### Quantum space-time marginal problem: global causal structure from local causal information

Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators, and quantum causality between the involved events in an experiment is encoded in the corresponding pseudo-density operator. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the pseudo-density operators; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle, which can be solved effectively by using a neural network. The notion of quantum pseudo-channel is also introduced and we demonstrate that the quantum pseudo-channel marginal problem can be solved by transforming it into a pseudo-density operator marginal problem via the channel-state duality.

### The power and limitations of learning quantum dynamics incoherently

Quantum process learning is emerging as an important tool to study quantum systems. While studied extensively in coherent frameworks, where the target and model system can share quantum information, less attention has been paid to whether the dynamics of quantum systems can be learned without the system and target directly interacting. Such incoherent frameworks are practically appealing since they open up methods of transpiling quantum processes between the different physical platforms without the need for technically challenging hybrid entanglement schemes. Here we provide bounds on the sample complexity of learning unitary processes incoherently by analyzing the number of measurements that are required to emulate well-established coherent learning strategies. We prove that if arbitrary measurements are allowed, then any efficiently representable unitary can be efficiently learned within the incoherent framework; however, when restricted to shallow-depth measurements only low-entangling unitaries can be learned. We demonstrate our incoherent learning algorithm for low entangling unitaries by successfully learning a 16-qubit unitary on \texttt{ibmq\_kolkata}, and further demonstrate the scalabilty of our proposed algorithm through extensive numerical experiments.

### Variational Quantum Time Evolution without the Quantum Geometric Tensor

The real- and imaginary-time evolution of quantum states are powerful tools in physics and chemistry to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. They also find applications in wider fields such as quantum machine learning or optimization. On near-term devices, variational quantum time evolution is a promising candidate for these tasks, as the required circuit model can be tailored to trade off available device capabilities and approximation accuracy. However, even if the circuits can be reliably executed, variational quantum time evolution algorithms quickly become infeasible for relevant system sizes. They require the calculation of the Quantum Geometric Tensor and its complexity scales quadratically with the number of parameters in the circuit. In this work, we propose a solution to this scaling problem by leveraging a dual formulation that circumvents the explicit evaluation of the Quantum Geometric Tensor. We demonstrate our algorithm for the time evolution of the Heisenberg Hamiltonian and show that it accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms. As an application, we calculate thermodynamic observables with the QMETTS algorithm.

### Thermal recall: Memory-assisted Markovian thermal processes

We develop a resource-theoretic framework that allows one to bridge the gap between two approaches to quantum thermodynamics based on Markovian thermal processes (which model memoryless dynamics) and thermal operations (which model arbitrarily non-Markovian dynamics). Our approach is built on the notion of memory-assisted Markovian thermal processes, where memoryless thermodynamic processes are promoted to non-Markovianity by explicitly modelling ancillary memory systems initialised in thermal equilibrium states. Within this setting, we propose a family of protocols composed of sequences of elementary two-level thermalisations that approximate all transitions between energy-incoherent states accessible via thermal operations. We prove that, as the size of the memory increases, these approximations become arbitrarily good for all transitions in the infinite temperature limit, and for a subset of transitions in the finite temperature regime. Furthermore, we present solid numerical evidence for the convergence of our protocol to any transition at finite temperatures. We also explain how our framework can be used to quantify the role played by memory effects in thermodynamic protocols such as work extraction. Finally, our results show that elementary control over two energy levels at a given time is sufficient to generate all energy-incoherent transitions accessible via thermal operations if one allows for ancillary thermal systems.

### Entanglement Routing Based on Fidelity Curves for Quantum Photonics Channels

The quantum internet promises to extend entanglement correlations from nearby neighbors to any two nodes in a network. How to efficiently distribute entanglement over large-scale networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks composed of photonic channels characterized by a trade-off between the entanglement generation rate and fidelity. For such networks we look at the two following problems: the one of finding the best path to connect any two given nodes in the network bipartite entanglement routing, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. We consider two entanglement distribution models: one where entangled qubit are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. We propose the use of continuous fidelity curves (i.e., entanglement generation fidelity vs rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the models and networks considered, we prove that the algorithm always converges to the optimal solution, and we show through simulation that its execution time grows polynomial with the number of nodes in the network. Our implementation grows with the number of nodes with a power between $1$ and $1.4$ depending on the network. This work paves the way for the development of path-finding algorithms for networks with complex entanglement distribution protocols, in particular for other protocols that exhibit a trade-off between generation fidelity and rate, such as repeater-and-purify protocols.

### Maximum tolerable excess noise in CV-QKD and improved lower bound on two-way capacities

The two-way capacities of quantum channels determine the ultimate entanglement distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since repeaters will likely be expensive to build and maintain, a central open problem of quantum communication is to understand what performances are achievable without them. In this paper, we find a new lower bound on the energy-constrained and unconstrained two-way quantum and secret-key capacities of all phase-insensitive bosonic Gaussian channels, namely thermal attenuator, thermal amplifier, and additive Gaussian noise, which are realistic models for the noise affecting optical fibres or free-space links. Ours is the first nonzero lower bound in the parameter range where the (reverse) coherent information becomes negative, and it shows explicitly that entanglement distribution is always possible when the channel is not entanglement breaking. In addition, our construction is fully explicit, i.e. we devise and optimise a concrete entanglement distribution and distillation protocol that works by combining recurrence and hashing protocols.

