This thesis explores adaptive inference as a tool to characterize quantum systems using experimental data, with applications in sensing, calibration, control, and metrology. I propose and test algorithms for learning Hamiltonian and Kraus operators using Bayesian experimental design and advanced Monte Carlo techniques, including Sequential and Hamiltonian Monte Carlo. Application to the characterization of quantum devices from IBMQ shows a robust performance, surpassing the built-in characterization functions of Qiskit for the same number of measurements. Introductions to Bayesian statistics, experimental design, and numerical integration are provided, as well as an overview of existing literature.

We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.

Graph states are a fundamental entanglement resource for multipartite quantum applications which are in general challenging to transform efficiently. While fusion operations for merging entangled states are well-developed, no direct protocol exists for the reverse process, which we term fission. We introduce a simple, yet powerful, protocol that achieves this, allowing a qubit to split while preserving selective connections with minimum entanglement overhead. This tool offers flexible entanglement management with potential applications in secure communication, error correction and adaptive entanglement distribution.

We uncover new features of generalized contextuality by connecting it to the Kirkwood-Dirac (KD) quasiprobability distribution. Quantum states can be represented by KD distributions, which take values in the complex unit disc. Only for ``KD-positive'' states are the KD distributions joint probability distributions. A KD distribution can be measured by a series of weak and projective measurements. We design such an experiment and show that it is contextual iff the underlying state is not KD-positive. We analyze this connection with respect to mixed KD-positive states that cannot be decomposed as convex combinations of pure KD-positive states. Our result is the construction of a noncontextual experiment that enables an experimenter to verify contextuality.

Non-projective measurements are resourceful in several information-processing protocols. In this work, we propose an operational task involving space-like separated parties to detect measurements that are neither projective nor a classical post-processing of data obtained from a projective measurement. In the case of qubits, we consider a bipartite scenario and different sets of target correlations. While some correlations in each of these sets can be obtained by performing non-projective measurements on some shared two-qubit state it is impossible to simulate correlation in any of them using projective simulable measurements on bipartite qubit states or equivalently one bit of shared randomness. While considering certain sets of target correlations we show that the detection of qubit non-projective measurement is robust under arbitrary depolarising noise (except in the limiting case). For qutrits, while considering a similar task we show that some correlations obtained from local non-projective measurements are impossible to be obtained while performing the same qutrit projective simulable measurements by both parties. We provide numerical evidence of its robustness under arbitrary depolarising noise. For a more generic consideration (bipartite and tripartite scenario), we provide numerical evidence for a projective-simulable bound on the reward function for our task. We also show a violation of this bound by using qutrit POVMs. From a foundational perspective, we extend the notion of non-projective measurements to general probabilistic theories (GPTs) and use a randomness-free test to demonstrate that a class of GPTs, called square-bits or box-world are unphysical.

This paper studies the energy decoherence of an interacting quantum system. It first reviews the experiments that motivated the postulates of quantum mechanics. It then discusses a decoherence that occurs dynamically in a closed system. This effect is studied in interacting quantum systems consisting of an oscillator and spins using analytical and numerical methods. The subsequent results are contrasted with cases with no decoherence. Connections of energy decoherence with thermodynamics are explored.

Quantum Embeddings (QE) are essential for loading classical data into quantum systems for Quantum Machine Learning (QML). The performance of QML algorithms depends on the type of QE and how features are mapped to qubits. Traditionally, the optimal embedding is found through optimization, but we propose framing it as a search problem instead. In this work, we use a Genetic Algorithm (GA) to search for the best feature-to-qubit mapping. Experiments on the MNIST and Tiny ImageNet datasets show that GA outperforms random feature-to-qubit mappings, achieving 0.33-3.33 (MNIST) and 0.5-3.36 (Tiny ImageNet) higher fitness scores, with up to 15% (MNIST) and 8.8% (Tiny ImageNet) reduced runtime. The GA approach is scalable with both dataset size and qubit count. Compared to existing methods like Quantum Embedding Kernel (QEK), QAOA-based embedding, and QRAC, GA shows improvements of 1.003X, 1.03X, and 1.06X, respectively.

Quantum Error Correction (QEC) is widely regarded as the most promising path towards quantum advantage, with significant advances in QEC codes, decoding algorithms, and physical implementations. The success of QEC relies on achieving quantum gate fidelities below the error threshold of the QEC code, while accurately decoding errors through classical processing of the QEC stabilizer measurements. In this paper, we uncover the critical system-level requirements from a controller-decoder system (CDS) necessary to successfully execute the next milestone in QEC, a non-Clifford circuit. Using a representative non-Clifford circuit, of Shor factorization algorithm for the number 21, we convert the logical-level circuit to a QEC surface code circuit and finally to the physical level circuit. By taking into account all realistic implementation aspects using typical superconducting qubit processor parameters, we reveal a broad range of core requirements from any CDS aimed at performing error corrected quantum computation. Our findings indicate that the controller-decoder closed-loop latency must remain within tens of microseconds, achievable through parallelizing decoding tasks and ensuring fast communication between decoders and the controller. Additionally, by extending existing simulation techniques, we simulate the complete fault-tolerant factorization circuit at the physical level, demonstrating that near-term hardware performance, such as a physical error rate of 0.1% and 1000 qubits, are sufficient for the successful execution of the circuit. These results are general to any non-Clifford QEC circuit of the same scale, providing a comprehensive overview of the classical components necessary for the experimental realization of non-Clifford circuits with QEC.

Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple marked items, Grover's algorithm has the property of finding one of them uniformly at random. To further broaden the application range, it was generalized so that it finds marked items with probabilities according to their priority by encoding the priority into amplitudes applied by Grover's oracle operator. In this paper, to achieve a similar generalization, we examine a different encoding that incorporates the priority into phases applied by the oracle operator. We compare the previous and our oracle operators and observe that which one performs better depends on priority parameters. Since the priority parameters can be considered as the magnitude of the correlated phase error on Grover's oracle operator, the analysis of our oracle operator also reveals the robustness of the original Grover's algorithm against correlated noises. We further numerically show that the coherence between multiple marked items increases the probability of finding the most prioritized one in Grover's algorithm with our oracle operator.

