Simulating the cold $^{87}Rb$ atom with a three-level quantum system interacting with two orthogonal standing-wave fields, the localization within half-wavelength domain in the x-y plane is achieved by monitoring the probe absorption. Within the half-wavelength domain, the single absorption peak increases from 0.2 to 1.0 via the spontaneously generated coherence (SGC), while the diameters of the single absorption peaks are diminished by the increasing incoherent pumping field. Our scheme provides the flexible parameters manipulating manner for the localization of cold $^{87}Rb$ atom.

The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The objective function and its derivatives required by the optimizer can efficiently be evaluated on a quantum computer by measuring an ancilla qubit, while the optimization procedure employs classical hardware. The focal aspect of the study is the treatment of boundary conditions, which is tailored to the properties of the quantum hardware using a correction technique. For this purpose, the boundary conditions and the discretized terms of the partial differential equation are decomposed into a sequence of unitary operations and subsequently compiled into quantum gates. The accuracy and gate complexity of the approach are assessed for second-order partial differential equations by classically emulating the quantum hardware. The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results of this flexible approach display a robust behavior and a strong predictive accuracy in combination with a remarkable polylog complexity scaling in the number of qubits of the involved quantum circuits. Remaining challenges refer to adaptive ansatz strategies that speed up the optimization procedure.

We study the non-equilibrium dynamics of a quantum spin 1/2 XXZ model confined in a two-dimensional bi-layer system, with couplings mediated by inverse power-law interactions, falling off with distance $r$ as $1/r^{\alpha}$, and spatio-temporal control of the spins enabled via local fields. An initial state of spins with opposite magnetization in the two layers is dynamically unstable resulting in exponential generation of correlated pairs of excitations. We find that scalable generation of entanglement in the form of two-mode squeezing between the layers can generically be achieved in powerlaw models. We further demonstrate that spatially-temporally engineered interactions allow to significantly increase the generated entanglement and in fact achieve Heisenberg limited scaling. This work is relevant to a wide variety of experimental atomic, molecular, and optical platforms, which realize powerlaw spin models, and demonstrates the advantage of spatio-temporal control to maximize the generation of metrologically useful entanglement, with potential applications in quantum-enhanced sensing.

A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, $f$-routing and $f$-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Our technique is based on the rank of a function $g$ that is zero if and only if the function $f$ which defines the given non-local quantum computation is zero. For the equality, non-equality, and greater-than functions we obtain explicit linear lower bounds on entanglement for $f$-routing and $f$-BB84 in the perfect setting. Because of a relationship between $f$-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we also obtain a new technique for lower bounding the randomness complexity of CDS.

A quantum position-verification scheme attempts to verify the spatial location of a prover. The prover is issued a challenge with quantum and classical inputs and must respond with appropriate timings. We consider two well-studied position-verification schemes known as $f$-routing and $f$-BB84. Both schemes require an honest prover to locally compute a classical function $f$ of inputs of length $n$, and manipulate $O(1)$ size quantum systems. Taking $f(x,y)=\sum_i x_i y_i$ to be the inner product function, we prove that a dishonest prover must execute $\Omega(n)$ quantum gates or single qubit measurements. Our proof uses a reduction to simultaneous message passing with classical communication and shared entanglement. The scheme is feasible for a prover with polynomial classical resources and $O(1)$ quantum resources, and secure against sub-linear quantum resources.

The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian and at most $t$ non-Gaussian gates. By Jordan-Wigner mapping, this also includes $n$-qubit states prepared by nearest-neighbour matchgate circuits with at most $t$ SWAP-gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is $\mathrm{poly}(n,2^t)$; thus if $t=O(\log(n))$, it is efficient. We also show that, if $t$ scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property testing algorithm that, given access to copies of a state, determines whether such state is far or close to the set of states for which our learning algorithm works. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity.

In the quantum compression scheme proposed by Schumacher, Alice compresses a message that Bob decompresses. In that approach, there is some probability of failure and, even when successful, some distortion of the state. For sufficiently large blocklengths, both of these imperfections can be made arbitrarily small while achieving a compression rate that asymptotically approaches the source coding bound. However, direct implementation of Schumacher compression suffers from poor circuit complexity. In this paper, we consider a slightly different approach based on classical syndrome source coding. The idea is to use a linear error-correcting code and treat the message to be compressed as an error pattern. If the message is a correctable error (i.e., a coset leader) then Alice can use the error-correcting code to convert her message to a corresponding quantum syndrome. An implementation of this based on polar codes is described and simulated. As in classical source coding based on polar codes, Alice maps the information into the ``frozen" qubits that constitute the syndrome. To decompress, Bob utilizes a quantum version of successive cancellation coding.

We study the quantum walk on the off-diagonal Aubry-Andre-Harper (AAH) lattice with quasiperiodic modulation using a digital quantum computer. Our investigation starts with exploring the single-particle quantum walk, where we study various initial states, hopping modulation strengths, and phase factors Initiating the quantum walk with a particle at the lattice edge highlights the robustness of the edge state due to the topological nature of the AAH model and reveals how this edge state is influenced by the phase factor. Conversely, when a particle starts the quantum walk from the lattice bulk, we observe the bulk walker being repelled from the edge, especially in the presence of strong hopping modulation. Furthermore, we investigate the quantum walk of two particles with nearest-neighbor interaction, emphasizing the repulsion between edge and bulk walkers caused by the interaction. Also, we explore the dynamics of two interacting particles in the lattice bulk and find interesting bulk localization through the formation of bound states influenced by the combined effect of hopping modulation and nearest-neighbor interaction. These features are analyzed by studying physical quantities like density evolution, quantum correlation, and participation entropy, and exploring their potential applications in quantum technologies.

The long term behaviour of a quantum channel under iterations (i.e. under repeated applications of itself) yields a plethora of interesting properties. These include ergodicity, mixing, eventual scrambling, becoming strictly positive, and the vanishing of its one-shot zero error capacities. We derive relations between these seemingly different properties and find novel bounds on indices which quantify the minimum number of iterations needed for the onset of some of these properties. We obtain a lower bound on the one-shot zero-error classical capacity of $n$ iterations of an ergodic channel (for any positive integer $n$) in terms of the cardinality of its peripheral spectrum. We also find upper bounds on the minimum number of iterations needed for the one-shot capacities of any channel to stabilize. We consider two classes of quantum channels, satisfying certain symmetries, for which upper bounds on the above indices are optimal, since they reduce to the corresponding indices for a stochastic matrix (for which the bounds are known to be optimal). As an auxiliary result, we obtain a trade-off relation between the one-shot zero error classical and quantum capacities of a quantum channel.