### Quantum computing of analytical functions by linear optics methods

We propose a model for computing of a certain set of analytical functions based on estimating the output distribution of multiphoton outcomes in an optical scheme with an initial single-mode squeezed vacuum (SMSV) state and photonic states measuring the number of photons in one of the output modes of the beam splitter (BS) by photon number resolving (PNR) detector. The set of considered analytical functions is polynomial expressions including arbitrary derivatives of certain functions which can take on very large values even on small interval in their argument and small values of the parameter indicating the number of the subtracted photons. The large values that the analytic functions can take are offset by a very small term including the factorial of the number of subtracted photons, which guarantees an output normalized distribution of multiphoton measurement outcomes. The quantum computing algorithm makes it possible to find the values of the analytical functions for each number of extracted photons after a sufficiently large number of trials that would allow replacing the measurement repetition rate of multiphoton events by their probabilities. Changing the initial parameters (squeezing amplitude of the SMSV state and BS parameter) makes it possible to implement calculations of the functions over the entire (or, at least, significant) continuous interval of alteration in their argument. The potential of optical quantum computing based on nonclassical states of a certain parity can be expanded both by adding new optical elements such as BSs, and by using other continuous variable (CV) states of definite parity.

### Signatures of a quantum phase transition on a single-mode bosonic model

Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined through the non-analytic behavior of thermodynamic potentials in the thermodynamic limit. This limit is obtained when the number of available configurations of the system approaches infinity, which is conventionally associated to spatially-extended systems formed by an infinite number of degrees of freedom (infinite number of particles or modes). Taking previous ideas to the extreme, we argue that such a limit can be defined even in non-extended systems, providing a specific example in the simplest form of a single-mode bosonic Hamiltonian. In contrast to previous non-extended models, the simplicity of our model allows us to find approximate analytical expressions that can be confronted with precise numerical simulations in all the parameter space, particularly as close to the thermodynamic limit as we want. We are thus able to show that the system undergoes a change displaying all the characteristics of a second-order phase transition as a function of a control parameter. We derive critical exponents and scaling laws revealing the universality class of the model, which coincide with that of more elaborate non-extended models such as the quantum Rabi or Lipkin-Meshkov-Glick models. Analyzing our model, we are also able to offer insights into the features of this type of phase transitions, by showing that the thermodynamic and classical limits coincide. In other words, quantum fluctuations must be tamed in order for the system to undergo a true phase transition.

### Quantum Efficiency of Single Dibenzoterrylene Molecules in para-Dichlorobenzene at Cryogenic Temperatures

We measure the quantum efficiency (QE) of individual dibenzoterrylene (DBT) molecules embedded in para-dichlorobenzene at cryogenic temperatures. To achieve this, we apply two distinct methods based on the maximal photon emission and on the power required to saturate the zero-phonon line. We find that the outcome of the two approaches are in good agreement, reporting a large fraction of molecules with QE values above 50%, with some exceeding 70%. Furthermore, we observe no correlation between the observed lower bound on the QE and the lifetime of the molecule, suggesting that most of the molecules have a QE exceeding the established lower bound. This confirms the suitability of DBT for quantum optics experiments. In light of previous reports of low QE values at ambient conditions, our results hint at the possibility of a strong temperature dependence of the QE.

### Initial-state dependent quantum speed limit for dissipative state preparation: Framework and optimization

Dissipation has traditionally been considered a hindrance to quantum information processing, but recent studies have shown that it can be harnessed to generate desired quantum states. To be useful for practical applications, the ability to speed up the dissipative evolution is crucial. In this study, we focus on a Markovian dissipative state preparation scheme where the prepared state is one of the energy eigenstates. We derive an initial-state-dependent quantum speed limit (QSL) that offers a more refined measure of the actual evolution time compared to the commonly used initial-state-independent relaxation time. This allows for a passive optimization of dissipative evolution across different initial states. By minimizing the dissipated heat during the preparation process, conditioned on the minimization of evolution time using the QSL, we find that the preferred initial state has a specific permutation of diagonal elements with respect to an ordered energy eigenbasis of increasing eigenvalues. In this configuration, the population on the prepared state is the largest, and the remaining diagonal elements are sorted in an order resembling that of a passive state in the same ordered energy eigenbasis. We demonstrate the effectiveness of our strategy in a dissipative Rydberg atom system for preparing the Bell state. Our work provides new insights into the optimization of dissipative state preparation processes and could have significant implications for practical quantum technologies.

### Optimal Synthesis of Multi-Controlled Qudit Gates

We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum algorithms implemented on qudits. In particular, we obtain (i) a linear-size and one-clean-ancilla synthesis of multi-controlled qudit gates; (ii) an optimal-size and one-clean-ancilla synthesis of unitaries on qudits; (iii) a near-optimal-size and ancilla-free/one-borrowed-ancilla implementation of classical reversible functions as qudit gates.

