categorical construction, and use this to gain new insights on controlled operations and quantum communication. We then study the special cases of Cartesian monoidal parameters and monoidal closed parameters, both endowing the parameterized semantics with useful this http URL conclude by showing that the monoidal closed case can be used to unify two perspectives on quantum control.

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

In this work, we address the problem of designing single-qubit quantum gates by means of a linearly-polarized field. We show that any desired one-qubit gate corresponding to a special unitary matrix can be generated by a modulated sinusoidal field. The only approximation involved is the rotating-wave-approximation. The formula for the control field is obtained by inverting the equation of motion for the evolution operator and imposing the conditions for the desired gate. We give a simple procedure to obtain closed analytical formulas for the fields in terms of a priori chosen dynamical functions. Additionally, these dynamical functions can depend on tunable free parameters intentionally introduced to meet a desired performance criteria.

Quantum LPDC codes provide a substantial reduction in qubit overhead required for fault-tolerant quantum computation compared to surface code, thanks to their high encoding rate. However, operating simultaneously on multiple logical qubits encoded in the same block is more challenging and may slow down logical operations. Prior work addresses this problem by designing complex resource states to perform logical measurements in LDPC codes. Here, we propose an approach that only consumes cat states. Whereas previous work on cat-based measurements focuses on a single logical measurement, we design a protocol for the joint measurement of $\ell$ commuting logical operators. The key ingredient is the design of a scheduler code determining the measurement sequence and allowing for the decoding of all logical measurement outcomes. Numerical simulations with the LDPC codes Q70 and Q102 of the walking cat architecture show a speed-up of nearly $3\times$ over Viterbi measurements for the measurement of $\ell=20$ commuting logical operators. Combining our fast logical measurements with a new variant of the CliNR partial error correction scheme, we achieve a speed up of up to up to $74\times$ for random Clifford circuits. Our approach also applies to non-Clifford gates, producing a speed up of up to $5\times$ for Toffoli gates.

We investigate how finite quantum systems with strong long-range interactions approach thermal equilibrium. Nearly conserved quantities inherited from the fully connected limit fragment the Hilbert space and give rise to a many-body spectrum split into energy bands. As a result, equilibration becomes anomalously slow and proceeds through long-lived prethermal plateaus. This two-stage equilibration process is, however, not universal. We uncover the mechanism that determines which observables and initial states exhibit, or evade, prethermal plateaus. We also develop a perturbative theory that provides analytical expressions for both the height of the prethermal plateau and its timescale. Despite the lack of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has direct consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply to a broad class of Hamiltonians exhibiting Hilbert-space fragmentation.

We characterize and compare the inherent interpretability offerings of a standard linear model with a single qubit mixed state model for the task of supervised binary classification. A side by side comparison reveals that a single qubit mixed state model for binary classification is just the ``ellipsoid version" of standard linear model classification. More precisely, rather than learning a hyperplane to classify data, we learn a hyperellipsoid. We discuss the consequences of the geometric inductive biases of both models, as well as how each model contains a different feature importance inductive bias. This short characterization offers an accessible route to quantum machine learning (ML) ideas for readers who have zero background in quantum and are only familiar with linear classification in ML. In support of ML pedagogy, we encourage instructors to utilize this piece to smoothly introduce quantum ML ideas into the undergraduate ML classroom.

Testing Lorentz invariance violation (LIV) is notoriously difficult, as its characteristic energy scale, $M_\star$, in modified dispersion relations typically lies beyond current experimental reach. To enable a low-energy probe, we investigate the quantum coherence of an inertial Unruh-DeWitt (UDW) detector interacting with a massless scalar field with a Lorentz-violating dispersion relation $\omega_{|\textbf{k}|}=|\textbf{k}|f(|\textbf{k}|/M_\star)$. Unlike the Lorentz-invariant case where quantum coherence is rapidity-independent, we find for the Lorentz-violating quantum field case the dynamics of detector's quantum coherence exhibits a strong dependence on its rapidity -- offering a potential low-energy signature of LIV. Applying this to the polymer-quantized scalar field theory inspired by loop quantum gravity, we show that the detector's quantum coherence exhibits a pronounced dependence on rapidity and undergoes a sharp transition near a critical rapidity $\beta_c \approx 1.3675$, a value within reach of existing facilities like the Relativistic Heavy Ion Collider. We also show how the detector's rapidity and its energy-level spacing enhance the response to the test of LIV. Our results establish quantum coherence as a sensitive and practical probe of LIV, providing a complementary avenue for testing quantum gravity-induced modifications to field theory.

Although hidden-photon dark matter with masses above $10^{-4}\,\mathrm{eV}$ is well motivated by inflationary production, it remains largely unexplored by terrestrial experiments. Through kinetic mixing, hidden photons induce a weak oscillating electric field above $10\,\mathrm{GHz}$. We propose to amplify this signal using a compact high-frequency distributed cavity and detect it with chip-scale Rydberg-atom superheterodyne spectroscopy. Combining resonant enhancement, large dipole moments of Rydberg atoms, and long-term stable integration, this approach can probe hidden-photon dark matter in the mass range $5 \times 10^{-5}\text{--}7\times 10^{-4}\,\mathrm{eV}$ with sensitivities $3$--$4$ orders of magnitude beyond existing limits.

Copropagating quantum Hall edge channels provide a promising platform for compact electron interferometry and flying quantum states. In silicon, the valley degree of freedom offers a natural alternative to spin-resolved edge channels because spin-flip scattering is strongly suppressed by the weak spin-orbit interaction. Here, we investigate interchannel transitions between copropagating valley edge channels in a double-layer-gated silicon metal-oxide-semiconductor field-effect transistor. With the bulk filling factor set to $\nu=2$, two spin-polarized valley edge channels are brought into close proximity near a depleted side gate. We observe strong intervalley mixing, with a transition probability close to 1/2, indicating nearly complete equilibration between the two valley edge channels. In contrast, interchannel transport between edge channels with different spin orientations shows negligible transition probability, consistent with suppressed spin-flip scattering in silicon. These results demonstrate that intervalley coupling at a Si/SiO$_2$ interface can provide a beam-splitter-like operation for copropagating valley edge channels, establishing a key building block toward compact silicon quantum Hall interferometers.

Quartet correlations in neutron-rich Te isotopes are investigated within the quartet Bardeen-Cooper-Schrieffer (BCS) framework. Taking \(^{100}\)Sn as an inert core, we consider two valence protons and valence neutrons occupying the \(2d_{5/2}\oplus1g_{7/2}\) model space, and solve the quartet BCS variational equations with a charge-independent isovector pairing interaction. The effective pairing strength is constrained from empirical neutron pairing gaps in the Te isotopic chain. We find that the valence quartet number increases as the valence neutron number is enlarged from \(N_{\rm val}=2\) to \(14\). The same increasing behavior is also found for the condensed quartet component. The proton occupation of the \(1g_{7/2}\) orbit is strongly enhanced relative to the conventional like-particle BCS reference and is driven close to the degeneracy-weighted limit. These results suggest that additional valence neutrons enhance the quartet admixture in the correlated quartet BCS state, while redistributing the fixed proton weight from pair-like configurations to quartet configurations.