We are presented with a graph, $G$, on $n$ vertices with $m$ edges whose edge set is unknown. Our goal is to learn the edges of $G$ with as few queries to an oracle as possible. When we submit a set $S$ of vertices to the oracle, it tells us whether or not $S$ induces at least one edge in $G$. This so-called OR-query model has been well studied, with Angluin and Chen giving an upper bound on the number of queries needed of $O(m \log n)$ for a general graph $G$ with $m$ edges. When we allow ourselves to make *quantum* queries (we may query subsets in superposition), then we can achieve speedups over the best possible classical algorithms. In the case where $G$ has maximum degree $d$ and is $O(1)$-colorable, Montanaro and Shao presented an algorithm that learns the edges of $G$ in at most $\tilde{O}(d^2m^{3/4})$ quantum queries. This gives an upper bound of $\tilde{O}(m^{3/4})$ quantum queries when $G$ is a matching or a Hamiltonian cycle, which is far away from the lower bound of $\Omega(\sqrt{m})$ queries given by Ambainis and Montanaro. We improve on the work of Montanaro and Shao in the case where $G$ has bounded degree. In particular, we present a randomized algorithm that, with high probability, learns cycles and matchings in $\tilde{O}(\sqrt{m})$ quantum queries, matching the theoretical lower bound up to logarithmic factors.

We study the coherence of two coupled spin qubits in the presence of a bath of nuclear spins simulated using generalized cluster correlation expansion (gCCE) method. In our model, two electron spin qubits coupled with isotropic exchange or magnetic dipolar interactions interact with an environment of random nuclear spins. We study the time-evolution of the two-qubit reduced density matrix (RDM) and resulting decay of the off diagonal elements, corresponding to decoherence, which allows us to calculate gate fidelity in the regime of pure dephasing. We contrast decoherence when the system undergoes free evolution and evolution with dynamical decoupling pulses applied. Moreover, we study the dependence of decoherence on external magnetic field and system parameters which mimic realistic spin qubits, emphasizing magnetic molecules. Lastly, we comment on the application and limitations of gCCE in simulating nuclear-spin induced two-qubit relaxation processes.

The Heisenberg limit (HL) and the standard quantum limit (SQL) are two quantum metrological limits, which describe the scalings of estimation precision $\Delta \hat\theta$ of an unknown parameter $\theta$ with respect to $n$, the number of one-parameter quantum channels applied. It was known that the HL ($\Delta \hat\theta \propto 1/n$) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL ($\Delta \hat\theta \propto 1/n^{1/2}$) is optimal and can be achieved with $n$ repeated measurements. However, it is unknown whether such limits are still achievable using restricted quantum devices where the required QEC operations are not available -- e.g., finite-size devices where only unitary controls are available or where noiseless ancilla is not available. In this work, we identify various new noisy metrological limits for estimating one-parameter qubit channels in different settings with restricted controls. The HL is proven to be unattainable in these cases, indicating the necessity of QEC in achieving the HL. Furthermore, we find a necessary and sufficient condition for qubit channels to attain the SQL, called the ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition. When RGNKS is satisfied, the SQL is achievable using only unitary controls and a single measurement. When RGNKS is violated, the estimation precision (in most cases) has a constant floor when repeated measurements are not allowed. Demonstration of this separation in metrological powers is within reach of current quantum technologies.

Constrained problems are frequently encountered in classical and quantum optimization. Particle conservation, in particular, is commonly imposed when studying energy spectra of chemical and solid state systems. Though particle number-constraining techniques have been developed for fermionic (e.g. molecular electronic structure) Hamiltonians, analogous techniques are lacking for non-binary and non-fermionic problems, as in the case of bosonic systems or classical optimization problems over integer variables. Here we introduce the binary encoded multilevel particles circuit ansatz (BEMPA) -- an ansatz which preserves particle count by construction -- for use in quantum variational algorithms. The key insight is to build the circuit blocks by carefully positioning a set of symmetry-preserving 2- and 3-qubit gates. We numerically analyze the problem of finding the ground state eigenvalues -- via the Variational Quantum Eigensolver (VQE) algorithm -- of the Bose-Hubbard Hamiltonian. For a range of model parameters spanning from Mott insulator to superfluid phase, we demonstrate that our proposed circuit ansatz finds the ground state eigenvalues within drastically shorter runtimes compared to penalty-based strategies methods. Finally, we analyze the potential resource benefits of changing the qubit encoding at the end of the optimization routine. Our results attest to the efficacy of BEMPA for simulating bosonic problems for which particle number is preserved.

Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of the class NP with multiple unentangled quantum proofs, the so-called QMA(2) and its variants. The complexity of QMA(2) is a longstanding open problem, and only the trivial bounds QMA $\subseteq$ QMA(2) $\subseteq$ NEXP are known. In this work, we study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $\text{QMA}^+(2)$. In this setting, we are able to design proof verification protocols for problems both using logarithmic size quantum proofs and having a constant probability gap in distinguishing yes from no instances. In particular, we design global protocols for small set expansion, unique games, and PCP verification. As a consequence, we obtain NP $\subseteq \text{QMA}^+_{\log}(2)$ with a constant gap. By virtue of the new constant gap, we are able to ``scale up'' this result to $\text{QMA}^+(2)$, obtaining the full characterization $\text{QMA}^+(2)$=NEXP by establishing stronger explicitness properties of the PCP for NEXP. One key novelty of these protocols is the manipulation of quantum proofs in a global and coherent way yielding constant gaps. Previous protocols (only available for general amplitudes) are either local having vanishingly small gaps or treat the quantum proofs as classical probability distributions requiring polynomially many proofs thereby not implying non-trivial bounds on QMA(2). Finally, we show that QMA(2) is equal to $\text{QMA}^+(2)$ provided the gap of the latter is a sufficiently large constant. In particular, if $\text{QMA}^+(2)$ admits gap amplification, then QMA(2)=NEXP.

A high-quality narrowband polarization-entangled source in the telecom band is preferred to avoid frequency dispersion for long-distance transmission in optical fibers and to efficiently couple with telecom band quantum memories. Here, we report narrowband, telecom-band, polarization-entangled photon pair generation based on the superposition of single-longitudinal-mode photon pairs from two monolithic nonlinear crystal cavities in a passively stable interferometer based on beam displacers. The photon pairs generated from the cavities exhibit a high coincidence to accidental coincidence ratio of 20000 and a bandwidth below 500 MHz. Two-photon polarization interference, Bell-inequality, and quantum state tomography are performed to indicate the high quality of the entangled source. The current configuration demonstrates greater stability than traditional free space cavity-enhanced polarization-entangled state generation, which is promising for quantum communication applications.

We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on $n$ bosonic modes, called a random displacement channel. We prove that if the $n$ modes are not entangled with an ancillary quantum memory, then the channel must be sampled a number of times exponential in $n$ in order to estimate its characteristic function to reasonable precision; this lower bound on sample complexity applies even if the channel inputs and measurements performed on channel outputs are chosen adaptively. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of $n$, given a sufficient amount of squeezing. This establishes an exponential separation in sample complexity. We then analyze the effect of photon loss and show that the entanglement-assisted scheme is still significantly more efficient than any lossless entanglement-free scheme under mild experimental conditions. Our work illuminates the role of entanglement in learning continuous-variable systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms.