### Exponential quantum speedup in simulating coupled classical oscillators

We present a quantum algorithm for simulating the classical dynamics of $2^n$ coupled oscillators (e.g., $2^n$ masses coupled by springs). Our approach leverages a mapping between the Schr\"odinger equation and Newton's equations for harmonic potentials such that the amplitudes of the evolved quantum state encode the momenta and displacements of the classical oscillators. When individual masses and spring constants can be efficiently queried, and when the initial state can be efficiently prepared, the complexity of our quantum algorithm is polynomial in $n$, almost linear in the evolution time, and sublinear in the sparsity. As an example application, we apply our quantum algorithm to efficiently estimate the kinetic energy of an oscillator at any time, for a specification of the problem that we prove is BQP-complete. Thus, our approach solves a potentially practical application with an exponential speedup over classical computers. Finally, we show that under similar conditions our approach can efficiently simulate more general classical harmonic systems with $2^n$ modes.

### A hierarchy of thermal processes collapses under catalysis

It is not possible to decompose generic thermal operations into combinations and concatenations of simpler thermal processes that only manipulate selected system energy levels. This creates a hindrance in providing realistically-implementable protocols to reach all thermodynamic state transitions. However, in this work we show that the recycling of thermal baths allows the decomposition of thermal operations into a series of elementary thermal operations, each involving only two system levels at a time. Such a scheme is equivalent to a catalytic version of elementary thermal operations, where the catalysts are prepared in Gibbs states and re-thermalized at a later time. Thus, the Gibbs state catalyst closes the gap between elementary thermal operations and thermal operations. Furthermore, when any catalyst can be employed, we prove that a hierarchy of different thermal processes converge to that of thermal operations.

### High-fidelity interconversion between Greenberger-Horne-Zeilinger and $W$ states through Floquet-Lindblad engineering in Rydberg atom arrays

Greenberger-Horne-Zeilinger and $W$ states feature genuine tripartite entanglement that cannot be converted into each other by local operations and classical communication. Here, we present a dissipative protocol for deterministic interconversion between the Greenberger-Horne-Zeilinger and the $W$ states of three neutral $^{87}$Rb atoms arranged in an equilateral triangle of a two-dimensional array. With three atomic levels and diagonal van der Waals interactions of Rydberg atoms, the interconversion between tripartite entangled states can be efficiently accomplished in the Floquet-Lindblad framework through the periodic optical pump and dissipation engineering. We evaluate the feasibility of the existing methodology using the experimental parameters accessible to current neutral-atom platforms. We find that our scheme is robust against typical noises, such as laser phase noise and geometric imperfection of the atom array. In addition, our scheme can integrate the Gaussian soft quantum control technique, which further reduces the overall conversion time and increases the resilience to timing errors and interatomic distance fluctuations. The high-fidelity and robust tripartite entanglement interconversion protocol provides a route to save physical resources and enhance the computational efficiency of quantum networks formed by neutral-atom arrays.

### Mid-infrared spectrally-pure single-photon states generation from 22 nonlinear optical crystals

We theoretically investigate the preparation of pure-state single-photon source from 14 birefringent crystals (CMTC, THI, LiIO$_3$, AAS, HGS, CGA, TAS, AGS, AGSe, GaSe, LIS, LISe, LGS, and LGSe) and 8 periodic poling crystals (LT, LN, KTP, KN, BaTiO$_3$, MgBaF$_4$, PMN-0.38PT, and OP-ZnSe) in a wavelength range from 1224 nm to 11650 nm. The three kinds of group-velocity-matching (GVM) conditions, the phase matching conditions, the spectral purity, and the Hong-Ou-Mandel interference are calculated for each crystal. This study may provide high-quality single-photon sources for quantum sensing, quantum imaging, and quantum communication applications at the mid-infrared wavelength range.

### Optimizing QAOA on Bipotent Architectures

Vigorous optimization of quantum gates has led to bipotent quantum architectures, where the optimized gates are available for some qubits but not for others. However, such gate-level improvements limit the application of user-side pulse-level optimizations, which have proven effective for quantum circuits with a high level of regularity, such as the ansatz circuit of the Quantum Approximate Optimization Algorithm (QAOA). In this paper, we investigate the trade-off between hardware-level and algorithm-level improvements on bipotent quantum architectures. Our results for various QAOA instances on two quantum computers offered by IBM indicate that the benefits of pulse-level optimizations currently outweigh the improvements due to vigorously optimized monolithic gates. Furthermore, our data indicate that the fidelity of circuit primitives is not always the best indicator for the overall algorithm performance; also their gate type and schedule duration should be taken into account. This effect is particularly pronounced for QAOA on dense portfolio optimization problems, since their transpilation requires many SWAP gates, for which efficient pulse-level optimization exists. Our findings provide practical guidance on optimal qubit selection on bipotent quantum architectures and suggest the need for improvements of those architectures, ultimately making pulse-level optimization available for all gate types.

### Non-Local Multi-Qubit Quantum Gates via a Driven Cavity

We present two protocols for implementing deterministic non-local multi-qubit quantum gates on qubits coupled to a common cavity mode. The protocols rely only on a classical drive of the cavity modes, while no external drive of the qubits is required. In the first protocol, the state of the cavity follows a closed trajectory in phase space and accumulates a geometric phase depending on the state of the qubits. The second protocol uses an adiabatic evolution of the combined qubit-cavity system to accumulate a dynamical phase. Repeated applications of this protocol allow for the realization of phase gates with arbitrary phases, e.g. phase-rotation gates and multi-controlled-Z gates. For both protocols, we provide analytic solutions for the error rates, which scale as $\sim N/\sqrt{C}$, with $C$ the cooperativity and $N$ the qubit number. Our protocols are applicable to a variety of systems and can be generalized by replacing the cavity by a different bosonic mode, such as a phononic mode. We provide estimates of gate fidelities and durations for atomic and molecular qubits coupled to an optical and a microwave cavity, respectively, and describe some applications for error correction.