We investigate the behavior of Einstein crystals in noncommutative backgrounds described by the Snyder and Snyder-de Sitter models. Possible novel effects, which may arise in realistic systems such as diamond crystals, are analyzed within a thermodynamical framework. We show that noncommutativity influences the key thermodynamic quantities, including internal energy and specific heat. These corrections can be directly related to modifications of the underlying uncertainty relations, of the generalized uncertainty principle (GUP) and generalized extended uncertainty principle (GEUP) types.

Quantum computing and quantum simulation with ultracold neutral atoms require Rydberg excitation of individual atoms in atomic arrays. Rydberg states are extremely sensitive to external electric fields, therefore precise three-dimensional control of the electric field is essential. We performed a spectroscopic study of three-photon Rydberg excitation of a single Rb atom in an optical dipole trap in the presence of an external DC electric field. The field was generated by eight electrodes deposited on the inner surfaces of an ultrahigh-vacuum glass cell. The used three-photon scheme of laser excitation of Rydberg \textit{nP} states allows the Stark shift and the splitting of the resonances to be observed simultaneously, which simplifies calibration of the electric field. In addition, in the commonly used two-photon Rydberg excitation schemes, the light shifts can complicate accurate determination of the DC Stark shift, particularly when the external electric field is scanned across different spatial directions, and different Stark components are excited. These shifts are absent in the three-photon excitation scheme used in our experiment. We demonstrated the ability to independently tune the electric field along all three spatial directions and to compensate for stray electric fields. The measured three-photon spectra exhibit Stark shifts and splittings of the three-photon resonance that are in good agreement with theoretical calculations. These results are also of interest for Rydberg electrometry.

We investigate the generation and control of both charge and spin currents via nonreciprocal dissipative mechanisms in a two-dimensional spinful fermionic atom quantum system with broken inversion and time-reversal symmetries. Within the Gorini-Kossakowski-Sudarshan-Lindblad master equation formalism and using an approach based on the time-dependent generalized Gibbs ensemble, we identify in the weak dissipative coupling regime the minimal set of nonreciprocal jump operators required to induce charge and spin currents and to control both their direction and magnitude. We find that in the presence of finite tunneling, Rashba coupling and magnetic field, the combine application of two jump operators nonreciprocally coupling each spin species to a different spatial direction of motion is sufficient to generate both types of current. Furthermore, by tuning the degree of nonreciprocity of the jump operators we modify the dominant transport mechanism from spin to charge. Finally, we checked that this nonreciprocal current generation mechanism is robust to the application of dephasing noise as even in the presence of this additional dissipative process the steady-state occupation distributions for the quasiparticle modes of the Hamiltonian remains non-trivial, an essential requirement to obtain non-zero currents.

Fermion parity is a fundamental property of superconducting many-body states. Here, we show that the global fermion parity of a delocalized superconducting state can be detected locally by exploiting the nonlocal Josephson effect. Using a carbon nanotube-based Andreev molecule formed by two coupled quantum-dot Josephson junctions, we observe a pronounced nonlocal Josephson response and demonstrate the formation of delocalized Andreev molecular states extending across both junctions. We further show that changes in the molecular ground-state parity manifest as characteristic $\pi$-phase shifts in the nonlocal response. Supported by a minimal theoretical model, these results identify global fermion parity as an experimentally accessible degree of freedom in hybrid superconducting circuits that can be readily revealed through the nonlocal Josephson effect.

Photoelectrical readout of the electronic spin state of the nitrogen-vacancy (NV) center in diamond is attracting significant interest due to the numerous advantages it possesses compared with conventional fluorescence readout. The higher charge carrier rate compared to the photon rate and the integration of the detection scheme on a chip can significantly advance quantum sensing and computing with color centers in diamond. Until now, photoelectric readout has been performed on ensembles of NV centers or single NV centers deep in ultrapure diamond substrates. However, many applications require the artificial creation and precise placement of shallow NV centers, and photoelectric detection of such centers has been challenging. Here we demonstrate photoelectrical readout and coherent control of the electronic spin of implanted shallow ($\sim$10 nm) NV centers buried by diamond overgrowth. The photoelectrically measured Ramsey $T_2^*$ agrees with conventional fluorescence readout and shows no measurable dependence on the readout photocurrent, for both shallow implanted and deep ingrown NV centers. We further find that overgrowth improves photoelectric readout by suppressing the background photocurrent. These results establish photoelectric readout as a viable route to chip-integrated, electrically detected nanoscale sensing and to spin registers based on engineered shallow NV centers.

In contrast to a classical bit, which can only take the value $0$ or $1$, its quantum counterpart -- a qubit -- can exist in a superposition of $0$ and $1$. This is a superposition of data values, naturally raising the question of whether one can superpose not only data but also programs. For example, a particular superposition of programs, known as the quantum SWITCH, has attracted much attention, and its implementations and computational advantages have been studied extensively within the physics community. A naive way to control a program by a qubit is by means of a controlled operation. Given an operation $F$, this amounts to considering an operation that behaves as $F$ when the control qubit is $|1\rangle$, and as the identity operation when the control qubit is $|0\rangle$. This idea works well when $F$ is a unitary operation, but it is not well-defined for a general quantum channel. By contrast, the quantum SWITCH is free from the well-definedness issue. This contrast leads to the key insight of this paper: controlled operations and the quantum SWITCH should be regarded as different kinds of quantum control mechanisms. Building on this insight, we develop a novel quantum programming language with quantum control and measurement that can express the quantum SWITCH over quantum channels. Using a semantic analysis based on program transformations, we identify the source of the ill-behavedness of controlled operations as the \emph{correspondence problem}: a lack of coordination between the measurements performed in the then- and else-branches of quantum conditional branching. We address this problem with a linear type system that enforces alignment of the quantum operations used in the two branches, yielding a well-behaved language capable of expressing the quantum SWITCH.

Indefinite causal order is a characteristic phenomenon in quantum computation, with examples including the quantum SWITCH and the OCB process. Not all such processes are believed to be physically realizable: while some implementations of the quantum SWITCH have been proposed, the OCB process is suspected to be unrealizable. This difference in realizability is commonly attributed to constraints imposed by physical causality. This paper studies such a causality issue in a higher-order setting, proposing a typed lambda calculus with quantum control and its categorical semantics. Our calculus extends pure quantum computation with higher-order functions and quantum conditional branching, and it is equipped with a type system based on intuitionistic BV logic to enforce causality. We also present a novel model that is closely related to the Caus construction, by which we prove that some physically-unrealizable processes are not definable in our language.

Unlike the gravitational waves classically generated by moving macroscopic masses, the diffuse backgrounds of gravitons originate most likely from zero-point fluctuations of the gravitational field amplified by the evolution of the space-time curvature. The resulting entangled states lead to specific second-order correlation effects that could be eventually detected. For a quantitative analysis of this empirical expectation we scrutinize the interactions between the cosmic gravitons and the fundamental mode of a quantized electromagnetic field confined inside a closed optical resonator with perfectly-reflecting walls. We show that the Hanbury-Brown Twiss correlations of the photons are insensitive to the degrees of second-order coherence of the gravitons even barring for the exceedingly small couplings of the problem. Since the degree of second-order coherence of the photons does not reflect the correlation properties of the gravitons, the statistical properties of the gravitons (and their super-Poissonian statistics) cannot be inferred, even in principle, from the intensity correlations of the cavity modes.