The Einstein-Podolsky-Rosen (EPR) paradox was presented as an argument that quantum mechanics is an incomplete description of physical reality. However, the premises on which the argument is based are falsifiable by Bell experiments. In this paper, we examine the EPR paradox from the perspective of Schrodinger's reply to EPR. Schrodinger pointed out that the correlated states of the paradox enable the simultaneous measurement of $\hat{x}$ and $\hat{p}$, one by direct, the other by indirect measurement. Schrodinger's analysis takes on a timely importance because a recent experiment realizes these correlations for macroscopic atomic systems. Different to the original argument, Schrodinger's analysis applies to the experiment at the time when the measurement settings have been fixed. In this context, a subset of local realistic assumptions (not negated by Bell's theorem) implies that $x$ and $p$ are simultaneously precisely defined. Hence, an alternative EPR argument can be presented that quantum mechanics is incomplete, based on a set of (arguably) nonfalsifiable premises. As systems are amplified, macroscopic realism can be invoked, and the premises are referred to as weak macroscopic realism (wMR). In this paper, we propose a realization of Schrodinger's gedanken experiment where field quadrature phase amplitudes $\hat{X}$ and $\hat{P}$ replace position and momentum. Assuming wMR, we derive a criterion for the incompleteness of quantum mechanics, showing that the criterion is feasible for current experiments. Questions raised by Schrodinger are resolved. By performing simulations based on an objective-field ($Q$-based) model for quantum mechanics, we illustrate the emergence on amplification of simultaneous predetermined values for $\hat{X}$ and $\hat{P}$. The values can be regarded as weak elements of reality, along the lines of Bell's macroscopic beables.

The simulation of non-Markovian quantum dynamics plays an important role in the understanding of charge and exciton dynamics in the condensed phase environment, and yet it remains computationally expensive on classical computers. We have developed a variational quantum algorithm that is capable of simulating non-Markovian quantum dynamics. The algorithm captures the non-Markovian effect by employing the Ehrenfect trajectories in the path integral formulation and the Monte Carlo sampling of the thermal distribution. We tested the algorithm with the spin-boson model on the quantum simulator and the results match well with the exact ones. The algorithm naturally fits into the parallel computing platform of the NISQ devices and is well suited for anharmonic system-bath interactions and multi-state systems.

In this work, we developed a rigorous procedure for mapping the exact non-Markovian propagator to the generalized Lindblad form. It allows us to extract the negative decay rate that is the indicator of the non-Markovian effect. As a consequence, we can investigate the influence of the non-Markovian bath on the system's properties such as coherence and equilibrium state distribution. The understanding of the non-Markovian contribution to the dynamical process points to the possibility of leveraging non-Markovianity for quantum control.

Active learning (AL) has been widely applied in chemistry and materials science. In this work we propose a quantum active learning (QAL) method for automatic structural determination of doped nanoparticles, where quantum machine learning (QML) models for regression are used iteratively to indicate new structures to be calculated by DFT or DFTB and this new data acquisition is used to retrain the QML models. The QAL method is implemented in the Quantum Machine Learning Software/Agent for Material Design and Discovery (QMLMaterial), whose aim is using an artificial agent (defined by QML regression algorithms) that chooses the next doped configuration to be calculated that has a higher probability of finding the optimum structure. The QAL uses a quantum Gaussian process with a fidelity quantum kernel as well as the projected quantum kernel and different quantum circuits. For comparison, classical AL was used with a classical Gaussian process with different classical kernels. The presented QAL method was applied in the structural determination of doped Si$_{11}$ with 4 Al (4Al@Si$_{11}$) and the results indicate the QAL method is able to find the optimum 4Al@Si$_{11}$ structure. The aim of this work is to present the QAL method -- formulated in a noise-free quantum computing framework -- for automatic structural determination of doped nanoparticles and materials defects.

We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on the spectral and dynamical properties of the system. Using a three-parameter unitary coin, we control the spectral properties of the noiseless step operator on the unit circle in the complex plane. One parameter governs the probability amplitudes and induces two spectral bands, with a gap proportional to its value. The half-sum of the two phase parameters rotates the spectrum and induces twofold degeneracy under specific conditions. Degenerate spectra yield eigenstates with sinusoidal probability distributions, whereas non-degenerate spectra produce flat distributions. By using the eigenstate participation ratio, we predict the behavior of a walker under static phase noise in the coin and sites, showing a correlation between low participation ratios and localization, and high ratios with delocalization. Our results show that the average eigenstate participation ratio provides insights equivalent to computationally intensive mean squared displacement calculations. We observe a transition from super-diffusive to sub-diffusive behavior for uniformly distributed noise within the range $-\pi/3$ to $\pi/3$ and saturation of the mean square distance when the number of steps exceeds the graph size by an order of magnitude. Finally, we propose a quantum circuit implementation of our model.

Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the expectation value of a random-exist quantified oracle. In this problem, Nature makes a decision randomly, i.e. chooses a bitstring according to some probability distribution, and a player has a chance to react by finding a complementary bitstring such that an black-box oracle evaluates to $1$ (or True). Our task is to approximate the probability that the player has a valid reaction to Nature's initial decision. We compare the quantum algorithm to the average-case performance of Monte-Carlo integration over brute-force search, which is, under reasonable assumptions, the best performing classical algorithm. We find the performance separation depends on some problem parameters, and show a regime where the canonical quadratic speedup exists.

Spontaneous collapse models use non-linear stochastic modifications of the Schroedinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that the Born rule for transition probabilities can be modeled using the linear Schroedinger equation with a Hamiltonian represented by a random matrix from the Gaussian unitary ensemble. The matrices representing the Hamiltonian at different time points throughout the observation period are assumed to be independent. Instead of suppressing superpositions, such Schroedinger evolution makes the state perform an isotropic random walk on the projective space of states. The relative frequency of reaching different eigenstates of an arbitrary observable in the random walk is shown to satisfy the Born rule. Here, we apply this methodology to investigate the behavior of a particle in the context of the double-slit experiment with measurement. Our analysis shows that, in this basic case, the evolution of the particle's state can be effectively captured through a random walk on a two-dimensional submanifold of the state space. This random walk reproduces the Born rule for the probability of finding the particle near the slits, conditioned on its arrival at one of them. To ensure that this condition is satisfied, we introduce a drift term representing a change in the variance of the position observable for the state. A drift-free model, based on equivalence classes of states indistinguishable by the detector, is also considered. The resulting random walk, with or without drift, serves as a suitable model for describing the transition from the initial state to an eigenstate of the measured observable in the experiment, offering new insights into its potential underlying mechanisms.

Protein chromatography is an important technique in biopharmaceutical manufacturing that separates proteins by filtering them through a tightly packed column of gels. Tighter packings yield better protein separation. To this end, we model chromatography as sphere packing, formulating three models, each with increasing complexity. The first, homogeneous circle packing, is recast as maximum independent set and solved by the Quantum Approximate Optimization Algorithm on a quantum computer. The second, heterogeneous circle packing, is formulated as a graphical optimization problem and solved via classical simulations, accompanied by a road map to a quantum solution. An extension to the third, heterogeneous sphere packing, is formulated mathematically in a manner suitable to a quantum solution, and detailed resource scaling is conducted to estimate the quantum resources required to simulate this most realistic model, providing a pathway to quantum advantage.