### Partially Fault-tolerant Quantum Computing Architecture with Error-corrected Clifford Gates and Space-time Efficient Analog Rotations

Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually becoming available, but it is still challenging to achieve useful quantum advantages in meaningful tasks at this moment. On the other hand, the full fault-tolerant quantum computing (FTQC) based on the quantum error correction (QEC) code remains far beyond realization due to its extremely large requirement of high-precision physical qubits. In this study, we propose a quantum computing architecture to close the gap between NISQ and FTQC. Our architecture is based on erroneous arbitrary rotation gates and error-corrected Clifford gates implemented by lattice surgery. We omit the typical distillation protocol to achieve direct analog rotations and small qubit requirements, and minimize the remnant errors of the rotations by a carefully-designed state injection protocol. Our estimation based on numerical simulations shows that, for early-FTQC devices that consist of $10^4$ physical qubits with physical error probability $p = 10^{-4}$, we can perform roughly $1.72 \times 10^7$ Clifford operations and $3.75 \times 10^4$ arbitrary rotations on 64 logical qubits. Such computations cannot be realized by the existing NISQ and FTQC architectures on the same device, as well as classical computers. We hope that our proposal and the corresponding development of quantum algorithms based on it bring new insights on realization of practical quantum computers in future.

### Photonic entanglement during a zero-g flight

Quantum technologies have matured to the point that we can test fundamental quantum phenomena under extreme conditions. Specifically, entanglement, a cornerstone of modern quantum information theory, can be robustly produced and verified in various adverse environments. We take these tests further and implement a high-quality Bell experiment during a parabolic flight, transitioning from microgravity to hypergravity of 1.8 g while continuously observing Bell violation, with Bell-CHSH parameters between $S=-2.6202$ and $-2.7323$, an average of $\overline{S} = -2.680$, and average standard deviation of $\overline{\Delta S} = 0.014$. This violation is unaffected both by uniform and non-uniform acceleration. This experiment both demonstrates the stability of current quantum communication platforms for space-based applications and adds an important reference point for testing the interplay of non-inertial motion and quantum information.

### Global quantum discord and von Neumann entropy in multipartite two-level atomic systems

We have computed the global quantum discord and von Neumann entropy of multipartite two-level atomic systems interacting with a single-mode Fock field. We use Tavis-Cumming model. We have explored how quantum correlations and quantum entanglement evolve with time in such systems. The quantum system is prepared initially in a mixed state and different parameters are varied to see how they affect the information processing in the system. The dynamical character of the global quantum discord and von Neumann entropy show an interplay between classical and non-classical correlations. Photons in this model play an important role to assist the global quantum discord and von Neumann entropy and we observed that the effects of the field on the global quantum discord and von Neumann entropy reside in the time evolution of the system indicating that both atom and field states have become entangled. The global quantum discord is assisted in a non-linear fashion with the number of photons in the system. The global quantum discord and von Neumann entropy show linear behavior with each other in the dynamics of the system. The effects of intrinsic decoherence on the dynamics of the global quantum discord and von Neumann entropy are also studied. We have extrapolated the results for a large photon number on the system. We have studied the effect of the change in the size of the system on the maximum value of global quantum discord and von Neumann entropy and we have estimated the scaling coefficients for this behavior.

### Free-electron interactions with photonic GKP states: universal control and quantum error correction

We show that the coherent interaction between free electrons and photons can be used for universal control of continuous-variable photonic quantum states in the form of Gottesman-Kitaev-Preskill (GKP) qubits. Specifically, we find that electron energy combs enable non-destructive measurements of the photonic state and can induce arbitrary gates. Moreover, a single electron interacting with multiple photonic modes can create highly entangled states such as Greenberger-Horne-Zeilinger states and cluster states of GKPs.

### Particle track reconstruction with noisy intermediate-scale quantum computers

The reconstruction of trajectories of charged particles is a key computational challenge for current and future collider experiments. Considering the rapid progress in quantum computing, it is crucial to explore its potential for this and other problems in high-energy physics. The problem can be formulated as a quadratic unconstrained binary optimization (QUBO) and solved using the variational quantum eigensolver (VQE) algorithm. In this work the effects of dividing the QUBO into smaller sub-QUBOs that fit on the hardware available currently or in the near term are assessed. Then, the performance of the VQE on small sub-QUBOs is studied in an ideal simulation, using a noise model mimicking a quantum device and on IBM quantum computers. This work serves as a proof of principle that the VQE could be used for particle tracking and investigates modifications of the VQE to make it more suitable for combinatorial optimization.