Hybrid quantum systems offer a route to combining the complementary strengths of distinct quantum platforms while mitigating their limitations. A particularly promising architecture combines neutral atoms and polar molecules: atoms provide fast, controllable interactions through excitation to Rydberg states, while molecules possess long-lived rotational states that are attractive for quantum memories and qudits. Although dipolar interactions between atoms and molecules have been observed in gas-phase and beam experiments, they have not previously been explored in a scalable optical tweezer platform that enables the controlled coherent interactions needed for quantum state transfer and entanglement. Here, we realise this goal, demonstrating coherent dipolar interactions between an individual Rydberg atom and an individual polar molecule. The separation of the particles is controlled using species-specific optical tweezers and their dipolar interactions are made strongly state-dependent by tuning two atom-molecule pair states into resonance. We exploit these interactions to demonstrate atom-mediated state readout of a molecular qubit, observe coherent spin exchange between the particles, and generate entanglement using a blockade-based controlled-NOT operation. Together, these results establish a coherent atom-molecule interface in which long-lived molecular quantum information can be rapidly mapped onto internal states of a Rydberg atom for readout or onward coherent transfer. This platform can be scaled to realise hybrid quantum processors utilising atom-mediated readout and entanglement of molecular qubits and mixed-species quantum simulators of dipolar systems.

We introduce combinatorial holographic quantum secret sharing (CHQSS) for a bulk subregion in AdS$_3$/CFT$_2$ to study how logical information of the bulk subregion is encoded in the boundary and protected from erasures of boundary subregions. We introduce a distance, a reconstruction threshold, and a secret threshold to characterize CHQSS schemes. We present the phase transitions of multipartite entanglement wedges in a symmetric setup and observe multiple distinct phase transition points. The distance and thresholds depend on the holographic phase and the choice of bulk subregion. We derive the maximum distance. Moreover, we derive the relations between the distance and the thresholds. We construct a family of CHQSS schemes in the symmetric setting that includes perfect threshold CHQSS and perfect non-threshold CHQSS.

Interactions of cosmic rays and other forms of ionizing radiation pose a significant challenge to the reliable operation of state-of-the-art quantum devices and error correction in quantum computing based on superconducting circuits which are typically fabricated on semiconductor substrates. Shielded by 2 km of rock overburden, the Cryogenic Underground TEst facility (CUTE) at SNOLAB provides a unique ultra-low radiation environment to probe the performance of quantum technologies with a particular interest in quantum coherence studies. In this article, we present the findings of an extensive material assaying program in preparation for the first underground operation of superconducting qubits at SNOLAB. The radioactivity levels identified by the material assays enter a thorough Monte Carlo study based on the Geant4 particle physics tracking code. From these simulations, we estimate the rates of energy deposits from radiogenic sources expected for a quantum-device assembly operated in the CUTE facility. We further characterize the spectral components of the projected background and identify the dominant particle interaction types. Finally, we outline how crystal dynamics simulations using the G4CMP solid-state physics extension for Geant4 can inform the community-wide efforts to identify effective strategies to mitigate the effects of high-energy particle impacts.

Quantum many-body systems in cavities combine the rich physics of condensed matter systems or quantum chemistry with strong coupling to the surrounding electromagnetic field. In these systems, large Hilbert spaces, many-body interactions and strong system-environment coupling are all fundamental, posing a significant barrier for established methods in quantum optics and condensed matter physics. Here we propose a novel method based on a combination of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy and the Hierarchical Equations of Motion (HEOM) to achieve a rigorous description of open many-body systems in contact with structured photonic and phononic baths. We rationalize that this stacked hierarchy accounts for spin-squeezing and superradiant emission despite its applicability to arbitrarily many emitters. The potential of BBGKY-HEOM is then demonstrated for many-body electronic systems embedded in host materials (e.g. molecules in organic crystals). We show that the impact of phononic coupling and charge noise can be as relevant as electronic correlation. Our work establishes an accessible, yet rigorous, route between condensed matter and quantum optics, fostering the growth of a new domain at their interface.

Critical metrology relies on the high sensitivity of systems to parameter changes near a phase transition to extract information with high precision. Such methods usually require working under adiabatic conditions, which implies long preparation times due to critical slowing down. Here instead we demonstrate how favorable sensitivity can be maintained for preparation rates exceeding the adiabatic limit by exploiting knowledge of the non-equilibrium dynamics of the system. Our work focuses on a model of collective dissipation (superradiance) balanced by collective pumping, analyzing the sensitivity around a first order dissipative phase transition. We devise a sensing protocol based on characterizing the hysteresis formed beyond adiabatic conditions, finding the sensing uncertainty $r^{\alpha}/N$ , exhibiting a favorable Heisenberg-like scaling with the particle number $N$ and only a weak power-law dependence $\alpha \approx 0.17$ on the preparation rate $r$. We discuss the implementation of the model and potential applications to metrology within cavity QED setups.

We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processor units (QPUs). Combining a concise diagrammatic formalism with high-precision numerical methods, our approach efficiently evaluates high-order, long-range Pauli string couplings and maps complete chip layouts onto exact effective Hamiltonians. Applying this method to surface-code architectures, such as Google's Sycamore lattice, we identify three distinct operational regimes: computationally stable, error-dominated, and hierarchy-inverted. Our analysis reveals that even modest increases in residual qubit-qubit crosstalk can invert the interaction hierarchy, driving the system from a computationally favorable phase into a topologically ordered regime. This framework thus serves as a powerful guide for optimizing next-generation high-fidelity surface-code hardware and provides a pathway to investigate emergent quantum many-body phenomena.

Minimal Kitaev chains host Majorana quasiparticles, which, although not topologically protected, exhibit spatial nonlocality and hence expected to be useful for quantum information tasks. In this work, we consider two- and three-site Kitaev chains and investigate the dynamics of bipartite and multipartite entanglement by means of concurrence and geometric measure of entanglement. In two-site Kitaev chains, we find that maximally entangled states can robustly emerge, with their stability and periodicity highly controllable by the interplay between the superconducting pair potential and the onsite energies. At the finely tuned sweet spot, where Majorana quasiparticles appear, the system exhibits oscillations between separable and entangled states, whereas detuning introduces tunable valleys in the entanglement dynamics. Extending to the three-site Kitaev chain, we uncover rich bipartite and multipartite entanglement by generalizing the concepts of concurrence and geometric measure of entanglement. At the sweet spot, the Majorana quasiparticles emerging at the edges suppress concurrence between the edges, while a finite detuning is able to restore it. Depending on the initial state, the three-site Kitaev chain can dynamically generate either a maximally entangled Greenberger-Horne-Zeilinger state or an imperfect W-type state exhibiting multipartite entanglement, although a (maximally entangled) pure W state cannot be realised due to parity constraints. Our results provide a resource for generating and characterising highly entangled states in minimal Kitaev chains, with potential relevance for quantum applications.