Pure dephasing and spontaneous emission are two non-unitary processes of atoms or spins interacting with fluctuating electromagnetic (EM) modes. Collective spontaneous emission (e.g., superradiance) originates from interactions with EM modes in resonance with atoms and has received considerable attention. Meanwhile, the analogous collective dephasing phenomena remain poorly understood. Here, we introduce the nano-EM super-dephasing phenomenon arising in the photonic environment near lossy material interfaces. We show that this effect is enhanced by over 10 orders of magnitude compared to free space or photonic cavities due to the presence of long-range correlations in low-frequency evanescent EM fluctuations. We unravel the universality of nano-EM super-dephasing behaviors near ferrimagnets, metals, and superconductors and their dependence on low-frequency material properties. We demonstrate that the scaling of nano-EM super-dephasing is independent of EM modes' wavelengths and differs from the conventional $N^2$ scaling of superradiance by analyzing the decoherence of entangled states, including GHZ states. Finally, we show how to experimentally isolate and control super-dephasing to open interesting frontiers for scalable quantum systems.

Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation approach based on virtual distillation, tailored for applications in near-term quantum devices. Our methodology leverages the qubit reset technique, thereby reducing the associated qubit overhead. Crucially, our approach ensures that the required qubit resources remain independent of the desired accuracy and avoid an exponential measurement overhead, marking a substantial advancement in practical applications. Furthermore, our technique accommodates a mixed Clifford and Pauli-type shadow, which can result in a reduction in the number of required measurements across various scenarios. We also study the trade-off between circuit depth and measurement overhead quantitatively. Through numerical simulations, we substantiate the efficacy of our error mitigation method, establishing its utility in enhancing the robustness of shadow estimations on near-term quantum devices.

A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is non-singular is based on a partition of Hilbert-space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions non-trivially under Hilbert-space partition, and we derive a Work Sum Rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. The thermodynamics of two classes of quasi-statically driven open quantum systems is analyzed: systems with a finite environment in the grand canonical ensemble, and systems with an unbounded environment. Our results are illustrated with applications to a time-dependent two-level system and the driven resonant-level model.

High-fidelity detection of quantum states is indispensable for implementing quantum error correction, a prerequisite for fault-tolerant quantum computation. For promising trapped ion qubits, however, the detection fidelity is inherently limited by state leakage. Here, we propose an efficient approach to enhance the fidelity of detecting $^{171} \mathrm{Yb}^+$ qubits through $^2D_{3/2}$ state shelving techniques. Leveraging selective shelving and state-dependent fluorescence, we mitigate the impact of state leakage and experimentally realize a fidelity of 99.88(2)%, while over 99.99% fidelity is predicted by utilizing state-of-the-art hardwares. Meanwhile, we demonstrate the feasibility of mid-circuit measurements, a crucial step for recent implementations of quantum error correction, by mapping the hyperfine qubit to metastable levels. Our research provides an essential component for realizing fault-tolerant quantum information processing with trapped-ion systems in the near future.

Virtual distillation (VD) using measurements of multiple copies of a quantum circuit have recently been proposed as a method of noise mitigation of expectation values. Circuit decompositions known as B gates were found only for single qubit expectation values however practical calculations require multi-qubit expectation values which cannot be corrected with B gates. We discover low depth circuit decompositions for multi-qubit expectation values by combining multiple projections to recover the correct measurement statistics or expectation values. Our method adds linear entangling gates with number of qubits, but requires extra measurements. Furthermore, in applications to find ground states such as the variational quantum eigensolver (VQE) algorithm, the variational principle is required which states the energy cannot go below the ground state energy. We discover that the variational principle is violated if noise is higher on single expectation values than multi-qubit which renders VQE useless. We show this occurs when using B gates and is preserved if using our low depth decomposition on all expectation values. We perform demonstration on real devices and demonstrate our decomposition can mitigate real experimental noise in VQE for the H$_2$ molecule with a two qubit tapered mapping, H$_3$ with three qubits, and H$_2$ with four qubits. Our decomposition provides a way to perform duplicate circuit virtual distillation on real devices at significantly lower depth and for arbitrary observables.

We demonstrate the establishment of quantum-secure data transfer links at two locations in Denmark: on the campus of Technical University of Denmark (DTU) in Lyngby and between two power grid nodes owned and operated by Energinet in Odense. Four different channels were investigated, one being a purely underground fiber and the other three being combinations of underground fibers and optical ground wires (OPGWs). Coherent `quantum' states at 1550 nm, prepared and measured using a semi-autonomous continuous-variable quantum key distribution (CVQKD) prototype, were multiplexed in wavelength with `classical' 100G encrypted data traffic from a pair of commercial layer-2 network encryption devices operating at around 1300 nm. At DTU, we estimate average secret key rates in the asymptotic limit of $1.12$ Mbps (channel loss of 5.5 dB at 1550 nm) while at Energinet, the figures corresponding to the three channels (with losses of 4.1, 6.7, and 8.9 dB) are $2.05$, $0.90$, and $0.23$ Mbps, respectively. The demonstration showcases that QKD can serve as an additional layer to protect sensitive network traffic propagating on insecure channels.

We derive a generalization of the Ehrenfest theorem valid for open quantum systems. From this result, we identify three factors contributing to the evolution of expected values: explicit time dependence of the observable, thermal interaction, and quantum coherence. When considering the local Hamiltonian as the observable, we obtain an alternative version of the first law of thermodynamics. In some cases, the non-thermal contributions to the energy rate of change can be expressed as the expected value of a Hermitian operator, so the power performed by the system can be considered a quantum observable. As an application, the pure dephasing process is reinterpreted from this perspective.

Striving for higher gate fidelity is crucial not only for enhancing existing noisy intermediate-scale quantum (NISQ) devices but also for unleashing the potential of fault-tolerant quantum computation through quantum error correction. A recently proposed theoretical scheme, the double-transmon coupler (DTC), aims to achieve both suppressed residual interaction and a fast high-fidelity two-qubit gate simultaneously, particularly for highly detuned qubits. Harnessing the state-of-the-art fabrication techniques and a model-free pulse-optimization process based on reinforcement learning, we translate the theoretical DTC scheme into reality, attaining fidelities of 99.92% for a CZ gate and 99.98% for single-qubit gates. The performance of the DTC scheme demonstrates its potential as a competitive building block for superconducting quantum processors.

The field of quantum deep learning presents significant opportunities for advancing computational capabilities, yet it faces a major obstacle in the form of the ``information loss problem'' due to the inherent limitations of the necessary quantum tomography in scaling quantum deep neural networks. This paper introduces an end-to-end Quantum Vision Transformer (QViT), which incorporates an innovative quantum residual connection technique, to overcome these challenges and therefore optimize quantum computing processes in deep learning. Our thorough complexity analysis of the QViT reveals a theoretically exponential and empirically polynomial speedup, showcasing the model's efficiency and potential in quantum computing applications. We conducted extensive numerical tests on modern, large-scale transformers and datasets, establishing the QViT as a pioneering advancement in applying quantum deep neural networks in practical scenarios. Our work provides a comprehensive quantum deep learning paradigm, which not only demonstrates the versatility of current quantum linear algebra algorithms but also promises to enhance future research and development in quantum deep learning.

We consider discrete time feedback aimed at reclaiming quantum information after a channel action. We compare Bayesian and Markovian strategies. We show that the former does not offer any advantage for qubit channels, while its superior performance can appear in higher dimensional channels. This is witnessed by cases study for qutrit channels.