### Universal and ultrafast quantum computation based on free-electron-polariton blockade

Cavity quantum electrodynamics (QED), wherein a quantum emitter is coupled to electromagnetic cavity modes, is a powerful platform for implementing quantum sensors, memories, and networks. However, due to the fundamental tradeoff between gate fidelity and execution time, as well as limited scalability, the use of cavity-QED for quantum computation was overtaken by other architectures. Here, we introduce a new element into cavity-QED - a free charged particle, acting as a flying qubit. Using free electrons as a specific example, we demonstrate that our approach enables ultrafast, deterministic and universal discrete-variable quantum computation in a cavity-QED-based architecture, with potentially improved scalability. Our proposal hinges on a novel excitation blockade mechanism in a resonant interaction between a free-electron and a cavity polariton. This nonlinear interaction is faster by several orders of magnitude with respect to current photon-based cavity-QED gates, enjoys wide tunability and can demonstrate fidelities close to unity. Furthermore, our scheme is ubiquitous to any cavity nonlinearity, either due to light-matter coupling as in the Jaynes-Cummings model or due to photon-photon interactions as in a Kerr-type many-body system. In addition to promising advancements in cavity-QED quantum computation, our approach paves the way towards ultrafast and deterministic generation of highly-entangled photonic graph states and is applicable to other quantum technologies involving cavity-QED.

### Unravelling the dynamics of entanglement in a non-Markovian bath

We analyse the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The qubits undergo an effective open-system dynamics in the presence of a non-Markovian reservoir, constituted by the chain's vibrations. The model is amenable to an analytical solution when the chain is initially in a thermal state. We study the dynamics of the qubits concurrence starting from a separable state and assuming that the chain spectrum is gapped. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak coupling regime, where the qubits are entangled at the asymptotics; (ii) the strong coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude; and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitation. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study identifies the resources of an environment for realising quantum coherent dynamics of open systems.

### How to determine the local unitary equivalence of sets of generalized Bell states in $\mathbb{C}^{p^α}\otimes \mathbb{C}^{p^α}$

Classification is a common method to study quantum entanglement,and local unitary equivalence (LU-equivalence) is an effective classification tool.The purpose of this work is show how to determine the LU-equivalence of sets of generalized Bell states (GBSs) in a bipartite quantum system $\mathbb{C}^{p^\alpha}\otimes \mathbb{C}^{p^\alpha}$ ($p$ is a prime number and $\alpha$ is a positive integer). The idea is that, for a given GBS set $\mathcal{M}$,try to find all the GBS sets that are LU-equivalent to $\mathcal{M}$, then we can determine whether another GBS set is LU-equivalent to $\mathcal{M}$ by comparison. In order to accomplish this intention,we first reduce the LU-equivalence of two GBS sets to the unitary conjugate equivalence (UC-equivalence) of the corresponding generalized Pauli matrix (GPM) sets.Then we show the necessary and sufficient conditions for a 2-GPM set UC-equivalent to a special 2-GPM set $\{ X^{p^\gamma}, Z^{p^\beta} \}$ ($0\leq \beta, \gamma <\alpha$). The general case, that is, the UC-equivalence of two general GPM sets,follows by the particular case.Moreover, these results are programmable, that is, we provide programs that can give all GPM sets UC-equivalent and unitary equivalent (U-equivalent) to a given GPM set,and then the LU-equivalence of two arbitrary GBS sets can be determined.To illustrate the role of the programs, we show a complete LU-equivalent classification of 4-GBS sets in the system $\mathbb{C}^{4}\otimes \mathbb{C}^{4}$.

### Experimental implementation of the optical fractional Fourier transform in the time-frequency domain

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing and computing. In this letter, we present the experimental realization of the fractional Fourier transform in the time-frequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing and super-resolved parameter estimation.

### Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions

We elucidate the role of dissipation on the emergence of time crystals in a periodically driven spin system with infinite-range interactions. By mapping out the phase diagrams for varying dissipation strengths, ranging from zero to infinitely strong, we demonstrate that the area in the phase diagram, where a time crystal exists, grows with the dissipation strength, but only up to an optimal point, beyond which most of the time crystals become unstable. We find signatures of time crystalline phases in both closed-system and dissipative regimes under the right conditions. However, the dissipative time crystals are shown to be more robust against random noise in the drive, and are only weakly affected by the choice of initial state. We present the finite-size behaviour and the scaling of the lifetime of the time crystals with respect to the number of spins and the interactions strength, within a fully quantum mechanical description.

### Interplay between charge and spin noise in the near-surface theory of decoherence and relaxation of $C_{3v}$ symmetry qutrit spin-1 centers

Decoherence and relaxation of solid-state defect qutrits near a crystal surface, where they are commonly used as quantum sensors, originates from charge and magnetic field noise. A complete theory requires a formalism for decoherence and relaxation that includes all Hamiltonian terms allowed by the defect's point-group symmetry. This formalism, presented here for the $C_{3v}$ symmetry of a spin-1 defect in a diamond, silicon cardide, or similar host, relies on a Lindblad dynamical equation and clarifies the relative contributions of charge and spin noise to relaxation and decoherence, along with their dependence on the defect spin's depth and resonant frequencies. The calculations agree with the experimental measurements of Sangtawesin $\textit{et al.}$, Phys. Rev. X $\textbf{9}$, 031052 (2019) and point to an unexpected importance of charge noise.