We propose a simplified open-quantum-system model for hydrogen-bond formation in water clusters, where each subsystem is mapped to a $\lambda$-type three-level system coupled to two effective phonon modes: a micro-vibration mode ($\Omega_{\mathrm{hyd}}$) representing the O--H stretching vibration, and a macro-displacement mode ($\Omega_{\mathrm{dist}}$) representing the intermolecular donor-acceptor motion. The $[(\mathrm{H}_2\mathrm{O})_2]^m$ cluster is studied for $m=2$ to $6$ in the incoherent case (independent phonon modes) and the coherent case (shared phonon modes). We find that phonon coherence significantly alters the dynamics. In the dissipative case, coherence induces a redistribution of steady-state populations: intermediate hydrogen-bond counts are enhanced while edge counts are suppressed -- a ``squeezing'' effect explained by the interplay of subradiant states and dark states. For $m\ge 3$, true dark states emerge, rooted in the permutation symmetry of the system. Inflow of $\Omega_{\mathrm{dist}}$ phonons promotes hydrogen bond formation, while inflow of $\Omega_{\mathrm{hyd}}$ phonons inhibits it. Our results reveal a nontrivial role of quantum coherence and dark states in hydrogen-bond dynamics, providing a foundation for extending the framework to more complex systems.

High-fidelity two-qubit gates are essential for scalable quantum computing. We present a scheme based on superconducting transmon qubits and a control pulse delivery protocol that enables arbitrary controlled-phase gates modulated solely by an independent arbitrary waveform generator pulse. We combined a tunable coupler design with bipolar flux-pulsing to demonstrate a high-fidelity gate with a peak performance of $99.5\%$. Our gates inherit the advantages of both approaches: minimal residual ZZ coupling, built-in echo-like low-frequency noise protection, and time-scale control pulse reproducibility, while remaining easy to calibrate. We optimize the system energy levels to mitigate leakage to the coupler and suppress residual interactions. Numerical simulations of the scheme as three qutrits indicate that an error below $1 \times 10^{-3}$ is achievable. We confirm the scalability potential of the proposed scheme on high-fidelity 4-qubit and 8-qubit quantum processors

Light-matter interaction in the regime of strong quantum coupling is usually treated within the framework of the Hopfield model. However, the picture of coupling well-defined modes of light and matter is correct only as long as the shapes of these eigenmodes are not substantially modified by the interaction. Moreover, parameters of theoretical models are usually obtained by fitting to experimental data. To date, there is no straightforward method to determine a quantum master equation corresponding to a system with specific dielectric structure, which may lead to incompatibility of theoretical descriptions and physical realizations. In this work, a recipe for obtaining a quantum model in the polariton eigenmode basis is presented, based on Bogoliubov transformation in the conservative case and third quantization technique in the dissipative case. It is shown how this method can be used for boosting interaction strength and engineering nonlocal many-body interactions in carefully designed nanostructures, resulting in strongly nonclassical correlations of emitted light.

Quantum batteries are prone to losing their stored charge, when interacting with a thermal environment. However, getting a limited assistance from the thermal environment, is it possible to recover the charge back, in a reusable form? Here, we answer this question, by involving an assistance of a suitable measurement performed on the environment. This framework resembles the structure of quantum instruments in the thermodynamic scenario. Our proposed framework involves two different kind of assistance from thermal environment - one by accessing only the thermal particle, actively participating in the interaction, providing a weak retrieval of charge, while the other involves local assistance from an additional quantum system purifying the thermal environment, resulting in the strong retrieval of the lost charges. By setting the upper-bound on the amount of charges retrieved in each of these two situations, we report that their difference characterizes the amount of entanglement generated between the quantum battery and the reference system due to the thermal interaction. Finally, we exemplify the extreme instances of the difference between the weak and the strongly retrieved charges for qubit batteries.

In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a string of its choice. Ambainis and Montanaro showed a quantum algorithm of cost $O(\sqrt{n} \log n)$ and a near-matching lower bound of $\Omega(\sqrt{n})$. Belovs [Comput.~Comp.'15] subsequently showed a tight $O(\sqrt{n})$ upper bound. We consider a natural generalization of this problem, parametrized by a subset $\cal{Q} \subseteq 2^{[n]}$, where an algorithm may test whether $x_S = b$ for an arbitrary $S \in \cal{Q}$ and $b \in \{-1,1\}^S$ of its choice, at unit cost. We show near-tight bounds when $\cal{Q}$ is any of the following collections: bounded-size sets, contiguous blocks, prefixes, and only the full set. All of these results are derived using a framework that we develop. Using symmetries of the task at hand we show that the quantum query complexity of learning $x$ is characterized, up to a constant factor, by an optimization program, which is succinctly described as follows: `maximize over all odd functions $f : \{-1,1\}^n \to \mathbb{R}$ the ratio of the maximum value of $f$ to the maximum (over $T \in \cal{Q}$) standard deviation of $f$ on a subcube whose free variables are exactly $T$.' To the best of our knowledge, ours is the first work to use the primal version of the negative-weight adversary bound (which is a maximization program typically used to show lower bounds) to show new quantum query upper bounds without explicitly resorting to SDP duality.

We investigate hydrogen molecule ionization within a unified framework combining finite-dimensional quantum electrodynamics with the Lindblad master equation, enabling systematic comparison across closed, dissipative, and influx-driven open systems. Our results reveal a universal tendency toward neutral $\mathrm{H}_2$ formation. Photon dissipation ($\gamma_\Omega$) accelerates stabilization, while electron ($\gamma_\mathrm{e}$) and phonon ($\gamma_\omega$) dissipation play distinct regulatory roles. Particle influx ($\mu_k$) induces complex energy redistribution, populating the atomic state $|\mathrm{H},\mathrm{H}\rangle$. The ionization pathway is highly sensitive to initial photon number and composition, which control spin-selective excitation channels. An embedded anode model confirms that orbital hybridization fundamentally constrains the maximum ionization probability to $3/4$. This work provides a unified theoretical foundation for quantum-controlled chemistry and cavity QED experiments.

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.

We introduce a framework to identify where the total correlations and entanglement with a chosen degree of freedom reside within the rest of a system, in the context of bosonic many-body Gaussian quantum systems. Our results are organized into two main propositions. First, for pure Gaussian states, we show that every correlated mode possesses a unique single-degree-of-freedom partner that fully captures its correlations (consisting of entanglement), and we provide an explicit construction of this partner from the complex structure of the system's state. Second, for mixed Gaussian states, we constructively demonstrate that the notion of a partner subsystem splits into two: a correlation partner, which contains all classical and quantum correlations and need not correspond to a single degree of freedom, and an entanglement partner, which is always at most single-mode. Finally, we extend the construction of partners to multi-mode subsystems. Together, these results provide conceptual practical tools to study how bipartite correlations and entanglement are structured and where they can be found in complex Gaussian many-body systems.

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.

Valence-bond wavefunctions such as spin-coupled generalized valence bond (SCGVB) provide compact and chemically interpretable descriptions of strong correlation, but their nonorthogonal determinant structure makes quantum evaluation of overlaps and Hamiltonian matrix elements difficult. Here we introduce an ancilla-free, measurement-driven framework that reformulates these quantities as vacuum expectation values of Pauli-string operators, enabling evaluation with shallow circuits, local Clifford rotations, and computational-basis measurements, without controlled operations. We validate the method for H$_4$ along a dissociation pathway and for a 70-determinant C$_2$ active-valence benchmark. The reconstructed matrices agree with the classical L{ö}wdin-based reference, while Chirgwin-Coulson weights remain chemically consistent. These results establish the proposed estimators as a low-depth, circuit-compatible formulation for evaluating SCGVB matrix elements, while making no claim of quantum computational advantage.