Convolutional neural network is a crucial tool for machine learning, especially in the field of computer vision. Its unique structure and characteristics provide significant advantages in feature extraction. However, with the exponential growth of data scale, classical computing architectures face serious challenges in terms of time efficiency and memory requirements. In this paper, we propose a novel quantum convolutional neural network algorithm. It can flexibly adjust the stride to accommodate different tasks while ensuring that the required qubits do not increase proportionally with the size of the sliding window. First, a data loading method based on quantum superposition is presented, which is able to exponentially reduce space requirements. Subsequently, quantum subroutines for convolutional layers, pooling layers, and fully connected layers are designed, fully replicating the core functions of classical convolutional neural networks. Among them, the quantum arithmetic technique is introduced to recover the data position information of the corresponding receptive field through the position information of the feature, which makes the selection of step size more flexible. Moreover, parallel quantum amplitude estimation and swap test techniques are employed, enabling parallel feature extraction. Analysis shows that the method can achieve exponential acceleration of data scale in less memory compared with its classical counterpart. Finally, the proposed method is numerically simulated on the Qiskit framework using handwritten digital images in the MNIST dataset. The experimental results provide evidence for the effectiveness of the model.

We aim to use quantum machine learning to detect various anomalies in image inspection by using small size data. Assuming the possibility that the expressive power of the quantum kernel space is superior to that of the classical kernel space, we are studying a quantum machine learning model. Through trials of image inspection processes not only for factory products but also for products including agricultural products, the importance of trials on real data is recognized. In this study, training was carried out on SVMs embedded with various quantum kernels on a small number of agricultural product image data sets collected in the company. The quantum kernels prepared in this study consisted of a smaller number of rotating gates and control gates. The F1 scores for each quantum kernel showed a significant effect of using CNOT gates. After confirming the results with a quantum simulator, the usefulness of the quantum kernels was confirmed on a quantum computer. Learning with SVMs embedded with specific quantum kernels showed significantly higher values of the AUC compared to classical kernels. The reason for the lack of learning in quantum kernels is considered to be due to kernel concentration or exponential concentration similar to the Baren plateau. The reason why the F1 score does not increase as the number of features increases is suggested to be due to exponential concentration, while at the same time it is possible that only certain features have discriminative ability. Furthermore, it is suggested that controlled Toffoli gate may be a promising quantum kernel component.

Dark photon is one of the promising candidates of light dark matter and could be detected by using its interaction with standard model particles via kinetic mixings. Here, we propose a feasible approach to detect the dark photons by nondestructively probing these mixing-induced quantum state transitions of atomic ensembles. Compared with the scheme by probing the mixing-induced quantum excitation of single-atom detector, the achievable detection sensitivity can be enhanced theoretically by a factor of $\sqrt{N}$ for the ensemble containing $N$ atoms. Specifically, we show that the dark photons, in both centimeter- and millimeter-wave bands, could be detected by using the artificial atomic ensemble detector, generated by surface-state electrons on liquid Helium. It is estimated that, with the detectable transition probability of $10^{-4}$, the experimental surface-state electrons (with $N = 10^8$ trapped electrons) might provide a feasible approach to search for the dark photons in $18.61-26.88$ $\mu$eV and $496.28-827.13$ $\mu$eV ranges, within about two months. The confidence level can exceed 95\% for the achievable sensitivities being $10^{-14} \sim 10^{-13}$ and $10^{-12} \sim 10^{-11}$, respectively. In principle, the proposal could also be generalized to the other atomic ensemble detectors for the detection of dark photons in different frequency bands.

Quantum entanglement and nonlocality are foundational to quantum technologies, driving quantum computation, communication, and cryptography innovations. To benchmark the capabilities of these quantum techniques, efficient detection and accurate quantification methods are indispensable. This paper focuses on the concept of "detection length" -- a metric that quantifies the extent of measurement globality required to verify entanglement or nonlocality. We extend the detection length framework to encompass various entanglement categories and nonlocality phenomena, providing a comprehensive analytical model to determine detection lengths for specified forms of entanglement. Furthermore, we exploit semidefinite programming techniques to construct entanglement witnesses and Bell's inequalities tailored to specific minimal detection lengths, offering an upper bound for detection lengths in given states. By assessing the noise robustness of these witnesses, we demonstrate that witnesses with shorter detection lengths can exhibit superior performance under certain conditions.

The rapid development of quantum computing technology has made it possible to study the thermodynamic properties of fermionic systems at finite temperatures through quantum simulations on a quantum computer. This provides a novel approach to the study of the chiral phase transition of fermionic systems. Among these, the quantum minimally entangled typical thermal states (QMETTS) algorithm has recently attracted considerable interest. The massive Thirring model, which exhibits a variety of phenomena at low temperatures, includes both a chiral phase transition and a topologically non-trivial ground state. It therefore raises the intriguing question of whether its phase transition can be studied using a quantum simulation approach. In this study, the chiral phase transition of the massive Thirring model and its dual topological phase transition are studied using the QMETTS algorithm. The results show that QMETTS is able to accurately reproduce the phase transition and thermodynamic properties of the massive Thirring model.

Closed-form expressions for the average amplitude of the optical field in the optomechanical system are obtained, in which, in addition to the linear interaction, quadratic and cubic interactions of the vibrational mode of the mechanical resonator with the mode of the optical resonator are considered. It is shown that the effects of photon blockade, collapse and revival of optical oscillations in such system can be realized.

Achieving quantum advantage in energy storage and power extraction is a primary objective in the design of quantum-based batteries. We explore how long-range (LR) interactions in conjunction with Floquet driving can improve the performance of quantum batteries, particularly when the battery is initialized in a fully polarized state. In particular, we exhibit that by optimizing the driving frequency, the maximum average power scales super extensively with system-size which is not achievable through next-nearest neighbor interactions or traditional unitary charging, thereby gaining genuine quantum advantage. We illustrate that the inclusion of either two-body or many-body interaction terms in the LR charging Hamiltonian leads to a scaling benefit. Furthermore, we discover that a super-linear scaling in power results from increasing the strength of interaction compared to the transverse magnetic field and the range of interaction with low fall-off rate, highlighting the advantageous role of long-range interactions in optimizing quantum battery charging.

We investigate the entanglement structure of a generic $M$-particle Bethe wavefunction (not necessarily an eigenstate of an integrable model) on a 1d lattice by dividing the lattice into L parts and decomposing the wavefunction into a sum of products of $L$ local wavefunctions. We show that a Bethe wavefunction accepts a fractal multipartite decomposition: it can always be written as a linear combination of $L^M$ products of $L$ local wavefunctions, where each local wavefunction is in turn also a Bethe wavefunction. Building upon this result, we then build exact, analytical tensor network representations with finite bond dimension $\chi=2^M$, for a generic planar tree tensor network (TTN), which includes a matrix product states (MPS) and a regular binary TTN as prominent particular cases. For a regular binary tree, the network has depth $\log_{2}(N/M)$ and can be transformed into an adaptive quantum circuit of the same depth, composed of unitary gates acting on $2^M$-dimensional qudits and mid-circuit measurements, that deterministically prepares the Bethe wavefunction. Finally, we put forward a much larger class of generalized Bethe wavefunctions, for which the above decompositions, tensor network and quantum circuit representations are also possible.