### A Quantum Theory with Non-collapsing Measurements

A collapse-free version of quantum theory is introduced to study the role of the projection postulate. We assume "passive" measurements that do not update quantum states while measurement outcomes still occur probabilistically, in accordance with Born's rule. All other defining features of quantum theory, such as the Hilbert space setting, are retained. The resulting quantum-like theory has only one type of dynamics, namely unitary evolution. Passive quantum theory shares many features with standard quantum theory. These include preparational uncertainty relations, the impossibility to dynamically clone unknown quantum states and the absence of signalling. However, striking differences emerge when protocols involve post-measurement states. For example, in the collapse-free setting, no ensemble is needed to reconstruct the state of a system by passively measuring a tomographically complete set of observables - a single system will do. Effectively, the state becomes an observable quantity, with implications for both the ontology of the theory and its computational power. At the same time, the theory is not locally tomographic and passive measurements do not create Bell-type correlations in composite systems.

### All this for one qubit? Bounds on local circuit cutting schemes

Small numbers of qubits are one of the primary constraints on the near-term deployment of advantageous quantum computing. To mitigate this constraint, techniques have been developed to break up a large quantum computation into smaller computations. While this work is sometimes called circuit knitting or divide and quantum we generically refer to it as circuit cutting (CC). Much of the existing work has focused on the development of more efficient circuit cutting schemes, leaving open questions on the limits of what theoretically optimal schemes can achieve. We develop bounds by breaking up possible approaches into two distinct regimes: the first, where the input state and measurement are fixed and known, and the second, which requires a given cutting to work for a complete basis of input states and measurements. For the first case, it is easy to see that bounds addressing the efficiency of any approaches to circuit cutting amount to resolving BPP$\stackrel{?}{=}$BQP. We therefore restrict ourselves to a simpler question, asking what \textit{locally-acting} circuit cutting schemes can achieve, a technical restriction which still includes all existing circuit cutting schemes. In our first case we show that the existence of a locally-acting circuit cutting scheme which could efficiently partition even a single qubit from the rest of a circuit would imply BPP$=$BQP. In our second case, we obtain more general results, showing inefficiency unconditionally. We also show that any (local or otherwise) circuit cutting scheme cannot function by only applying unital channels.

### Generalization with quantum geometry for learning unitaries

Generalization is the ability of quantum machine learning models to make accurate predictions on new data by learning from training data. Here, we introduce the data quantum Fisher information metric (DQFIM) to determine when a model can generalize. For variational learning of unitaries, the DQFIM quantifies the amount of circuit parameters and training data needed to successfully train and generalize. We apply the DQFIM to explain when a constant number of training states and polynomial number of parameters are sufficient for generalization. Further, we can improve generalization by removing symmetries from training data. Finally, we show that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work opens up new approaches to improve generalization in quantum machine learning.

### Quantum rotation sensor with real-time readout based on an atom-cavity system

Using an atom-cavity platform, we propose to combine the effective gauge phase of rotated neutral atoms and the superradiant phase transition to build a highly sensitive and fast quantum rotation sensor. The atoms in a well-controlled array of Bose-Einstein condensates are coupled to a single light mode of an optical cavity. The photon emission from the cavity indicates changes in the rotation frequency in real time, which is crucial for inertial navigation. We derive an analytical expression for the phase boundaries and use a semi-classical method to map out the phase diagram numerically, which provides the dependence of the photon emission on the rotation. We further suggest to operate the sensor with a bias rotation, and to enlarge the enclosed area, to enhance the sensitivity of the sensor.

### Calculating the many-body density of states on a digital quantum computer

Quantum statistical mechanics allows us to extract thermodynamic information from a microscopic description of a many-body system. A key step is the calculation of the density of states, from which the partition function and all finite-temperature equilibrium thermodynamic quantities can be calculated. In this work, we devise and implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer which is inspired by the kernel polynomial method. Classically, the kernel polynomial method allows to sample spectral functions via a Chebyshev polynomial expansion. Our algorithm computes moments of the expansion on quantum hardware using a combination of random state preparation for stochastic trace evaluation and a controlled unitary operator. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18 qubits. This not only represents a state-of-the-art calculation of thermal properties of a many-body system on quantum hardware, but also exploits the controlled unitary evolution of a many-qubit register on an unprecedented scale.

### On the stability of solutions to Schrödinger's equation short of the adiabatic limit

We prove an adiabatic theorem that applies at timescales short of the adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger's equation under perturbation. We directly characterize cross-subspace effects of perturbation, which are typically significantly less than suggested by the perturbation's operator norm. This stability has numerous consequences: we can (1) find timescales where the solution of Schrodinger's equation converges to the ground state of a block, (2) lower bound the convergence to the global ground state by demonstrating convergence to some other known quantum state, (3) guarantee faster convergence than the standard adiabatic theorem when the ground state of the perturbed Hamiltonian ($H$) is close to that of the unperturbed $H$, and (4) bound tunneling effects in terms of the global spectral gap when $H$ is stoquastic'' (a $Z$-matrix). Our results apply to quantum annealing protocols with faster convergence than usually guaranteed by a standard adiabatic theorem. Our upper and lower bounds demonstrate that at timescales short of the adiabatic limit, subspace dynamics can dominate over global dynamics. Thus, we see that convergence to particular target states can be understood as the result of otherwise local dynamics.

### Detecting Bell correlations in multipartite non-Gaussian spin states

We expand the toolbox for studying Bell correlations in multipartite systems by introducing permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we present around twenty families of PIBIs with up to three- or four-body correlators, that are valid for arbitrary number of particles. Compared to known inequalities, these show higher noise robustenss, or the capability to detect Bell correlations in highly non-Gaussian spin states. We then focus on finding PIBIs that are of practical experimental implementation, in the sense that the associated operators require collective spin measurements along only a few directions. To this end, we formulate this search problem as a semidefinite program that embeds the constraints required to look for PIBIs of the desired form.