The Variational Quantum Eigensolver (VQE) is widely considered to be a promising candidate for a quantum-classical algorithm which could achieve near-term quantum advantage. However, current levels of hardware noise can require extensive application of error-mitigation techniques to achieve reliable computations. In this work, we use several IBM devices to explore a finite-size spin model with multiple `phase-like' regions characterized by distinct ground-state configurations. Using pre-optimized VQE solutions, we demonstrate that in contrast to calculating the energy, where zero-noise extrapolation is required in order to obtain qualitatively accurate yet still unreliable results, calculations of the energy derivative, two-site spin correlation functions, and the fidelity susceptibility yield accurate behavior across multiple regions, even with minimal or no application of error-mitigation approaches. Taken together, these sets of observables could be used to identify level crossings in VQE solutions in a simple and noise-robust manner, with potential near-term application to identifying quantum phase transitions, avoided crossings and non-adiabatic conical intersections in electronic structure calculations.

In trapped ion system, accurate thermometry of ion is crucial for evaluating the system state and precisely performing quantum operations. However, when the motional state of a single ion is far away from the ground state, the spatial dimension of the phonon state sharply increases, making it difficult to realize accurate and mode-resolved thermometry with existing methods. In this work, we apply deep learning for the first time to the thermometry of trapped ion, providing an efficient and mode-resolved method for accurately estimating large mean phonon numbers. Our trained neural network model can be directly applied to other experimental setups without retraining or post-processing, as long as the related parameters are covered by the model's effective range, and it can also be conveniently extended to other parameter ranges. We have conducted experimental verification based on our surface trap, of which the result has shown the accuracy and efficiency of the method for thermometry of single ion under large mean phonon number, and its mode resolution characteristic can make it better applied to the characterization of system parameters, such as evaluating cooling effectiveness, analyzing surface trap noise.

We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed [Fawzi et al., 2022]. Combining several algorithmic techniques previously used for related problems, we propose an algorithm outperforming this result asymptotically and give rigorous bounds on its runtime. Our main techniques are the use of Araki expansionals, known from results on the nonexistence of phase transitions, and a matrix product operator construction. We also review a related approach using the Quantum Belief Propagation [Kuwahara et al., 2018], which in combination with our findings yields an equivalent result.

In theory, quantum key distribution (QKD) provides unconditional security; however, its practical implementations are susceptible to exploitable vulnerabilities. This investigation tackles the constraints in practical QKD implementations using weak coherent pulses. We improve on the conventional approach of using decoy pulses by integrating it with the coincidence detection (CD) protocol. Additionally, we introduce an easy-to-implement algorithm to compute asymptotic key rates for the protocol. Furthermore, we have carried out an experimental implementation of the protocol, where we demonstrate that monitoring coincidences in the decoy state protocol leads to enhanced key rates under realistic experimental conditions.

In this work, we delve into the dynamic traits of the relative entropy of quantum coherence (REQC) as the quantum system interacts with the different noisy channels, drawing comparisons with entanglement (concurrence). The research results demonstrate the broader prevalence and stronger robustness of the REQC as opposed to concurrence. It's worth noting that the bit flip channel cannot uphold a constant nonzero frozen the REQC, besides, the concurrence follows a pattern of temporary reduction to zero, followed by recovery after a certain time span. More importantly, the REQC maintains its presence consistently until reaching a critical threshold, whereas concurrence experiences completely attenuation to zero under the influence of phase damping and amplitude damping channels.

Interferometric phase estimation is an essential tool for precise measurements of quantities such as displacement, velocity and material properties. The lower bound on measurement uncertainty achievable with classical resources is set by the shot-noise limit (SNL) that scales asymptotically as $1/\sqrt{N}$, where $N$ is the number of resources used. The experiment of [S. Daryanoosh et al., Nat. Commun. ${\bf 9}$, 4606 (2018)] showed how to achieve the ultimate precision limit, the exact Heisenberg limit (HL), in ab-initio phase estimation with $N=3$ photon-passes, using an entangled biphoton state in combination with particular measurement techniques. The advantage of the HL over the SNL increases with the number of resources used. Here we present, and implement experimentally, a scheme for generation of the optimal $N=7$ triphoton state. We study experimentally and theoretically the generated state quality and its potential for phase estimation. We show that the expected usefulness of the prepared triphoton state for HL phase estimation is significantly degraded by even quite small experimental imperfections, such as optical mode mismatch and unwanted higher-order multi-photon terms in the states produced in parametric down-conversion.

Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures for quantum computation: gate-based quantum computers and quantum annealing. In gate-based quantum computation, we implement a sequence of quantum gates that manipulate qubits. This approach allows us to perform universal quantum computation, yet they pose significant experimental challenges for large-scale integration. On the other hand, with quantum annealing, the solution of the optimization problem can be obtained by preparing the ground state. Conventional quantum annealing devices with transverse-field Ising Hamiltonian, such as those manufactured by D-Wave Inc., achieving around 5000 qubits, are relatively more amenable to large-scale integration but are limited to specific computations. In this paper, we present a practical method for implementing universal quantum computation within the conventional quantum annealing architecture using the transverse-field Ising Hamiltonian. Our innovative approach relies on an adiabatic transformation of the Hamiltonian, changing from transverse fields to a ferromagnetic interaction regime, where the ground states become degenerate. Notably, our proposal is compatible with D-Wave devices, opening up possibilities for realizing large-scale gate-based quantum computers. This research bridges the gap between conventional quantum annealing and gate-based quantum computation, offering a promising path toward the development of scalable quantum computing platforms.

Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently being investigated in the context of superfluid hydrodynamics, quantum sensing and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work, we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing and quantum information.

Quantum (Poincar\'e) recurrence theorem are known for closed quantum (classical) systems. Can recurrence happen in open systems? We provide the recurrence theorem for open quantum systems via non-Hermitian (NH) description. We find that PT symmetry and pseudo-Hermitian symmetry protect recurrence for NH open quantum systems and the recurrence fails with the symmetry breaking. Applying our theorem to PT-symmetric systems, we reveal why quantum recurrence happens in PT-unbroken phase but fails in PT-broken phase, which was misunderstood before. A contradiction emerges when we apply our theorem to anti-PT symmetric systems and we settle it, revealing that distinguishability and von Neumann entropy are generally not effective to describe the information dynamics in NH systems. A new approach is developed to investigate the information dynamics of NH systems. For anti-PT symmetric systems in PT-broken phase, we find there are three information-dynamics patterns: oscillations with an overall decrease (increase) , and periodic oscillations. The periodic oscillations (information complete retrieval) happen only if the spectrum of NH Hamiltonian is real. The three patterns degenerate to the periodic oscillation using distinguishability or von Neumann entropy because normalization of non-unitary evolved states leads to loss of information. We conclude with a discussion of the physical meaning behind the recurrence in open systems and give the direction of recurrence theorem not limited to conservative systems in classical mechanics.