High-precision, robust quantum gates are essential components in quantum computation and information processing. In this study, we present an alternative perspective, exploring the potential applicability of quantum gates that exhibit heightened sensitivity to errors. We investigate such sensitive quantum gates, which, beyond their established use in in vivo NMR spectroscopy, quantum sensing, and polarization optics, may offer significant utility in precision quantum metrology and error characterization. Utilizing the composite pulses technique, we derive three fundamental quantum gates with narrowband and passband characteristics -- the X (NOT) gate, the Hadamard gate, and gates enabling arbitrary rotations. To systematically design these composite pulse sequences, we introduce the SU(2), modified-SU(2), and regularization random search methodologies. These approaches, many of which are novel, demonstrate superior performance compared to established sequences in the literature, including NB1, SK1, and PB1.

We discuss an expansion of the detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude. The expansion enables efficient time- or frequency-resolved numerical simulations involving quantum states exhibiting a high degree of spectral entanglement. Contrary to usual approaches based on one- or two-pair approximations, we expand the expressions in terms corresponding to the amount of correlations between different pairs. The lowest expansion order corresponds to the limit of infinitely entangled states, where different pairs are completely uncorrelated and the full multi-pair statistics are inferred from a single pair. We show that even this limiting case always yields more accurate results than the single-pair approximation. Higher expansion orders describe deviations from the infinitely entangled case and introduce correlations between the photons of different pairs.

We present time- and frequency-resolved simulations of quantum key distribution~(QKD) systems employing highly entangled biphoton quantum states. Our simulations are based on expansions of the covariance matrix and photon detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude that were introduced in the first part of this series. Employing these expansions allows us to efficiently evaluate the impact of multi-pair events on the performance of the QKD systems while systematically taking into account effects from the photon spectra and many relevant imperfections of the setup. The results are shown to be in agreement with corresponding measurements of the key rates and quantum bit error rates.

We develop the theory of equilibration in quantum dynamics for the case were the dynamics-generating Hamiltonians have continuous spectrum. The main goal of this paper will be to propose a framework to extend the results obtained by Short in [11], where estimates for equilibration on average and effective equilibration are derived. We will primarily focus on the case where the quantum dynamics are generated by a semi-group whose generator, i.e. the Hamiltonian, has purely absolutely continuous spectrum, and show that for such a case it is compulsory to constrain ourselves to finite time equilibration; we then develop estimates analogous to the main results in the proposed setting

The recent advances in quantum information processing, sensing and communications are surveyed with the objective of identifying the associated knowledge gaps and formulating a roadmap for their future evolution. Since the operation of quantum systems is prone to the deleterious effects of decoherence, which manifests itself in terms of bit-flips, phase-flips or both, the pivotal subject of quantum error mitigation is reviewed both in the presence and absence of quantum coding. The state-of-the-art, knowledge gaps and future evolution of quantum machine learning are also discussed, followed by a discourse on quantum radar systems and briefly hypothesizing about the feasibility of integrated sensing and communications in the quantum domain. Finally, we conclude with a set of promising future research ideas in the field of ultimately secure quantum communications with the objective of harnessing ideas from the classical communications field.

Equilibrium probes have been widely used in various noisy quantum metrology schemes. However, such an equilibrium-probe-based metrology scenario severely suffers from the low-temperature-error divergence problem in the weak-coupling regime. To circumvent this limit, we propose a strategy to eliminate the error-divergence problem by utilizing the strong coupling effects, which can be captured by the reaction-coordinate mapping. The strong couplings induce a noncanonical equilibrium state and greatly enhance the metrology performance. It is found that our metrology precision behaves as a polynomial-type scaling relation, which suggests the reduction of temperature can be used as a resource to improve the metrology performance. Our result is sharply contrary to that of the weakcoupling case, in which the metrology precision exponentially decays as the temperature decreases. Paving a way to realize a high-precision noisy quantum metrology at low temperatures, our result reveals the importance of the non-Markovianity in quantum technologies.

Private set intersection (PSI) and private set union (PSU) are the crucial primitives in secure multiparty computation protocols, which enable several participants to jointly compute the intersection and union of their private sets without revealing any additional information. Quantum homomorphic encryption (QHE) offers significant advantages in handling privacy-preserving computations. However, given the current limitations of quantum resources, developing efficient and feasible QHE-based protocols for PSI and PSU computations remains a critical challenge. In this work, a novel quantum private set intersection and union cardinality protocol is proposed, accompanied by the corresponding quantum circuits. Based on quantum homomorphic encryption, the protocol allows the intersection and union cardinality of users' private sets to be computed on quantum-encrypted data with the assistance of a semi-honest third party. By operating on encrypted quantum states, it effectively mitigates the risk of original information leakage. Furthermore, the protocol requires only simple Pauli and CNOT operations, avoiding the use of complex quantum manipulations (e.g., $T$ gate and phase rotation gate). Compared to related protocols, this approach offers advantages in feasibility and privacy protection.

Photonic quantum computer (PQC) is an emerging and promising quantum computing paradigm that has gained momentum in recent years. In PQC, which leverages the measurement-based quantum computing (MBQC) model, computations are executed by performing measurements on photons in graph states (i.e., sets of entangled photons) that are generated before measurements. The graph state in PQC is generated deterministically by quantum emitters. The generation process is achieved by applying a sequence of quantum gates to quantum emitters. In this process, i) the time required to complete the process, ii) the number of quantum emitters used, and iii) the number of CZ gates performed between emitters greatly affect the fidelity of the generated graph state. However, prior work for determining the generation sequence only focuses on optimizing the number of quantum emitters. Moreover, identifying the optimal generation sequence has vast search space. To this end, we propose RLGS, a novel compilation framework to identify optimal generation sequences that optimize the three metrics. Experimental results show that RLGS achieves an average reduction in generation time of 31.1%, 49.6%, and 57.5% for small, medium, and large graph states compared to the baseline.

Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. To estimate an arbitrary analytic function of the parameters it suffices that a DQM scheme can measure an arbitrary linear combination of these parameters, and a number of schemes have now been devised to achieve this at the Heisenberg limit. The most practical to-date requires d coherent inputs and one squeezed vacuum. Here we provide a full understanding of the minimal input resources and linear networks required to achieve DQM of arbitrary functions. We are able to fully elucidate the structure of any linear network for DQM that has two non-vacuum inputs, and we show that two non-vacuum inputs, one non-classical, is the minimum required to achieve DQM with arbitrary weights at the Heisenberg limit. We characterize completely the properties of the nonclassical input required to obtain a quantum advantage, showing that a wide range of inputs make this possible, including a squeezed vacuum. We further elucidate two distinct regimes of the distributed sensing network. The first achieves Heisenberg scaling. In the second the nonclassical input is much weaker than the coherent input, nevertheless providing a significant quantum enhancement to the otherwise classical sensitivity.