### Classification and emergence of quantum spin liquids in chiral Rydberg models

We investigate the nature of quantum phases arising in chiral interacting Hamiltonians recently realized in Rydberg atom arrays. We classify all possible fermionic chiral spin liquids with $\mathrm{U}(1)$ global symmetry using parton construction on the honeycomb lattice. The resulting classification includes six distinct classes of gapped quantum spin liquids: the corresponding variational wave functions obtained from two of these classes accurately describe the Rydberg many-body ground state at $1/2$ and $1/4$ particle density. Complementing this analysis with tensor network simulations, we conclude that both particle filling sectors host a spin liquid with the same topological order of a $\nu=1/2$ fractional quantum Hall effect. At density $1/2$, our results clarify the phase diagram of the model, while at density $1/4$, they provide an explicit construction of the ground state wave function with almost unit overlap with the microscopic one. These findings pave the way to the use of parton wave functions to guide the discovery of quantum spin liquids in chiral Rydberg models.

### Observation of non-Hermitian edge burst in quantum dynamics

The non-Hermitian skin effect, by which the eigenstates of Hamiltonian are predominantly localized at the boundary, has revealed a strong sensitivity of non-Hermitian systems to the boundary condition. Here we experimentally observe a striking boundary-induced dynamical phenomenon known as the non-Hermitian edge burst, which is characterized by a sharp boundary accumulation of loss in non-Hermitian time evolutions. In contrast to the eigenstate localization, the edge burst represents a generic non-Hermitian dynamical phenomenon that occurs in real time. Our experiment, based on photonic quantum walks, not only confirms the prediction of the phenomenon, but also unveils its complete space-time dynamics. Our observation of edge burst paves the way for studying the rich real-time dynamics in non-Hermitian topological systems.

### Anti-symmetric Barron functions and their approximation with sums of determinants

A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite neural networks with one hidden layer. By explicitly encoding the anti-symmetric structure, we prove that the anti-symmetric functions which belong to the Barron space can be efficiently approximated with sums of determinants. This yields a factorial improvement in complexity compared to the standard representation in the Barron space and provides a theoretical explanation for the effectiveness of determinant-based architectures in ab-initio quantum chemistry.

### Lightwave-controlled band engineering in quantum materials

Stacking and twisting atom-thin sheets create superlattice structures with unique emergent properties, while tailored light fields can manipulate coherent electron transport on ultrafast timescales. The unification of these two approaches may lead to ultrafast creation and manipulation of band structure properties, which is a crucial objective for the advancement of quantum technology. Here, we address this by demonstrating a tailored lightwave-driven analogue to twisted layer stacking. This results in sub-femtosecond control of time-reversal symmetry breaking and thereby band structure engineering in a hexagonal boron nitride monolayer. The results practically demonstrate the realization of the topological Haldane model in an insulator. Twisting the lightwave relative to the lattice orientation enables switching between band configurations, providing unprecedented control over the magnitude and location of the band gap, and curvature. A resultant asymmetric population at complementary quantum valleys lead to a measurable valley Hall current, detected via optical harmonic polarimetry. The universality and robustness of the demonstrated sub-femtosecond control opens a new way to band structure engineering on the fly paving a way towards large-scale ultrafast quantum devices for real-world applications.

### Quantum Dot Source-Drain Transport Response at Microwave Frequencies

Quantum dots are frequently used as charge sensitive devices in low temperature experiments to probe electric charge in mesoscopic conductors where the current running through the quantum dot is modulated by the nearby charge environment. Recent experiments have been operating these detectors using reflectometry measurements up to GHz frequencies rather than probing the low frequency current through the dot. In this work, we use an on-chip coplanar waveguide resonator to measure the source-drain transport response of two quantum dots at a frequency of 6 GHz, further increasing the bandwidth limit for charge detection. Similar to the low frequency domain, the response is here predominantly dissipative. For large tunnel coupling, the response is still governed by the low frequency conductance, in line with Landauer-B\"uttiker theory. For smaller couplings, our devices showcase two regimes where the high frequency response deviates from the low frequency limit and Landauer-B\"uttiker theory: When the photon energy exceeds the quantum dot resonance linewidth, degeneracy dependent plateaus emerge. These are reproduced by sequential tunneling calculations. In the other case with large asymmetry in the tunnel couplings, the high frequency response is two orders of magnitude larger than the low frequency conductance G, favoring the high frequency readout.

### Meson Instability of Quantum Many-body Scars in a 1D Lattice Gauge Theory

We investigate the stability of meson excitations (particle-antiparticle bound states) in quantum many-body scars of a 1D $\mathbb{Z}_2$ lattice gauge theory coupled to spinless fermions. By introducing a string representation of the physical Hilbert space, we express a scar state $|{\Psi_{n,l}}\rangle$ as a superposition of all string bases with an identical string number $n$ and a total length $l$. The string correlation function of lattice fermions hosts an exponential decay as the distance increases for the small-$l$ scar state $|{\Psi_{n,l}}\rangle$, indicating the existence of stable mesons. However, for large $l$, the correlation function exhibits a power-law decay, signaling the emergence of a meson instability. Furthermore, we show that this mesonic-nonmesonic crossover can be detected by the quench dynamics, starting from two low-entangled initial states, respectively, which are experimentally feasible in quantum simulators. Our results expand the physics of quantum many-body scars in lattice gauge theories, and reveal that the nonmesonic state can also manifest ergodicity breaking.