There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive strategy proposed by Cabello [Phys. Rev. Lett. 127, 070401 (2021)], Bell inequalities can be violated by state-independent contextuality sets. However, the experimental realization of such ideas is challenging as it requires high-dimensional entanglement. Orbital angular momentum provides an unlimited state space and the number of effective dimensions can be readily tailored as required. We performed an experimental test of non-locality based on Bell inequalities from contextuality, using orbital angular momentum entanglement in a bipartite photonic system. Our experiment not only shows a new way to produce non-locality but also connects contextuality and non-locality, two fundamental quantum resources that are critical for quantum computation and secure communication tasks.

We propose a simple scheme to estimate fermionic observables and Hamiltonians relevant in quantum chemistry and correlated fermionic systems. Our approach is based on implementing a measurement that jointly measures noisy versions of any product of two or four Majorana operators in an $N$ mode fermionic system. To realize our measurement we use: (i) a randomization over a set of unitaries that realize products of Majorana fermion operators; (ii) a unitary, sampled at random from a constant-size set of suitably chosen fermionic Gaussian unitaries; (iii) a measurement of fermionic occupation numbers; (iv) suitable post-processing. Our scheme can estimate expectation values of all quadratic and quartic Majorana monomials to $\epsilon$ precision using $\mathcal{O}(N \log(N)/\epsilon^2)$ and $\mathcal{O}(N^2 \log(N)/\epsilon^2)$ measurement rounds respectively, matching the performance offered by fermionic shadow tomography. In certain settings, such as a rectangular lattice of qubits which encode an $N$ mode fermionic system via the Jordan-Wigner transformation, our scheme can be implemented in circuit depth $\mathcal{O}(N^{1/2})$ with $\mathcal{O}(N^{3/2})$ two-qubit gates, offering an improvement over fermionic and matchgate classical shadows that require depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ two-qubit gates. We also benchmark our method on molecular Hamiltonians and observe performances comparable to those offered by fermionic classical shadows.

Random and uncontrollable noises from the environment during the design and measurement of superconducting qubits lead to limitations in qubit coherence time and gate fidelity, which is a major challenge in the current state of the art for superconducting quantum computing. To advance superconducting qubits technologies it is essential to understand and mitigate environmentally induced errors. This requires modeling superconducting qubits as open quantum systems coupled to their surroundings. The present study aims to provide useful open quantum system approaches to analyze and quantify the interaction between the superconducting qubits and their environment. We provide an accessible introduction to open quantum systems for newcomers to the field. For experts we discuss recently developed methods for analyzing qubit dynamics under realistic noises. We outline how these techniques provide quantitative insights into the decoherence mechanism and how they can guide design improvements to enhance qubits' coherence time. This self-contained review of open quantum system approaches can be used to model, understand, and improve superconducting qubit performance in the presence of unavoidable environmental noises.

Macroscopic rotors are interesting model systems to test quantum theory and for quantum sensing. A promising approach for bringing these systems to the quantum regime is to combine sensitive detection with feedback cooling to reduce the thermal occupation of the mechanics. Here, we implement a backward-scattering scheme to efficiently detect all three libration modes of an optically levitated nanoparticle. We demonstrate parametric feedback cooling of all three libration degrees of freedom to below 16~mK, with one of the modes reaching the temperature of 1.3~mK, corresponding to a mean phonon number of 84. Finally, we characterize the backward-scattering scheme by determining its measurement efficiency to be 0.5\%.

We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as $O(n^{2})$ for $n$ qubits representing the solution on $2^n$ grid points, and leads to infidelities of $O(2^{-4n} t^{2})$ for simulation time $t$ assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can readily be adapted to other quantum processors and serve as an application-oriented benchmark.

Thermodynamic trade-off relations reveal the costs inherent in quantum information processing. Using the framework of trace-preserving completely positive maps, we derive a generalized quantum thermodynamic uncertainty relation applicable to arbitrary observables. Exploiting this relation, we establish multiple trade-offs that connect thermodynamic costs with the precision, evolution of observables, and quantum time correlations. We experimentally demonstrate the trade-off relations using superconducting qubits on a quantum computer to verify the theory. The empirical results not only show remarkable agreement with the theoretical predictions but also reveal that the precision of an observable and the quantum time correlator are tightly constrained by the thermodynamic cost. Our findings highlight the relevance of the thermodynamic trade-off relations in current quantum technologies.

A simplified model of an initially excited oscillator as a quantum system interacting with a large number of oscillators acting as a reservoir has been developed in this work. All these oscillators are in their ground state uncoupled each other and at the limit of the weak coupling between the system and the reservoir. This system could be an oscillator excited in a microcavity that interacts with the vacuum's electromagnetic field at zero temperature. This work's primary goal is to obtain the system's density matrix's exact solution in these conditions. The general approach calculates all oscillators' evolution as a single isolated entity using the evolution operator. Starting from a total initial state that can be factored between the system and the reservoir, the evolution is unitary, and the partial trace is taken in all the degrees of freedom of the environment to obtain the density matrix of the system at any instant of time; this procedure requires diagonalizing Hamiltonian. The results are evaluated for a reservoir of N=1000 oscillators, particular values of the coupling force, and ohmic order of the spectral density, contrasted with the corresponding Markovian solution described in section [2.3.1].

Nonlinear quantum photonics serves as a cornerstone in photonic quantum technologies, such as universal quantum computing and quantum communications. The emergence of integrated photonics platform not only offers the advantage of large-scale manufacturing but also provides a variety of engineering methods. Given the complexity of integrated photonics engineering, a comprehensive simulation framework is essential to fully harness the potential of the platform. In this context, we introduce a nonlinear quantum photonics simulation framework which can accurately model a variety of features such as adiabatic waveguide, material anisotropy, linear optics components, photon losses, and detectors. Furthermore, utilizing the framework, we have developed a device scheme, chip-scale temporal walk-off compensation, that is useful for various quantum information processing tasks. Applying the simulation framework, we show that the proposed device scheme can enhance the squeezing parameter of photon-pair sources and the conversion efficiency of quantum frequency converters without relying on higher pump power.

In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.

An important class of fermionic observables, relevant in tasks such as fermionic partial tomography and estimating energy levels of chemical Hamiltonians, are the binary measurements obtained from the product of anti-commuting Majorana operators. In this work, we investigate efficient estimation strategies of these observables based on a joint measurement which, after classical post-processing, yields all sufficiently unsharp (noisy) Majorana observables of even-degree. By exploiting the symmetry properties of the Majorana observables, as described by the braid group, we show that the incompatibility robustness, i.e., the minimal classical noise necessary for joint measurability, relates to the spectral properties of the Sachdev-Ye-Kitaev (SYK) model. In particular, we show that for an $n$ mode fermionic system, the incompatibility robustness of all degree--$2k$ Majorana observables satisfies $\Theta(n^{-k/2})$ for $k\leq 5$. Furthermore, we present a joint measurement scheme achieving the asymptotically optimal noise, implemented by a small number of fermionic Gaussian unitaries and sampling from the set of all Majorana monomials. Our joint measurement, which can be performed via a randomization over projective measurements, provides rigorous performance guarantees for estimating fermionic observables comparable with fermionic classical shadows.

This article explores the application of coding techniques for fault-tolerant quantum computation and extends their usage to fault-tolerant quantum communication. We review repeater-based quantum networks, emphasizing the roles of coding theory and fault-tolerant quantum operations, particularly in the context of quantum teleportation. We highlight that fault-tolerant implementation of the Bell measurement enables reliable quantum communication without requiring a universal set of quantum gates. Finally, we discuss various quantum code candidates for achieving higher transmission rates.