We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent $\alpha$. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that, irrespective of the values of $\alpha$, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at non-critical points, signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both $\alpha = 0$ and $\alpha = 2$. Therefore, information of the universality class can be inferred from the stationary state.

We investigate the interaction of spontaneous emission photons generated by a strongly driven laser-cooled atom sample with that same sample after a time delay, which is important for establishing long-distance entanglement between quantum systems. The photons are emitted into an optical nanofiber, connected to a length of conventional optical fiber and reflected back using a Fiber-Bragg Grating mirror. We show that the photon count rates as a function of exciting laser frequency and intensity follow a simple model.

In quantum multi-parameter estimation, the uncertainty in estimating unknown parameters is lower-bounded by Cram\'{e}r-Rao bound (CRB), defined as an inverse of the Fisher information matrix (FIM) associated with the multiple parameters. However, in particular estimation scenarios, the FIM is non-invertible due to redundancy in the parameter set, which depends on the probe state and measurement observable. Particularly, this has led to the use of a weaker form of the CRB to bound the estimation uncertainty in distributed quantum sensing. This weak CRB is generally lower than or equal to the exact CRB, and may, therefore, overestimate the achievable estimation precision. In this work, we propose an alternative approach, employing the Moore-Penrose pseudoinverse of the FIM for constrained parameters, providing a unified CRB, attainable with an unbiased estimator. This allows us to construct simple strategies for each case in both simultaneous estimation and distributed quantum sensing, covering paradigmatic examples considered in the literature. We believe this study to provide a unified framework for addressing non-invertible FIMs and improving the precision of quantum multi-parameter estimation in various practical scenarios.

Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral sensitivity arises and leads to novel quantum engineering. Here we theoretically study the multipartite entanglement properties in non-Hermitian superconducting qubits, where high-fidelity entangled states can be created under strong driving fields or strong couplings among the qubits. Under an interplay between driving fields, couplings, and non-Hermiticity, we focus on generations of GHZ states or GHZ classes in three and four qubits with all-to-all couplings, which allows a fidelity approaching unity when relatively low non-Hermitian decay rates are considered. This presents an ultimate capability of non-Hermitian qubits to host a genuine and maximal multipartite entanglement. Our results can shed light on novel quantum engineering of multipartite entanglement generations in non-Hermitian qubit systems.

In this study, the Quantum-Train Quantum Fast Weight Programmer (QT-QFWP) framework is proposed, which facilitates the efficient and scalable programming of variational quantum circuits (VQCs) by leveraging quantum-driven parameter updates for the classical slow programmer that controls the fast programmer VQC model. This approach offers a significant advantage over conventional hybrid quantum-classical models by optimizing both quantum and classical parameter management. The framework has been benchmarked across several time-series prediction tasks, including Damped Simple Harmonic Motion (SHM), NARMA5, and Simulated Gravitational Waves (GW), demonstrating its ability to reduce parameters by roughly 70-90\% compared to Quantum Long Short-term Memory (QLSTM) and Quantum Fast Weight Programmer (QFWP) without compromising accuracy. The results show that QT-QFWP outperforms related models in both efficiency and predictive accuracy, providing a pathway toward more practical and cost-effective quantum machine learning applications. This innovation is particularly promising for near-term quantum systems, where limited qubit resources and gate fidelities pose significant constraints on model complexity. QT-QFWP enhances the feasibility of deploying VQCs in time-sensitive applications and broadens the scope of quantum computing in machine learning domains.

Optimizing the frequency configuration of qubits and quantum gates in superconducting quantum chips presents a complex NP-complete optimization challenge. This process is critical for enabling practical control while minimizing decoherence and suppressing significant crosstalk. In this paper, we propose a neural network-based frequency configuration approach. A trained neural network model estimates frequency configuration errors, and an intermediate optimization strategy identifies optimal configurations within localized regions of the chip. The effectiveness of our method is validated through randomized benchmarking and cross-entropy benchmarking. Furthermore, we design a crosstalk-aware hardware-efficient ansatz for variational quantum eigensolvers, achieving improved energy computations.

Quantum error mitigation is regarded as a possible path to near-term quantum utility. The methods under the quantum error mitigation umbrella term, such as probabilistic error cancellation, zero-noise extrapolation or Clifford data regression are able to significantly reduce the error for the estimation of expectation values, although at an exponentially scaling cost, i.e., in the sampling overhead. In this work, we present a straightforward method for reducing the sampling overhead of PEC on Clifford circuits (and Clifford subcircuits) via Pauli error propagation alongside some classical preprocessing. While the methods presented in this work are restricted to Clifford circuits, we argue that Clifford sub circuits often occur in relevant calculations as for example the resource state generation in measurement based quantum computing.

Complex Hadamard matrices (CHMs) are intimately related to the number of distinct matrix elements. We investigate CHMs containing exactly three distinct elements, which is also the least number of distinct elements. In this paper, we show that such CHMs can only be complex equivalent to two kind of matrices, one is $H_2$-reducible and the other is the Tao matrix. Using our result one can further narrow the range of MUB trio (a set of four MUBs in $\mathbb{C}^6$ consists of an MUB trio and the identity) since we find that the two CHMs neither belong to MUB trios. Our results may lead to the more complete classification of $6\times 6$ CHMs whose elements in the first row are all 1.

In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present a method to reduce this scaling constant for the electronic Hamiltonians represented as a linear combination of unitaries. Our approach combines the double tensor-factorization method of Burg et al. with the the block-invariant symmetry shift method of Loaiza and Izmaylov. By extending the electronic Hamiltonian with appropriately parametrized symmetry operators and optimizing the tensor-factorization parameters, our method achieves a 25% reduction in the block-encoding scaling constant compared to previous techniques. The resulting savings in the number of non-Clifford T-gates, which are an essential resource for fault-tolerant quantum computation, are expected to accelerate the feasiblity of practical Hamiltonian simulations. We demonstrate the effectiveness of our technique on Hamiltonians of industrial and biological relevance, including the nitrogenase cofactor (FeMoCo) and cytochrome P450.

We propose hardware-efficient schemes for implementing logical H and S gates transversally on rotated surface codes with reconfigurable neutral atom arrays. For logical H gates, we develop a simple strategy to rotate code patches efficiently with two sets of 2D-acousto-optic deflectors (2D-AODs). Our protocol for logical S gates utilizes the time-dynamics of the data and ancilla qubits during syndrome extraction (SE). In particular, we break away from traditional schemes where transversal logical gates take place between two SE rounds and instead embed our fold-transversal logical operation inside a single SE round, leveraging the fact that data and ancilla qubits can be morphed to an unrotated surface code state at half-cycle. Under circuit noise, we observe the performance of our S gate protocol is on par with the quantum memory. Together with transversal logical CNOT gates, our protocols complete a transversal logical Clifford gate set on rotated surface codes and admit efficient implementation on neutral atom array platforms.