The relativistic quantum phase space (QPS) formalism extends classical phase space by incorporating both mean values and variance-covariance matrices of quantum states, thereby providing a unified setting where the uncertainty principle and relativistic covariance coexist. In this work we explore the basic geometric structure of the QPS for the signature \((1,4)\). We construct a scalar invariant built from the mean values and the inverse variance-covariance matrix, and prove its invariance under linear canonical transformations. For quantum states that saturate the uncertainty relations, and define the QPS itself, the invariant takes a value that encodes two fundamental length scales: a large scale characterising maximal coordinate uncertainties and a small scale characterising minimal coordinate uncertainties. From this invariance we derive a geometric equation that unifies the mean values and the quantum fluctuations. Analysing two asymptotic regimes reveals two physically significant limits: one leads to a curved spacetime geometry, consistent with current cosmological observations; the other yields a curved momenta space structure. These limits suggest a direct connection between quantum phase space geometry, cosmology, and quantum gravity, offering new perspectives on the origin of the quantum structure of spacetime. The results also resonate with the principle of Born reciprocity, which posits a fundamental duality between coordinates and momenta, and align with recent works on the relation between QPS and neutrino physics.

A random access code (RAC) encodes an $L$-bit string into a $k$-bit message, $L>k$, so that any requested bit can be recovered with high probability; a quantum RAC (QRAC) uses $k$ qubits instead. We give a geometric characterization of optimal classical $(L,k)$-RACs under average and worst-case decoding criteria. The average criterion is reduced to choosing $2^k$ representatives in $\{0,1\}^L$, while the worst-case criterion is reduced to a minimax problem over $2^k$ points in $[0,1]^L$ with a distance-like objective. This framework proves optimality for several parameter families, with many optimal constructions arising from standard infinite families of binary linear codes. It also yields two explicit classical--quantum separations. First, for every $L>1$, we construct a $(L,1)$-QRAC whose average decoding success probability strictly exceeds the optimal classical value. Second, for the family $(2^k-1,k)$, we prove worst-case optimality of a classical RAC and construct a QRAC with strictly larger worst-case success probability. For the family $(L,L-1)$, the framework identifies a classical RAC that is average-case optimal and, under a stated conjecture, also worst-case optimal. The same viewpoint further recovers explicit $(L,L-1)$-QRACs attaining a previously conjectured upper-bound value.

Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and irreversible relaxation. This work studies a continuous coherent noise model for quantum circuits and compares it with a discrete Pauli model. The focus is on small, coherent gate errors that accumulate across circuit depth. These errors are modeled as random rotations on the Bloch sphere using a von Mises-Fisher distribution. In the small-angle limit, the model reduces to an isotropic Gaussian distribution. We test the model on quantum error-correction circuits based on the [[5,1,3]] and [[7,1,3]] codes. A variant of Grover's search circuit with different qubit counts is also examined. To enable fair comparison, we introduce a model-independent matching scheme. Pauli and continuous noise channels are aligned using the binary entropy at readout. This isolates the effect of noise structure at fixed uncertainty. An approximate analytical method for the propagation of coherent errors is also developed. The method tracks error distributions both on Clifford and non-Clifford circuits without full Monte Carlo sampling. It reduces simulation cost while preserving accuracy for circuit-level error estimates. The approximation is validated against brute-force simulations, identifying its regime of validity with Clifford and non-Clifford circuits under error correction. Our results show that continuous coherent noise and Pauli noise lead to comparable logical-error trends in the stabilizer-code circuits studied here. This behavior is consistent with syndrome extraction projecting a general single-qubit error onto Pauli-error subspaces before recovery. They also show where simplified propagation models work well and where their accuracy is reduced.

We present the results of an experimental study of the anomalous anisotropy of alignment signals in cesium vapors under strong spin-exchange conditions near zero magnetic field with linearly polarized optical pumping. We show that the anisotropy of the Hanle resonances in the plane perpendicular to the pump beam increases with concentration: in one direction the widths remain broadened by spin-exchange, whereas in the other they approach the spin-exchange relaxation free limit. With a further increase in concentration, additional nonlinear effects arise, such as signal amplification, bistability, hysteresis, and memory. To explain these effects we construct a illustrative theoretical model incorporating spontaneous polarization effects under strong spin exchange conditions. The model qualitatively shows that the ultra-narrow alignment resonances may originate from quadrupole anisotropy arising from the projection of spontaneous transverse orientation onto the detection axis. The unique properties of these resonances, such as their extremely small width and magnetic field-controlled bistability with a long-term memory effect, make them promising for use in quantum sensing and information.

We introduce the Motte model, a software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each disjoint layer of gates accompanied by a pairwise or k-local quantum state tomography of the device. We prove that the model is equivalent to the coupling-graph-restricted circuit model, and hence universal for BQP, with only polynomial overhead: emulating a depth-D circuit on N qubits requires O(D^2 N log N) elementary operations. Because the gate applied at each step is fixed exactly by the tomographic report, this emulation is robust to both the sampling and readout noise of the tomography. The model formalizes an idiom shared by existing work that ranges from quantum imaginary time evolution for the study of quantum systems to the use of quantum computers for procedural generation in games. It therefore provides a natural interface for designing quantum software entirely in terms of physically observable quantities, relevant for the NISQ era and into fault-tolerance, with gate and decoherence noise lying outside the present scope.

Electric field noise produced by the surface of ion trap electrodes reduces the fidelity of quantum computing operations. Despite decades of investigation its microscopic origins remain unclear. Here, we measure electric field noise at trapping locations along the symmetry axis of a linear surface Paul trap. We find that noise levels vary by three orders-of-magnitude in one 600$\,\mu$m section of the trap. Optical and scanning electron microscope images show micron-sized particles close to the trapping locations with the highest noise levels. We find that modeling the particles as a lossy dielectric with a effective loss tangent $\tan\theta=0.33(0.06)$ describes the magnitude of the noise, as well as its spatial and frequency dependence. Our observations may explain the large variation of reported noise levels in literature.

We propose a direct Ramsey-interferometric test of Continuous Spontaneous Localization (CSL) in which a trapped charged nanoparticle acts as a reversible mesoscopic measurement pointer. A microscopic system is prepared in a two-branch Ramsey superposition; during the Ramsey interval, the two branches exert opposite weak forces on the nanoparticle. The nanoparticle center of mass therefore follows two branch-conditioned trajectories that temporarily separate and close again after one weak-trap period. The nanoparticle is then disentangled from the microscopic system, and the measured observable is the final Ramsey visibility of the microscopic system. Ordinary quantum mechanics predicts recovery of this visibility at the recombination time, while CSL predicts an irreversible visibility loss accumulated during the temporary separation of the nanoparticle mass distributions. The main value of the protocol is a stronger direct visibility-loss test of CSL using reversible measurement-like amplification. At the benchmark exposure $N_0=5\times10^5$, the baseline polar-molecule and aggressive Rydberg-Stark operating points improve over digitized direct matter-wave CSL bounds by about $1.3\times10^4$ and $2.1\times10^5$, respectively. These factors scale as $\sqrt{N/N_0}$; equivalently, $\lambda_{\min}\propto N^{-1/2}$. At the same exposure, the projected sensitivities remain above the strongest non-interferometric bounds, which probe CSL through different observables.