We show the fault-tolerance of the not-so-well known [[8,1,4]] non-CSS code and study the logical error rates of the code. To do so, we adopt the procedure of the bare ancilla method presented by Brown \emph{et al.} We choose the encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class of non-CSS codes. We consider two types of noise models for this study, namely the depolarizing noise and anisotropic noise to depict the logical error rates obtained in decoding.

We characterize the single-electron energies and the wavefunction structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic tight-binding calculations and analyzing wavefunction overlaps to identify the single-dopant states that hybridize to make the array states. The energy spectrum and wavefunction overlap variation as a function of dopant separation for these arrays shows that hybridization mostly occurs between single-dopant states of the same type, with some cross-hybridization between $A_1$ and $E$ states occurring at short separations. We also observe energy crossings between hybrid states of different types as a function of impurity separation. We then extract tunneling rates for electrons in different dopants by mapping the state energies into hopping Hamiltonians in the site representation. Significantly, we find that diagonal and nearest neighbor tunneling rates are similar in magnitude in a square array. Our analysis also accounts for the shift of the on-site energy at each phosphorus atom resulting from the nuclear potential of the other dopants. This approach constitutes a solid protocol to map the electron energies and wavefunction structure into Fermi-Hubbard Hamiltonians needed to implement and validate analog quantum simulations in these devices.

We develop a compact four-port superconducting switch with a tunable operating frequency in the range of 4.8 GHz -- 7.3 GHz. Isolation between channel exceeds 20~dB over a bandwidth of several hundred megahertz, exceeding 40 dB at some frequencies. The footprint of the device is $80\times420~\mu$m. The tunability requires only a global flux bias without either permanent magnets or micro-electromechanical structures. As the switch is superconducting, the heat dissipation during operation is negligible. The device can operate at up to -80~dBm, which is equal to $2.5\times 10^6$ photons at 6 GHz per microsecond. The device show a possibility to be operated as a beamsplitter with tunable splitting ratio.

We investigate the effect of magnetic field on a photonic-crystal Josephson traveling-wave parametric amplifier (TWPA). We show that the observed change in photonic bandgap and plasma frequency of the TWPA can be modeled by considering the suppression of the critical current in the Josephson junctions (JJs) of the TWPA due to the Fraunhofer effect and closing of the superconducting gap. Accounting for the JJ geometry is crucial for understanding the field dependence. In one in-plane direction, the TWPA bandgap can be shifted by 2 GHz using up to 60 mT of field, without losing gain or bandwidth, showing that TWPAs without SQUIDs can be field tunable. In the other in-plane direction, the magnetic field is perpendicular to the larger side of the Josephson junctions, so the Fraunhofer effect has a smaller period. This larger side of the JJs is modulated to create the bandgap. The field interacts more strongly with the larger junctions, and as a result, the TWPA bandgap closes and reopens as the field increases, causing the TWPA to become severely compromised already at 2 mT. A slightly higher operating limit of 5 mT is found in out-of-plane field, for which the TWPA's response is hysteretic. These measurements reveal the requirements for magnetic shielding needed to use TWPAs in experiments where high fields at the sample are required; we show that with magnetic shields we can operate the TWPA while applying over 2 T to the sample.

Monitored quantum systems evolve along stochastic trajectories correlated with the observer's knowledge of the system's state. Under such dynamics, certain quantum resources like entanglement may depend on the observer's state of knowledge. Here, we quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring using a mixed state-entanglement measure -- the configuration coherence. We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is suppressed in different ways by the measurement strength and inefficiency. In principle, strong measurements can lower the amount of entanglement indefinitely. However, at a given measurement strength, efficient readout can crucially increase the system entanglement, making high-fidelity detectors essential for successful quantum computing.

Optically accessible solid state defect spins are primary platform for quantum information processing where tight control of the electron spin and ancilla nuclear spins is pivotal for the operation. We demonstrate on the exemplary nitrogen-vacancy (NV) color center in diamond by means of a combined group theory and density functional theory study that spin-phonon relaxation rate of the nitrogen nuclear spin is with several orders of magnitude enhanced by the strong electron-phonon coupling in the optical excited state of the defect. The mechanism is common to other solid state defect spins sharing similar optical excited states with that of the NV center.

Quantum simulation using synthetic quantum systems offers unique opportunities to explore open questions in many-body physics and a path for the generation of useful entangled states. Nevertheless, so far many quantum simulators have been fundamentally limited in the models they can mimic. Here, we are able to realize an all-to-all interaction with arbitrary quadratic Hamiltonian or effectively an infinite range tunable Heisenberg XYZ model. This is accomplished by engineering cavity-mediated four-photon interactions between 700 rubidium atoms in which we harness a pair of momentum states as the effective pseudo spin or qubit degree of freedom. Using this capability we realize for the first time the so-called two-axis counter-twisting model, an iconic XYZ collective spin model that can generate spin-squeezed states that saturate the Heisenberg limit bound. The versatility of our platform to include more than two relevant momentum states, combined with the flexibility of the simulated Hamiltonians by adding cavity tones opens rich opportunities for quantum simulation and quantum sensing in matter-wave interferometers and other quantum sensors such as optical clocks and magnetometers.

High-fidelity quantum non-demolition qubit measurement is critical to error correction and rapid qubit feedback in large-scale quantum computing. High-fidelity readout requires passing a short and strong pulse through the qubit's readout resonator, which is then processed by a sufficiently high bandwidth, high saturation power, and quantum-limited amplifier. We have developed a design pipeline that combines time-domain simulation of the un-truncated device Hamiltonian, fabrication constraints, and maximization of saturation power. We have realized an amplifier based on a modified NIST tri-layer Nb fabrication suite which utilizes an array of 25 radio frequency Superconducting QUantum Interference Devices (rf SQUIDs) embedded within a low-Q resonator powered by a high-power voltage pump delivered via a diplexer on the signal port. We show that, despite the intensity of the pump, the device is quantum-efficient and capable of high-fidelity measurement limited by state transitions in the transmon. We present experimental data demonstrating up to -91.2 dBm input saturation power with 20 dB gain, up to 28 MHz instantaneous bandwidth, and phase-preserving qubit measurements with 62% quantum efficiency.

In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state. This set of various measurements on a quantum system indicates a rich internal structure. We illuminate this structure for both individual and composite systems by conceptualizing measurements as questions with a finite number of outcomes. We create a mathematical question structure to explore the underlying properties, employing the concept of information as a key tool representing our knowledge gained from asking these questions. We subsequently propose informational assumptions based on properties observed from measurements on qubits, generalizing these to higher dimensional systems. Our informational assumptions shape the correlations between subsystems, which are symbolized as classical logical gates. Interestingly, systems with prime number dimensions exhibit unique property: the logical gate can be expressed simply as a linear equation under modular arithmetic. We also identify structures in quantum theory that correspond to those in the structure of quantum questions. For instance, the questions determining the system correspond to generalized Pauli matrices, and the logical gate connecting questions in subsystems is directly related to the tensor product combining operators. Based on these correspondences, we present two equivalent scenarios regarding the evolution of systems and the change of information within both quantum questions and quantum mechanics.