This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two novel lattice surgery-based protocols (local and non-local) are introduced to establish logical Bell states between distant nodes using an intermediary node. In the local protocol, the intermediary node creates and directly transmits the logical Bell states to quantum memories. In contrast, the non-local protocol distributes auxiliary Bell states, merging boundaries between pre-existing codes in the quantum memories. We simulate the protocols using realistic experimental parameters, including cavity-enhanced atomic frequency comb quantum memories and multimode fiber-optic noisy channels. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances (\(d = 3, 5\)) under standard and realistic noise models. We observe pseudo-thresholds, indicating that when physical error rates exceed approximately \(p_{\text{err}} \sim 10^{-3}\), QEC codes do not provide any benefit over using unencoded Bell states. Moreover, to achieve an advantage over unencoded Bell states for a distance of \(1 \, \mathrm{km}\) between the end node and the intermediary, gate error rates must be reduced by an order of magnitude (\(0.1p_{\text{err}_H}\), \(0.1p_{\text{err}_{CX}}\), and \(0.1p_{\text{err}_M}\)), highlighting the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Finally, both protocols were analyzed for their achieved rates, with the non-local protocol showing higher rates, ranging from \(6.64 \, \mathrm{kHz}\) to \(1.91 \, \mathrm{kHz}\), over distances of \(1\) to \(9 \, \mathrm{km}\) between the end node and the intermediary node.

Machine learning offers a promising methodology to tackle complex challenges in quantum physics. In the realm of quantum batteries (QBs), model construction and performance optimization are central tasks. Here, we propose a cavity-Heisenberg spin chain quantum battery (QB) model with spin-$j (j=1/2,1,3/2)$ and investigate the charging performance under both closed and open quantum cases, considering spin-spin interactions, ambient temperature, and cavity dissipation. It is shown that the charging energy and power of QB are significantly improved with the spin size. By employing a reinforcement learning algorithm to modulate the cavity-battery coupling, we further optimize the QB performance, enabling the stored energy to approach, even exceed its upper bound in the absence of spin-spin interaction. We analyze the optimization mechanism and find an intrinsic relationship between cavity-spin entanglement and charging performance: increased entanglement enhances the charging energy in closed systems, whereas the opposite effect occurs in open systems. Our results provide a possible scheme for design and optimization of QBs.

The quantization of an optical field is a frontier in quantum optics with implications for both fundamental science and technological applications. Here, we demonstrate that a dinickel complex (Ni$_2$) traps and quantizes classical visible light, behaving as an individual quantum system or the Jaynes Cummings molecule.The composite system forms through coherently coupling the two level NiNi charge transfer transition with the local scattering field, which produces nonclassical light featuring photon anti bunching and squeezed states, as verified by a sequence of discrete photonic modes in the incoherent resonance fluorescence. Notably, in this Ni$_2$ system, the collective coupling of N molecule ensembles scales as N, distinct from the Tavis-Cummings model, which allows easy achievement of ultrastrong coupling. This is exemplified by a vacuum Rabi splitting of 1.2 eV at the resonance (3.25 eV) and a normalized coupling rate of 0.18 for the N = 4 ensemble. The resulting quantum light of single photonic modes enables driving the molecule field interaction in cavity free solution, which profoundly modifies the electronic states. Our results establish Ni$_2$ as a robust platform for quantum optical phenomena under ambient conditions, offering new pathways for molecular physics, polaritonic chemistry and quantum information processing.

The surface code family is a promising approach to implementing fault-tolerant quantum computations by providing the desired reliability via scaling the code size. For universal fault-tolerance requiring logical non-Clifford quantum operations in addition to Clifford gates, it is imperative to experimentally demonstrate the implementation of additional resources known as magic states, which is a highly non-trivial task. Another key challenge is efficient embedding of surface code in quantum hardware layout to harness its inherent error resilience and magic state preparation techniques, which becomes a difficult task for hardware platforms with connectivity constraints. This work simultaneously addresses both challenges by proposing a qubit-efficient rotated heavy-hexagonal surface code embedding in IBM quantum processors (\texttt{ibm\_fez}) and implementing the code-based magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, obtaining $\approx0.37\%$ and $\approx0.31\%$, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states $|H_L\rangle$ and $|T_L\rangle$ achieve fidelities of $0.8806\pm0.0002$ and $0.8665\pm0.0003$, respectively, which are both above the magic state distillation threshold. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as $0.8356\pm0.0003$. Our work demonstrates the potential for implementing non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.

In recent decades, significant progress has been made in construction and study of individual quantum systems consisting of the basic single matter and energy particles, i.e., atoms and photons, which show great potentials in quantum computation and communication. Here, we demonstrate that the quadruply-bonded Mo$_2$ unit of the complex can trap photons of visible light under ambient conditions, producing intense local electromagnetic (EM) field that features squeezed states, photon antibunching, and vacuum Rabi splitting. Our results show that both the electronic and vibrational states of the Mo$_2$ molecule are modified by coherent coupling with the scattered photons of the Mo$_2$ unit, as evidenced by the Rabi doublet4 and the Mollow triplet in the incoherent resonance fluorescence and the Raman spectra. The Mo$_2$ molecule, acting as an independent emitter-resonator integrated quantum system, allows optical experiments to be conducted in free space, enabling fundamental quantum phenomena to be observed through conventional spectroscopic instrumentation. This provides a new platform for study of field effects and quantum electrodynamics (QED) in the optical domain. The insights gained from this study advance our understanding in metal-metal bond chemistry, molecular physics and quantum optics, with applications in quantum information processing, optoelectronic devices and control of chemical reactivity.

Quantum metrology leverages quantum effects such as squeezing, entanglement, and other quantum correlations to boost precision in parameter estimation by saturating quantum Cramer Rao bound, which can be achieved by optimizing quantum Fisher information or Wigner-Yanase skew information. This work provides analytical expressions for quantum Fisher and skew information in a general three-qubit X-state and examines their evolution under phase damping, depolarization, and phase-flip decoherence channels. To illustrate the validity of our method, we investigate their dynamics for a three-qubit Greenberger-Horne-Zeilinger (GHZ) state subjected to various memoryless decoherence channels. Closed-form expressions for QFI and SQI are derived for each channel. By comparing these metrics with the entanglement measure of concurrence, we demonstrate the impact of decoherence on measurement precision for quantum metrology. Our results indicate that phase damping and phase-flip channels generally allow for better parameter estimation compared to depolarization. This study provides insights into the optimal selection of noise channels for enhancing precision in quantum metrological tasks involving multi-qubit entangled states.