We develop a quantized screw-mode mechanism for chirality-induced spin selectivity (CISS). The corresponding quantum, termed a heliciton, is a screw-symmetric environmental excitation with phase $\phi-qz$, longitudinal momentum $\hbar q$, and energy $\hbar\Omega_q$. Its absorption and emission convert the static local chiral vertex developed in our preceding work into an inelastic resonant scattering process. In first Born approximation, absorption maps $\uparrow,k$ to the $\downarrow,k+q$ sideband, whereas emission maps $\downarrow,k$ to the $\uparrow,k-q$ sideband. The two outputs share the sampled-current overlap $\mathcal J_\chi(k)$ but differ in ladder factors, final momenta, and detunings. With spectral factors $\mathcal S_+$ and $\mathcal S_-$, $P_{\rm sb}=[\mathcal S_--\mathcal O(T)\mathcal S_+]/ [\mathcal S_-+\mathcal O(T)\mathcal S_+]$, where $\mathcal O(T)=\exp[-\hbar\Omega_q/(k_BT)]$. An isolated emission or absorption resonance yields $P_{\rm sb}\simeq+1$ or $-1$, respectively, in the resolved sideband sector. Reversing the screw handedness interchanges the spin identities of the two sidebands while leaving their spectral and occupation weights unchanged, and therefore reverses $P_{\rm sb}$ at every temperature. At high temperature, absorption and emission have nearly equal occupation weights; at low temperature, absorption is exponentially suppressed while spontaneous emission remains. Liquid-nitrogen temperature can already produce a pronounced asymmetry for higher-$\Omega_q$ modes. Thus a spatially resolved Dirac wave with spin-dependent helical conserved current couples locally to a heliciton and produces thermally weighted spin- and momentum-resolved sidebands without an ad hoc spin-dependent potential.

Leveraging data symmetries has recently become a key strategy in quantum neural networks (QNNs) to improve training efficiency. In this study, we propose a symmetry-informed regularization method for QNNs based on an input density matrix. By introducing a penalty term that encourages the model to align with data symmetry, our method enables improved training speed. This symmetry-based regularization is simple to implement and does not require an explicitly specified symmetry group, although it requires access to training samples or to the input distribution from which an empirical or theoretical input density matrix can be constructed. We evaluate the method through numerical experiments on both classification tasks and quantum generative adversarial networks. In the small-scale classification experiments, the regularizer produced modest improvements in early-stage convergence and test loss. Our findings highlight the potential of symmetry-aware regularization in enhancing the performance of QML models.

Nonlinear differential equations play a crucial role in modeling a wide range of phenomena, yet their solutions remain notoriously difficult to obtain. With the rapid development of quantum computing, quantum algorithms for efficiently solving such equations are actively being explored. One promising approach is based on Carleman linearization, which transforms nonlinear differential equations into linear systems. However, this method suffers from exponential divergence beyond a certain time scale. By reformulating the solutions in terms of eigenvalues and eigenvectors, we identify that this divergence originates from the Laurent expansion outside its neighborhood of convergence. To address this issue, we insert a regularized function to the divergent solution hinted by analytical continuation. We validate this divergence-correction method on both the logistic equation and some other partial differential equations like KPP-Fisher equations and Phase-Field models under periodic conditions. We implement our method for the logistic equation using the Linear Combination of Unitaries (LCU) quantum algorithm, providing a detailed complexity and error analysis.

The description of the optomechanical systems is commonly based on the quantum Langevin equation formalism. This framework is introduced phenomenologically or based on a model Hamiltonian. However, once dealing with the optomechanical Fabry-Perot cavity or the modified Michelson-Sagnac interferometer with a semitransparent mechanically active membrane inside, a model-free consideration is also possible by using an alternative approach. Such an approach, which is based on the classical wave equations, is popular in the gravitational-wave community where it is termed as input-output relations approach. In this work, using the aforementioned approach, we derived the equations for the ladder operator of the intracavity field, stochastic back-action force, and the relation between the fields at the input mirror. Then we simplified the obtained results down to the range of applicability of the Langevin equation formalism and compared these with the corresponding predictions of the latter formalism. This enabled us to critically assess the validity of the Langevin equation formalism and rectify its range of applicability to find that the latter is more stringent than that intuitively expected. In the case where the dissipative optomechanical coupling is involved we identified appreciable problems with this formalism. It was found that, disregarding the fact that decay rate of the optomechanical Fabry-Perot cavity depends on its length, no dissipative optomechanical coupling is generated. This is in contrast with the prediction of the standard Langevin-equation based treatment. It was found that the Langevin equation formalism misses a phase factor at the input field; this factor turns out to be important for the situation involving the dissipative optomechanical coupling.

Quantum subspace-diagonalization methods, particularly Quantum Krylov Diagonalization (QKD), provide a promising route for computing low-energy spectra of quantum many-body Hamiltonians. However, existing quantum Krylov approaches rely on non-orthogonal Krylov bases, requiring overlap-matrix regularization that limits numerical stability and accuracy. In this work, we introduce an Orthogonal Quantum Krylov Diagonalization (OQKD) framework that reformulates the classical Lanczos recursion at the operator level, enabling an orthogonal quantum implementation of Krylov-subspace diagonalization. By expressing Lanczos vectors as polynomial transformations of the Hamiltonian, OQKD reproduces the orthogonality, tridiagonal structure, and convergence behavior of the classical Lanczos algorithm thus eliminating the need for overlap-matrix regularization. We further show that the required Lanczos polynomials can be implemented using block encoding and Generalized Quantum Signal Processing with the same asymptotic query complexity as Chebyshev-based QKD methods. Numerical simulations of the $J_1$--$J_2$ Heisenberg model confirm the classical Lanczos convergence and numerical stability of the proposed method, while the measurement-complexity scaling is established analytically. Building upon the OQKD framework, we then introduce a restarted state-preparation protocol that replaces a single high-degree polynomial transformation with a sequence of fixed low-degree transformations, maintaining an affordable block encoding success probability while retaining comparable convergence. These results establish OQKD as an orthogonal quantum analog of the classical Lanczos algorithm and identify the restarted protocol as a promising state-preparation strategy for Quantum Phase Estimation.

We revisit von Neumann's theory of infinite tensor products of Hilbert spaces. On the set $\Gamma$ of equivalence classes of $C_0$-sequences, which labels the incomplete tensor products inside the complete tensor product, we introduce a natural pseudo-ultrametric $d$: the distance between two classes is the convergence exponent of the series $\sum_j|\langle\varphi_j,\psi_j\rangle-1|$ formed from any pair of representatives. We show that $d$ is well defined on equivalence classes, satisfies the strong triangle inequality, and is complete. Distinct classes may lie at distance zero, so $d$ separates points only after passing to the quotient $\widetilde\Gamma$ of $\Gamma$ by the relation $d=0$; the pair $(\widetilde\Gamma,d)$ is then a complete ultrametric space. As an application, we show that a product unitary $\bigotimes_j U$ whose factor $U$ satisfies $\inf_{\|x\|=1}|\langle x,Ux\rangle-1|>0$ (in particular, a unitary on a finite dimensional space with $1\notin\sigma(U)$) displaces every class to the maximal distance $1$. Guided by the intended application -- a caricature of Everettian branching, in which the sectors of the infinite tensor product play the role of worlds -- we also develop a gauge-invariant variant $\tilde d$ of the metric, based on von Neumann's weak equivalence and matched to the quasi-equivalence of product states on the quasi-local algebra. The displacement of a class under a product unitary, measured by $\tilde d$, is class dependent and realizes every value in $[0,1]$. We interpret $\tilde d$ as a decoherence exponent: it measures the polynomial rate at which two branches of the universal state vector become operationally distinct as ever larger portions of the environment are monitored.