The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model, which exhibits a statistical-computational gap classically. We prove that the weak recovery threshold of $1$-step QAOA matches that of $1$-step tensor power iteration. Additional heuristic calculations suggest that the weak recovery threshold of $p$-step QAOA matches that of $p$-step tensor power iteration when $p$ is a fixed constant. This further implies that multi-step QAOA with tensor unfolding could achieve, but not surpass, the classical computation threshold $\Theta(n^{(q-2)/4})$ for spiked $q$-tensors. Meanwhile, we characterize the asymptotic overlap distribution for $p$-step QAOA, finding an intriguing sine-Gaussian law verified through simulations. For some $p$ and $q$, the QAOA attains an overlap that is larger by a constant factor than the tensor power iteration overlap. Of independent interest, our proof techniques employ the Fourier transform to handle difficult combinatorial sums, a novel approach differing from prior QAOA analyses on spin-glass models without planted structure.

In recent years, various notions of dynamical phase transitions have emerged to describe far-from-equilibrium criticality. A unifying framework connecting these different concepts is still missing, and would provide significant progress towards understanding far-from-equilibrium quantum many-body universality. Initializing our system in a thermal ensemble and subsequently performing quantum quenches in the Lipkin-Meshkov-Glick model, we establish a direct connection between excited-state quantum phase transitions (ESQPTs) and two major types of dynamical phase transitions (DPTs), by relating the phases of the latter to the critical energies and conservation laws in the former. Our work provides further insight into how various concepts of non-ground-state criticality are intimately connected, paving the way for a unified framework of far-from-equilibrium universality.

Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parameterize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multi-valued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multi-valuedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be non-perturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates.

Due to photon-assisted transport processes, chiral edge modes induced by periodic driving do not directly mediate quantized transport. Here we show how narrow bandwidth "energy filters" can restore quantization by suppressing photon assisted transport through Floquet sidebands. We derive a Floquet Landauer type equation to describe transport through such an energy-filtered setup, and show how the filter can be integrated out to yield a sharply energy-dependent renormalized system-lead coupling. We show analytically and through numerical simulations that a nearly quantized conductance can be achieved in both off-resonantly and resonantly induced quasienergy gaps when filters are introduced. The conductance approaches the appropriate quantized value on each plateau with increasing system and filter size. We introduce a "Floquet distribution function" and show both analytically and numerically that it approaches the equilibrium Fermi-Dirac form when narrow-band filters are introduced, highlighting the mechanism that restores quantized transport.

Quantum Annealing (QA)-accelerated MIMO detection is an emerging research approach in the context of NextG wireless networks. The opportunity is to enable large MIMO systems and thus improve wireless performance. The approach aims to leverage QA to expedite the computation required for theoretically optimal but computationally-demanding Maximum Likelihood detection to overcome the limitations of the currently deployed linear detectors. This paper presents \textbf{X-ResQ}, a QA-based MIMO detector system featuring fine-grained quantum task parallelism that is uniquely enabled by the Reverse Annealing (RA) protocol. Unlike prior designs, X-ResQ has many desirable system properties for a parallel QA detector and has effectively improved detection performance as more qubits are assigned. In our evaluations on a state-of-the-art quantum annealer, fully parallel X-ResQ achieves near-optimal throughput (over 10 bits/s/Hz) for $4\times6$ MIMO with 16-QAM using six levels of parallelism with 240 qubits and $220~\mu$s QA compute time, achieving 2.5--5$\times$ gains compared against other tested detectors. For more comprehensive evaluations, we implement and evaluate X-ResQ in the non-quantum digital setting. This non-quantum X-ResQ demonstration showcases the potential to realize ultra-large $1024\times1024$ MIMO, significantly outperforming other MIMO detectors, including the state-of-the-art RA detector classically implemented in the same way.

Vibrational resonance (VR) is a nonlinear phenomenon in which the system response to a weak signal can be resonantly enhanced by applying a high-frequency modulation signal with an appropriate amplitude. The majority of VR research has focused on amplifying the amplitude or intensity of the system response to a weak signal, whereas the study of the phase information of system responses in VR remains limited. Here, we investigate the VR phenomena in both amplitude and phase quadratures of an optical field in a Kerr nonlinear cavity driven by a near-resonant weak signal and a far-detuned modulation signal. Analytical and numerical results demonstrated that the resonant enhancement in the amplitude and phase quadratures of the system response to a weak signal simultaneously occurs as the amplitude of the modulation signal is varied. There is a linear relation between the amplitude and frequency of the modulation signal for achieving an optimal VR effect. Furthermore, we generalized our study to investigate the quadrature at an arbitrary phase and determined that the VR enhancement sensitively depends on the phase. Our findings not only broaden the scope of VR research by incorporating phase information but also introduces an approach for amplifying an optical field by manipulating another optical field.

The exquisite precision of atom interferometers has sparked the interest of a large community for use cases ranging from fundamental physics to geodesy and inertial navigation. However, their practical use for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift in free-fall atom interferometers, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. Here we present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. An accurate model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using two fibre-optic gyroscopes and a tip-tilt platform to rotate the reference mirror and maintain the full contrast of the atom interferometer. Using these theoretical and practical tools, we reconstruct the fringes and demonstrate a single-shot sensitivity to acceleration of 24 $\mu$g, for a total interrogation time of 2T = 20 ms, for angles and rotation rates reaching 30$^\circ$ and 14 $^\circ$/s respectively. Our hybrid rotating atom interferometer unlocks the full potential of quantum inertial sensors for onboard applications, such as autonomous navigation or gravity mapping.

Directly evaluated enhanced perturbative continuous unitary transformations (deepCUTs) are used to calculate non-perturbatively extrapolated numerical data for the ground-state energy and the energy gap. The data coincides with the perturbative series up to the order with respect to which the deepCUT is truncated. We develop a general scheme to extract quantum-critical properties from the deepCUT data based on critical scaling and a strict correspondence between the truncation used for deepCUT and the length scale of correlations at the critical point. We apply our approach to transverse-field Ising models (TFIMs) as paradigmatic systems for quantum phase transitions of various universality classes depending on the lattice geometry and the choice of antiferromagnetic or ferromagnetic coupling. In particular, we focus on the quantum phase diagram of the bilayer antiferromagnetic TFIM on the triangular lattice with an Ising-type interlayer coupling. Without a field, the model is known to host a classically disordered ground state, and in the limit of decoupled layers it exhibits the 3d-XY 'order by disorder' transition of the corresponding single-layer model. Our starting point for the unknown parts of the phase diagram is a high-order perturbative calculation about the limit of isolated dimers where the model is in a gapped phase.

We fill some of existed gaps in the correspondence between Supersymmetric Quantum Mechanics and the Inverse Scattering Transform by extending the consideration to the case of paired stationary and non-stationary Hamiltonians. We formulate the corresponding to the case Goursat problem and explicitly construct the kernel of the non-local Inverse Scattering Transform, which solves it. As a result, we find the way of constructing non-hermitian Hamiltonians from the initially hermitian ones, that leads, in the case of real-valued spectra of both potentials, to pairing of ${\cal CPT/PT}$-invariant Hamiltonians. The relevance of our proposal to Quantum Optics and optical waveguides technology, as well as to non-linear dynamics and Black Hole Physics is briefly discussed.

Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions.

We discuss dynamics obtained by increasing powers of non-normal matrices that are roots of the identity, and therefore have all eigenvalues on the unit circle. Naively, one would expect that the expectation value of such powers cannot grow as one increases the power. We demonstrate that, rather counterintuitively, a completely opposite behavior is possible. In the limit of infinitely large matrices one can have an exponential growth. For finite matrices this exponential growth is a part of repeating cycles of exponential growths followed by exponential decays. The effect can occur if the spectrum is different than the pseudospectrum, with the exponential growth rate being given by the pseudospectrum. We show that this effect appears in a class of transfer matrices appearing in studies of two-dimensional non-interacting systems, for a matrix describing the Ehrenfest urn, as well as in previously observed purity dynamics in a staircase random circuit.

Measurements have historically presented a problem for the consistent description of quantum theories, be it in non-relativistic quantum mechanics or in quantum field theory. Drawing on a recent surge of interest in the description of measurements in Algebraic Quantum Field theory, it was decided that this dissertation would be focused on trying to close the gap between the description of measurements proposed by K. Hepp in the 70's, considering decoherence of states in quasilocal algebras and the new framework of generally covariant measurement schemes proposed recently by C. Fewster and R. Verch. Another recent result that we shall also consider is the Frauchinger-Renner Gedankenexperiment, that has taken inspiration on Hepp's article about decoherence based measurements to arrive at a no-go result about the consistency of quantum descriptions of systems containing rational agents, we shall seek to provide a closure for the interpretation of this result. In doing so we naturally arrive at the study of the contextual properties of measurement setups.

We investigate many-body topological and transport properties of a one-dimensional Su-Schrieffer-Heeger (SSH) topological chain coupled to the quantum field of a cavity mode. The quantum conductance is determined via Green's function formalism in terms of light-matter eigenstates calculated via exact diagonalization for a finite number of electrons. We show that the topology of the cavity-embedded many-electron system is described by a generalized electron-photon Zak marker. We reveal how the quantization of transport is modified by the cavity vacuum fields for a finite-size chain and how it is impacted by electronic disorder. Moreover, we show that electron-photon entanglement produces dramatic differences with respect to the prediction of mean-field theory, which strongly underestimates cavity-modified effects.

Quantum dots are semiconductor nano-structures where particle motion is confined in all three spatial dimensions. Since their first experimental realization, nanocrystals confining the quanta of polarization waves, termed excitons, have found numerous applications in fields ranging from single photon sources for quantum information processing to commercial displays. A major limitation to further extending the range of potential applications has been the large inhomogeneity in, and lack-of tunability of, exciton energy that is generic to quantum dot materials. Here, we address this challenge by demonstrating electrically-defined quantum dots for excitons in monolayer semiconductors where the discrete exciton energies can be tuned using applied gate voltages. Resonance fluorescence measurements show strong spectral jumps and blinking of these resonances, verifying their zero-dimensional nature. Our work paves the way for realizing quantum confined bosonic modes where nonlinear response would arise exclusively from exciton--exciton interactions.

Coupling a single spin to high-frequency mechanical motion is a fundamental bottleneck of applications such as quantum sensing, intermediate and long-distance spin-spin coupling, and classical and quantum information processing. Previous experiments have only shown single spin coupling to low-frequency mechanical resonators, such as diamond cantilevers. High-frequency mechanical resonators, having the ability to access the quantum regime, open a range of possibilities when coupled to single spins, including readout and storage of quantum states. Here we report the first experimental demonstration of spin-mechanical coupling to a high-frequency resonator. We achieve this all-electrically on a fully suspended carbon nanotube device. A new mechanism gives rise to this coupling, which stems from spin-orbit coupling, and it is not mediated by strain. We observe both resonant and off-resonant coupling as a shift and broadening of the electric dipole spin resonance (EDSR), respectively. We develop a complete theoretical model taking into account the tensor form of the coupling and non-linearity in the motion. Our results propel spin-mechanical platforms to an uncharted regime. The interaction we reveal provides the full toolbox for promising applications ranging from the demonstration of macroscopic superpositions, to the operation of fully quantum engines, to quantum simulators.

Spin parity effects refer to those special situations where a dichotomy in the physical behavior of a system arises, solely depending on whether the relevant spin quantum number is integral or half-odd integral. As is the case with the Haldane conjecture in antiferromagnetic spin chains, their pursuit often provides deep insights and invokes new developments in quantum condensed matter physics. Here we put forth a simple and general scheme for generating such effects in any spatial dimension through the use of anisotropic interactions, a setup within reasonable reach of state-of-the-art cold-atom implementations. We demonstrate its utility through a detailed analysis of the magnetization behavior of a specific one-dimensional spin chain model -- an anisotropic antiferromagnet in a transverse magnetic field, unraveling along the way the quantum origin of finite-size effects observed in the magnetization curve that had previously been noted but not clearly understood.

The nitrogen-vacancy (NV) center in diamond is a prime candidate for quantum sensing technologies. Ongoing miniaturization calls for ever-smaller sensors maintaining good measurement performance. Here, we present a fully integrated mechanically robust fiber-based endoscopic sensor capable of $5.9\,\mathrm{nT}/ \sqrt{\mathrm{Hz}}$ magnetic field sensitivity utilizing $15\,\mathrm{\mu m}$ sized microdiamonds at a microwave power of $50\,\mathrm{mW}$ and optical power of $2.15\,\mathrm{mW}$. A direct laser writing process is used to localize a diamond containing NV centers above the fiber's core by a polymer structure. This structure enables stable optical access and independent guiding of excitation and fluorescent light in different optical fibers. This separation strongly reduces the contribution of autofluorescence from the excitation light in the optical fiber. Moreover, a metallic direct laser written antenna structure is created next to the fibers' facet, allowing microwave manipulation of the NV centers' spins. The fabricated endoscopic sensor provides a robust platform with a tip diameter of $1.25\,\mathrm{mm}$. The device enables remote optical and microwave access to perform the full range of coherent spin measurements with NV centers at a spatial resolution of $15\,\mathrm{\mu m}$. We demonstrate the capability of vector magnetic field measurements in a magnetic field as used in state-of-the-art ultracold quantum gas experiments, opening a potential field in which high resolution and high sensitivity are necessary.

Information propagation in the one-dimensional infinite temperature Hubbard model with a dissipative particle sink at the end of a semi-infinite chain is studied. In the strongly interacting limit, the two-site mutual information and the operator entanglement entropy exhibit a rich structure with two propagating information fronts and superimposed interference fringes. A classical reversible cellular automaton model quantitatively captures the transport and the slow, classical part of the correlations, but fails to describe the rapidly propagating information jet. The fast quantum jet resembles coherent free particle propagation, with the accompanying long-ranged interference fringes that are exponentially damped by short-ranged spin correlations in the many-body background.