We present a general-purpose algorithm for automatic production of a structure that induces a desired Casimir-Polder force. As a demonstration of the capability and wide applicability of the method, we use it to develop a geometry that leads to a repulsive Casimir-Polder force on a ground-state atom. The results turn out to be reminiscent of the ring-like geometries previously used to induce repulsion, but with some new features and -- importantly -- discovered completely independently of any input from the user. This represents a powerful new paradigm in the study of atom-surface forces -- instead of the user testing various geometries against a desired figure of merit, the goal can be specified and then an appropriate geometry created automatically.

In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the simulation of measurement-induced quantum phenomena. In particular, we focus on the measurement-altered quantum criticality protocol and generate local reduced density matrices of the critical chain given random measurement results. Such generation is enabled by a physics-preserving conditional diffusion generative model, which learns an observation-indexed probability distribution of an ensemble of quantum states, and then samples from that distribution given an observation.

Due to their quantum nature, single-photon emitters generate individual photons in bursts or streams. They are paramount in emerging quantum technologies such as quantum key distribution, quantum repeaters, and measurement-based quantum computing. Many such systems have been reported in the last three decades, from Rubidium atoms coupled to cavities to semiconductor quantum dots and color centers implanted in waveguides. This review article highlights different material systems with deterministic and controlled single photon generation. We discuss and compare the performance metrics, such as purity and indistinguishability, for these sources and evaluate their potential for different applications. Finally, a new potential single-photon source, based on the Rydberg exciton in solid state metal oxide thin films, is introduced, briefly discussing its promising qualities and advantages in fabricating quantum chips for quantum photonic applications.

The steady progress of quantum hardware is motivating the search for novel quantum algorithm optimization strategies for near-term, real-world applications. In this study, we propose a novel feature map optimization strategy for Quantum Support Vector Machines (QSVMs), designed to enhance binary classification while taking into account backend-specific parameters, including qubit connectivity, native gate sets, and circuit depth, which are critical factors in noisy intermediate scale quantum (NISQ) devices. The dataset we utilised belongs to the neutrino physics domain, with applications in the search for neutrinoless double beta decay. A key contribution of this work is the parallelization of the classification task to commercially available superconducting quantum hardware to speed up the genetic search processes. The study was carried out by partitioning each quantum processing unit (QPU) into several sub-units with the same topology to implement individual QSVM instances. We conducted parallelization experiments with three IBM backends with more than 100 qubits, ranking the sub-units based on their susceptibility to noise. Data-driven simulations show how, under certain restrictions, parallelized genetic optimization can occur with the tested devices when retaining the top 20% ranked sub-units in the QPU.

Impurity-bound excitons in II-VI semiconductors are promising optically active solid-state spin qubit systems. Previous work relied on incoherent optical excitation to generate photons from these impurities. However, many quantum applications require resonant driving to directly excite optical transitions and maintain coherence. Here, we demonstrate coherent optical emission from a resonantly driven single impurity-bound exciton in ZnSe. We observe resonance fluorescence and verify the emission coherence through polarization interferometry. Resonant excitation also enables the direct measurement of the Debye-Waller factor, determined to be 0.94, indicating high efficiency emission to the zero-phonon line. Time-resolved resonance fluorescence measurements reveal a fast optically driven ionization process attributed to Auger recombination, along with a slower spontaneous ionization process having a lifetime of 21 {\mu}s due to charge tunneling from the impurity. We demonstrate that a low-power incoherent pump laser efficiently stabilizes the charge of the impurity-bound exciton on the timescale of 9.3 ns. Our results pave the way for direct coherent optical and spin control through resonant excitation of impurity-bound excitons in II-VI semiconductors.

Efficient estimation of nonlinear functions of quantum states is crucial for various key tasks in quantum computing, such as entanglement spectroscopy, fidelity estimation, and feature analysis of quantum data. Conventional methods using state tomography and estimating numerous terms of the series expansion are computationally expensive, while alternative approaches based on a purified query oracle impose practical constraints. In this paper, we introduce the quantum state function (QSF) framework by extending the SWAP test via linear combination of unitaries and parameterized quantum circuits. Our framework enables the implementation of arbitrary degree-$n$ polynomial functions of quantum states with precision $\varepsilon$ using $\mathcal{O}(n/\varepsilon^2)$ copies. We further apply QSF for developing quantum algorithms of fundamental tasks, achieving a sample complexity of $\tilde{\mathcal{O}}(1/(\varepsilon^2\kappa))$ for both von Neumann entropy estimation and quantum state fidelity calculations, where $\kappa$ represents the minimal nonzero eigenvalue. Our work establishes a concise and unified paradigm for estimating and realizing nonlinear functions of quantum states, paving the way for the practical processing and analysis of quantum data.

We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin decay of matrix-valued quantum conditional mutual information (MCMI) can be quasi-optimally prepared on a quantum computer. We do this by controlling the mixing time of the corresponding Davies evolution in a normalized quantum Wasserstein distance of order one. To the best of our knowledge, this is the first time that such a non-commutative transport metric has been used in the study of quantum dynamics, and the first time quasi-rapid mixing is implied by solely an explicit clustering condition. Our result is based on a weak approximate tensorization and a weak modified logarithmic Sobolev inequality for such systems, as well as a new general weak transport cost inequality. If we furthermore assume a constraint on the local gap of the thermalizing dynamics, we obtain rapid mixing in trace distance for interactions beyond the range of two, thereby extending the state-of-the-art results that only cover the nearest neighbor case. We conclude by showing that systems that admit effective local Hamiltonians, like quantum CSS codes at high temperature, satisfy this MCMI decay and can thus be efficiently prepared and sampled from.

Quantum states at optical frequencies are often generated inside cavities to facilitate strong nonlinear interactions. However, measuring these quantum states with traditional homodyne techniques poses a challenge, as outcoupling from the cavity disturbs the state's quantum properties. Here, we propose a framework for reconstructing quantum states generated inside nonlinear optical cavities and observing their dynamics. Our approach directly imprints the field distribution of the cavity quantum state onto the statistics of bistable cavity steady-states. We propose a protocol to fully reconstruct the cavity quantum state, visualized in 2D phase-space, by measuring the changes in the steady-state statistics induced by a probe signal injected into the cavity under different condition. We experimentally demonstrate our approach in a degenerate optical parametric oscillator, generating and reconstructing the quasi-probability distribution of different quantum states. As a validation, we reconstruct the Husimi Q function of the cavity squeezed vacuum state. In addition, we observe the evolution of the quantum vacuum state inside the cavity as it undergoes phase-sensitive amplification. By enabling generation and measurement of quantum states in a single nonlinear optical cavity, our method realizes an "end-to-end" approach to intracavity quantum tomography, facilitating studies of quantum optical phenomena in nonlinear driven-dissipative systems.