The field of quantum machine learning (QML) evolved to value models believed to most directly rival those providing utility in classical ML, namely large-scale neural networks. Although more recently, classical ML has been learning a hard lesson with respect to deploying un-interpretable neural networks in the wild: model interpretability matters for domain-adapted co-design and human adoption. We adopt this larger ML perspective to argue that quantum ML model value can be found through the characterization of its inherent interpretability offerings -- i.e. its mathematical structure that contributes meaningfully to desired model behavior for the specific ML task. To support our perspective, we provide a motivating example of a characterization with quantum Fourier models and random Fourier features (RFF) as approaches to approximate Gaussian process (GP) kernels for uncertainty quantification tasks in ML. The top-down and bottom-up complementarity of the two mathematical constructions reveals that quantum Fourier models offer different tools than RFFs for principled GP kernel design and interpretable discovery for uncertainty quantification with real-world data. To showcase the rich variety of inductive biases enabled by quantum information tools, we review examples from the QML literature -- including symmetry, metric geometry, and topology -- that can be used to design inherently interpretable ML models for specific tasks. We hope this framing encourages the QML community to value the inherent components and mechanisms of quantum models separately from task performance, as inherent interpretability might be the reason that a quantum model, and potentially a quantum computer, gets used in practice for ML.

We investigate how quantum computers can be used to emulate quantum networks and study their performance under practical impairments. In particular, we evaluate how degraded entanglement and communication latency affect teleportation-based distributed multipartite-entanglement-state construction. We model imperfect Bell-pair sources using depolarizing noise channels and classical communication delays using thermal relaxation. We implement the depolarization using Stinespring dilation, randomly applied Pauli errors, and quasi-probability decompositions, evaluating the latter two on IQM quantum hardware and all three in simulation. We then study the performance of the entanglement distribution under noise generated by the aforementioned models. Although these noise models are mathematically equivalent, we find that hardware constraints result in profound differences in the corresponding results, highlighting the importance of careful experiment design.

Nonlinear kinetic plasma simulation is high-dimensional and classically demanding, while quantum algorithms face different bottlenecks: embedding nonlinear dynamics into a linear computation, loading dense field-interaction data, and efficiently extracting information. We present an end-to-end quantum algorithm, with rigorous convergence guarantees, for a weakly nonlinear kinetic plasma model. The system describes a 3D electron-ion plasma with adiabatic electrons, kinetic ions, Debye screening, and Krook relaxation. After Fourier-Hermite truncation, the dynamics reduces to a high-dimensional quadratic ordinary differential equation. To tackle quantum bottlenecks we combine three key ingredients. First, we use a plasma free energy to identify a Lyapunov transform under which a Carleman linear embedding converges exponentially in the truncation order within a certified weakly nonlinear regime. Second, we develop a hierarchical block-encoding protocol for dense matrices, exploiting the spatial decay of the field to avoid polynomial overhead from sparse access encodings. Third, we introduce a subroutine for information extraction that exploits nonlinear components encoded in the full Carleman history state to improve the estimation of linear observables. We construct a quantum algorithm to estimate the spacetime-averaged kinetic energy using $\widetilde{O}\!\left( N_F N_H^{1/2} \operatorname{polylog}\!\left(\frac{T}{\epsilon}\right)\frac{1}{\epsilon}\right)$ gates and $\widetilde{O}\!\left(\log\!\left(N_F N_H^{1/2}T\right)\log\!\left(\frac{1}{\epsilon}\right)\right)$ qubits, where $N_F$ and $N_H$ are the Fourier and Hermite cutoffs. Relative to a Fourier-Hermite spectral solver, this yields exponential memory savings and superquadratic improvements in time. Together, these results establish a controlled nonlinear plasma benchmark for quantum simulation.

A critical limitation of solid-state quantum devices arises from the materials from which they are fabricated: uncontrolled surfaces, interfaces, and structural imperfections introduce numerous sources of loss and decoherence. Despite extensive efforts, linking these decoherence mechanisms to their microscopic material origins -- essential for developing effective mitigation strategies -- remains an outstanding challenge that has slowed coherence improvements. Here, using scanning gate microscopy on live superconducting circuits we identify a previously unrecognised decoherence mechanism originating from Coulomb blockade and microwave-driven charge tunnelling in metallic grains. Such grains are ubiquitous in thin-film devices fabricated by standard lithography processes. By characterising multiple defects across different devices, we find such defects to be as common and as debilitating to device performance as two-level system (TLS) defects, while originating from a fundamentally different physical mechanism. Importantly, conventional characterisation techniques would misattribute this loss to other, microwave power-independent processes. Our observations thus reveal a widespread source of decoherence in superconducting circuits, challenging the prevailing paradigm that coherence lifetimes are primarily limited by TLS defects. Eliminating metallic grains during fabrication provides a clear and practical route to suppress this mechanism, offering a pathway towards improved coherence and reduced noise in microwave-based solid-state quantum devices.

It is well established that causal linear response functions can be found by computing the much simpler imaginary time-ordered Matsubara functions and performing an analytic continuation. This principle is the basis for much of our understanding of linear response for interacting and disordered systems, via diagrammatic perturbation theory. Similar imaginary-time approaches have recently been introduced for computing nonlinear response functions as well, for example in [Annalen der Physik 536, 2300504 (2024); Physical Review X 11, 041006 (2021)], where the authors analytically continue the Matsubara functions to obtain the Keldysh response functions. In this work, we provide a proof of this connection to all orders in perturbation theory using an equation of motion based approach. We show by induction that causal nonlinear response functions at every order can be obtained from an analytic continuation of an appropriate time-ordered Matsubara function. We demonstrate this connection explicitly for second order response functions in the Lehmann representation. As a byproduct of our approach, we derive an explicit expression for the Lehmann representation of $n$-th order response functions by solving the equations of motion. We also use our result to find an analytic spectral density representation for both causal response functions and Matsubara functions. As an example, we apply our method to derive the non-linear $A^3$ term in the $SU(2)$ spin Hall response of an insulator with spin rotation symmetry. Finally, we show how our results lead to a family of generalized sum rules, focusing explicitly on the asymptotic expression for $n$-th harmonic generation rate. Our work opens the door to using imaginary time approaches to study nonlinear response functions in general condensed matter systems.

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where conventional magnetic long-range order vanishes in the thermodynamic limit, while the Edwards-Anderson order parameter remains finite, signaling the emergence of a quantum spin-glass phase. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass-order is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.

We propose novel classical and quantum online algorithms for learning finite- and infinite-horizon Markov Decision Processes (MDPs). Our algorithms are based on a hybrid online-offline reinforcement learning model wherein the agent can, from time to time, freely interact with the environment in a generative sampling fashion, i.e., by having access to a "simulator". By employing known classical and new quantum algorithms for approximating optimal policies under a generative model within our learning algorithms, we show that it is possible to avoid several paradigms from RL like "optimism in the face of uncertainty" and "posterior sampling" and instead compute and use optimal policies directly, which yields better regret bounds compared to previous works. Our quantum algorithms obtain regret bounds which only a $\operatorname{poly}\log{T}$ dependence on the number of time steps $T$, thus breaking the $O(\sqrt{T})$ classical barrier. Our infinite-horizon discounted regret bound is brand new, while in the finite- and infinite-horizon undiscounted settings, our results match the time dependence of some prior quantum works, but with improved dependence on other parameters like state space size $S$ and action space size $A$.