### Relativistic quantum communication between harmonic oscillator detectors

We propose a model of communication employing two harmonic oscillator detectors interacting through a scalar field in a background Minkowski spacetime. In this way, the scalar field plays the role of a quantum channel, namely a Bosonic Gaussian channel. The classical and quantum capacities of the communication channel are found, assuming that the detectors' spatial dimensions are negligible compared to their distance. In particular, we study the evolution in time of the classical capacity after the detectors-field interaction is switched on for various detectors' frequencies and coupling strengths with the field. As a result, we find a finite value of these parameters optimizing the communication of classical messages. Instead, a reliable communication of quantum messages turns out to be always inhibited.

### Typical Macroscopic Long-Time Behavior for Random Hamiltonians

We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each of which has large dimension. We extend previous work on the question what the evolution of $\psi_t$ looks like macroscopically, specifically on how much of $\psi_t$ lies in each $\mathcal{H}_\nu$. Previous bounds concerned the \emph{absolute} error for typical $\psi_0$ and/or $t$ and are valid for arbitrary Hamiltonians $H$; now, we provide bounds on the \emph{relative} error, which means much tighter bounds, with probability close to 1 by modeling $H$ as a random matrix, more precisely as a random band matrix (i.e., where only entries near the main diagonal are significantly nonzero) in a basis aligned with the macro spaces. We exploit particularly that the eigenvectors of $H$ are delocalized in this basis. Our main mathematical results confirm the two phenomena of generalized normal typicality (a type of long-time behavior) and dynamical typicality (a type of similarity within the ensemble of $\psi_0$ from an initial macro space). They are based on an extension we prove of a no-gaps delocalization result for random matrices by Rudelson and Vershynin.

### Vortices in dipolar Bose-Einstein condensates

Quantized vortices are the hallmark of superfluidity, and are often sought out as the first observable feature in new superfluid systems. Following the recent experimental observation of vortices in Bose-Einstein condensates comprised of atoms with inherent long-range dipole-dipole interactions [Nat. Phys. 18, 1453-1458 (2022)], we thoroughly investigate vortex properties in the three-dimensional dominantly dipolar regime, where beyond-mean-field effects are crucial for stability, and investigate the interplay between trap geometry and magnetic field tilt angle.

### Tailoring potentials by simulation-aided design of gate layouts for spin qubit applications

Gate-layouts of spin qubit devices are commonly adapted from previous successful devices. As qubit numbers and the device complexity increase, modelling new device layouts and optimizing for yield and performance becomes necessary. Simulation tools from advanced semiconductor industry need to be adapted for smaller structure sizes and electron numbers. Here, we present a general approach for electrostatically modelling new spin qubit device layouts, considering gate voltages, heterostructures, reservoirs and an applied source-drain bias. Exemplified by a specific potential, we study the influence of each parameter. We verify our model by indirectly probing the potential landscape of two design implementations through transport measurements. We use the simulations to identify critical design areas and optimize for robustness with regard to influence and resolution limits of the fabrication process.

### SLD Fisher information for kinetic uncertainty relations

We investigate a symmetric logarithmic derivative (SLD) Fisher information for kinetic uncertainty relations (KURs) of open quantum systems described by the GKSL quantum master equation with and without the detailed balance condition. In a quantum kinetic uncertainty relation derived by Vu-Saito [Phys. Rev. Lett. 128, 140602 (2022)], the Fisher information of probability of quantum trajectory with a time-rescaling parameter plays an essential role. This Fisher information is upper bounded by the SLD Fisher information. For a finite time and arbitrary initial state, we give concise coupled first-order ordinary differential equations to calculate the SLD Fisher information given by a double integral concerning time. We also derive a simple lower bound of the Fisher information of quantum trajectory. The SLD Fisher information also appears in the speed limit based on the Mandelstam-Tamm relation [Hasegawa, arXiv:2203.12421v4]. When the jump operators connect eigenstates of the system Hamiltonian, we show that the Bures angle is upper bounded by the square root of the dynamical activity at short times, which contrasts with the classical counterpart.

### Majorana-Magnon Interactions in Topological Shiba Chains

A chain of magnetic impurities deposited on the surface of a superconductor can form a topological Shiba band that supports Majorana zero modes and hold a promise for topological quantum computing. Yet, most experiments scrutinizing these zero modes rely on transport measurements, which only capture local properties. Here we propose to leverage the intrinsic dynamics of the magnetic impurities to access their non-local character. We use linear response theory to determine the dynamics of the uniform magnonic mode in the presence of external $ac$ magnetic fields and the coupling to the Shiba electrons. We demonstrate that this mode, which spreads over the entire chain of atoms, becomes imprinted with the parity of the ground state and, moreover, can discriminate between Majorana and trivial zero modes located at the end of the chain. Our approach offers a non-invasive alternative to the scanning tunnelling microscopy techniques used to probe Majorana zero modes. Conversely, the magnons could facilitate the manipulation of Majorana zero modes in topological Shiba chains.