Alternative theories of quantum statistics provide an avenue for exploring novel physics beyond bosons and fermions, yet experimental verification of their existence in nature proves a challenging task. Among these theories, it has recently been suggested that $R$ parastatistics can be realized as quasiparticle excitations in many-body systems. In this paper, we build on this idea by showing that signatures of $R$ parastatistics can be observed as flavor-charge separation in one-dimensional (1D) systems. We consider a generalized version of the Luttinger model (LM) and show that bosonization persists when the $R$ paraparticles have Fermi-surface-like structures. These $R$ parafermions can satisfy generalized exclusion principles beyond conventional Pauli's. We show that density waves of all $R$ parafermions can always be bosonized, but flavor waves act like bosons only for a certain subclass of $R$ parafermions. We derive the conditions for bosonization by analyzing the LM spectrum, showing that bosonization applies only to low-temperature systems. Signatures of flavor-charge separation then become apparent as distinct dispersion profiles when we turn on interparticle interactions. This points to potential observations of flavor-charge separation in 1D systems that host emergent $R$ paraparticles.

Experiments with ultracold quantum gases are a rapidly advancing research field with many applications in fundamental physics and quantum technology. Here, we report on a high-flux generation of Bose-Einstein condensate mixtures of $^{41}$K and $^{87}$Rb, using a fully integrated sounding rocket setup. We compare the release and the free expansion of the quantum mixtures obtained with the apparatus placed on ground or in free fall in an Einstein-Elevator. The release dynamics are governed by the intra- and interspecies interactions as well as the decaying magnetic field during the release. The latter can be minimized by a dedicated switch-off protocol of the trap generating currents where an exact model enabled us to characterize the interaction effects. Our results establish a new benchmark for generating ultracold mixtures on mobile platforms, with direct relevance for future experiments on interacting quantum gases and tests of the equivalence principle in space.

Strongly interacting fermions represent the key constituent of several intriguing phases of matter. However, due to the inherent complexity of these systems, important regimes are still inaccessible. Here, we derive a realistic and flexible setup based on ultracold magnetic lanthanide atoms trapped in a one-dimensional optical lattice. Leveraging their large magnetic moments, we design a fermionic $t-J$ model with independently tunable hopping, spin-spin couplings, and onsite interaction. Through combined analytical and numerical analysis, we uncover a variety of many-body quantum phases$-$including superconducting and topological states. Crucially, in the regime of attractive onsite interaction we reveal that topology and superconductivity coexist, thus giving rise to an exotic state of matter: a topological triplet superconductor. We also outline a practical protocol to prepare and detect all discovered phases using current experimental techniques. Our results establish an alternative and powerful route for a deeper understanding of strongly interacting fermionic quantum matter.

Understanding how information spreads in non-relativistic many-body systems is a central issue for quantum information processing. While short-range interactions confine information within a local light cone, long-range interactions typically lead to uncontrolled nonlocal spread across the entire system. Here, we demonstrate that this apparent dichotomy is not fundamental and that nonlocality in systems with long-range interactions can be deterministically controlled. By mapping spin dynamics to a hard-core boson chain, we identify a regime in which the causal space-time landscape can be precisely shaped. We show that placing spin excitations in a polarized background allows a local perturbation to trigger nonlocal signals exactly at the positions of these excitations. These pre-selected sites act as seeds for new, effective light cones, allowing information to bypass the bulk and re-emerge at distant, programmable locations. This mechanism avoids uncontrollable global nonlocality while circumventing the speed limits associated with local transport. By engineering these nonlocal communication channels, our findings offer a versatile framework for information distribution relevant to quantum memories, error correction, and programmable platforms such as trapped ions.

Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a first and comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of $^{174}$Yb in $6sns\,^1S_0$ Rydberg states across nearly two decades in principal quantum number $n$ and three orders of magnitude in molecular binding energy. Using the Coulomb Green's function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy $s$-wave scattering length and the positions of two spin-orbit split $p$-wave shape resonances. Our results provide strong evidence that the Yb$^{-}$ anion exists only as a metastable resonance.% We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the $6s23f\, ^1F_3$ state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.

We report high-precision frequency ratio measurements between optical atomic clocks based on $^{27}$Al$^+$, $^{171}$Yb, and $^{87}$Sr. With total fractional uncertainties at or below $3.2 \times 10^{-18}$, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in $^{87}$Sr ratios at approximately $1\times10^{-16}$ and the Al$^+$/Yb ratio at $1.6\times10^{-17}$ in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of $1.3 \times 10^{-16}$ at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.

Recent experiments on K3C60 revealed a giant enhancement of the light-induced superconducting-like optical response for pump frequencies near 10 THz, with an efficiency roughly two orders of magnitude larger than for off resonant excitation. Here we show that a resonant enhancement of pair correlations arises naturally in a driven purely electronic model of K$_3$C$_{60}$ with ab initio parameters. The underlying mechanism is a symmetry constrained two-photon pathway: the first photon drives the system from the even-parity ground state to an intermediate odd-parity manifold, while the second photon induces a transition to an even-parity excited state with enhanced pair correlations. Larger-cluster calculations show that the corresponding resonance energy is strongly renormalized downward with system size and connectivity, reflecting the kinetic-energy gain of delocalized photo-excited doublon-holon configurations. A simplified single-orbital model reproduces this scaling trend and reaches a 14-site fcc cluster, where the resonant peak is pushed to 30 THz, with a trend compatible with a further reduction toward the experimental 10 THz scale in larger systems. Varying the Hubbard coupling strength, we find that the resonance is lowest and the pairing enhancement strongest near intermediate couplings, where doublon-holon excitations are both well defined and mobile. Our results establish a purely electronic mechanism for resonant light-enhanced pair correlations in K$_3$C$_{60}$ and support the interpretation of the experimental 10 THz resonance as optical access to a paired many-body excited state rather than improved metallicity. More broadly, they suggest that related resonant pathways may arise in other intermediate-coupling Hubbard materials.

Unitary time evolution of initially simple quantum many-body states rapidly generates entanglement and complex correlations, which limits direct numerical simulations. The late-time dynamics of physical observables, however, typically exhibits an effective simplicity in the form of hydrodynamics or kinetic theory. This leads to the question whether microscopic equations of motion can remain accurate and tractable up to long time scales by discarding irrelevant information in a controlled manner. Here, we introduce compressed minimum-purity time evolution (CoMPuTE) as an approach to keep track of a consistent set of reduced local density matrices, closing the hierarchical equations of motion using a minimum-purity principle. In benchmark applications we demonstrate (i) accurate description of energy diffusion in the one-dimensional mixed-field Ising model, (ii) the applicability to genuinely out-of-equilibrium Floquet dynamics starting from a pure state, and (iii) the limitations of the local reduced density matrix approximation when describing transport in the XXZ chain at $\Delta=1$ that is governed by increasingly non-local integrals of motion. The CoMPuTE method enhances computational efficiency in comparison to the closely related local-information time evolution algorithm, opening a possible route towards an extension to systems in higher spatial dimensions.