The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies $n_i$ of orbitals $\varphi_i$ according to $0 \leq n_i \leq 2$. In this work, we first refine the underlying one-body $N$-representability problem by taking into account simultaneously spin symmetries and a potential degree of mixedness $\boldsymbol w$ of the $N$-electron quantum state. We then derive a comprehensive solution to this problem by using basic tools from representation theory, convex analysis and discrete geometry. Specifically, we show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers, defining a convex polytope $\Sigma_{N,S}(\boldsymbol w) \subset [0,2]^d$. These constraints are independent of $M$ and the number $d$ of orbitals, while their dependence on $N, S$ is linear, and we can thus calculate them for arbitrary system sizes and spin quantum numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.

We present a comprehensive analysis of boundary phenomena in a spin-$\frac{1}{2}$ anisotropic Heisenberg chain (XXZ-$\frac{1}{2}$) in the gapped antiferromagnetic phase, with a particular focus on the interplay between fractionalized spin-$\frac{1}{4} $ edge modes and a coupled spin-$\frac{1}{2}$ impurity at the edge. Employing a combination of Bethe Ansatz, exact diagonalization, and density matrix renormalization group (DMRG) methods, we explore the intricate phase diagram that emerges when the impurity is coupled either integrably or non-integrably to the chain. For integrable antiferromagnetic impurity couplings, we identify two distinct phases: the Kondo phase, where the impurity is screened by a multiparticle Kondo effect, and the antiferromagnetic bound mode phase, where an exponentially localized bound state screens the impurity in the ground state. When coupled ferromagnetically while maintaining integrability, the impurity behaves as a free spin-$\frac{1}{2}$, leading to either a ferromagnetic bound mode phase, where the impurity remains free in the ground state but may be screened at higher energy excitations or an unscreened (or local moment) phase where impurity remains unscreened in every eigenstate whereas for non-integrable ferromagnetic coupling, the impurity is not free. In the case of non-integrable antiferromagnetic coupling, a third phase emerges, characterized by mid-gap excitations with two degenerate states below the mass gap on top of the Kondo and antiferromagnetic bound mode phases, further enriching the phase diagram. Our findings highlight the nuanced behavior of boundary impurities in gapped antiferromagnetic systems, offering new insights into Kondo effects and impurity screening in the presence of fractionalized edge modes and bulk antiferromagnetic order.

We report on experimental investigation of potential high-performance cavity length stabilization using odd-indexed higher-order spatial modes. Schemes based on higher-order modes are particularly useful for micro-cavities that are used for enhanced fluorescence detection of a few emitters, which need to minimize photons leaking from a stabilization beam. We describe the design and construction of an assembly for a microcavity setup with tunable high passive stability. In addition, different types of active stabilization techniques based on higher-order modes, are then implemented and characterized based on their performance. We achieved a stability of about 0.5 pm RMS, while the error photons leaking from the continuous locking beam to a fluorescence detector are suppressed by more than 100-fold. We expect these results to be important for quantum technology implementations of various emitter-cavity setups, where these techniques provide a useful tool to meet the highly challenging demands.

Combinatorial problems such as combinatorial optimization and constraint satisfaction problems arise in decision-making across various fields of science and technology. In real-world applications, when multiple optimal or constraint-satisfying solutions exist, enumerating all these solutions -- rather than finding just one -- is often desirable, as it provides flexibility in decision-making. However, combinatorial problems and their enumeration versions pose significant computational challenges due to combinatorial explosion. To address these challenges, we propose enumeration algorithms for combinatorial optimization and constraint satisfaction problems using Ising machines. Ising machines are specialized devices designed to efficiently solve combinatorial problems. Typically, they sample low-cost solutions in a stochastic manner. Our enumeration algorithms repeatedly sample solutions to collect all desirable solutions. The crux of the proposed algorithms is their stopping criteria for sampling, which are derived based on probability theory. In particular, the proposed algorithms have theoretical guarantees that the failure probability of enumeration is bounded above by a user-specified value, provided that lower-cost solutions are sampled more frequently and equal-cost solutions are sampled with equal probability. Many physics-based Ising machines are expected to (approximately) satisfy these conditions. As a demonstration, we applied our algorithm using simulated annealing to maximum clique enumeration on random graphs. We found that our algorithm enumerates all maximum cliques in large dense graphs faster than a conventional branch-and-bound algorithm specially designed for maximum clique enumeration. This demonstrates the promising potential of our proposed approach.

We study collective quantum phases and quantum phase transitions occurring in frustrated sawtooth arrays of small quantum Josephson junctions. Frustration is introduced through the periodic arrangement of $0$- and $\pi$- Josephson junctions with the Josephson coupling energies $\alpha E_\mathrm{J}$ of different signs, $-1\leq \alpha \leq 1$. The complexity of the potential landscape of the system is controlled by the frustration parameter $f=(1-\alpha)/2$. The potential energy has a single global minimum in the non-frustrated regime ($f<f_\mathrm{cr}=0.75$) and a macroscopic number of equal minima in the frustrated regime ($f>f_\mathrm{cr}=0.75$). We address the coherent quantum regime and identify several collective quantum phases: disordered (insulating) and ordered (superconducting) phases in the non-frustrated regime, as well as highly entangled patterns of vortices and anti-vortices in the frustrated regime. These collective quantum phases are controlled by several physical parameters: the frustration $f$, the Josephson coupling, and the charging energies of junctions and islands. We map the control parameter phase diagram by characterizing the quantum dynamics of frustrated Josephson junction arrays by spatially and temporally resolved quantum-mechanical correlation function of the local magnetization.

We introduce an attention-based fermionic neural network (FNN) to variationally solve the problem of two-dimensional Coulomb electron gas in magnetic fields, a canonical platform for fractional quantum Hall (FQH) liquids, Wigner crystals and other unconventional electron states. Working directly with the full Hilbert space of $N$ electrons confined to a disk, our FNN consistently attains energies lower than LL-projected exact diagonalization (ED) and learns the ground state wavefunction to high accuracy. In low LL mixing regime, our FNN reveals microscopic features in the short-distance behavior of FQH wavefunction beyond the Laughlin ansatz. For moderate and strong LL mixing parameters, the FNN outperforms ED significantly. Moreover, a phase transition from FQH liquid to a crystal state is found at strong LL mixing. Our study demonstrates unprecedented power and universality of FNN based variational method for solving strong-coupling many-body problems with topological order and electron fractionalization.

We study the dynamics of the open Bose-Hubbard chain confined in the superfluid phase submitted to a sudden global quench on the dissipations and the repulsive interactions. The latter is investigated by calculating the equations of motion of relevant quadratic correlators permitting to study the equal-time connected one-body and density-density correlations functions. We then compute the quench spectral function associated to each observable to perform the quench spectroscopy of this dissipative quantum lattice model. This permits to unveil the quasiparticle dispersion relation of the Bose-Hubbard chain in the superfluid phase in the presence of loss processes. The applicability of the quench spectroscopy is also generalized to non-Hermitian quantum lattice models by considering the non-Hermitian transverse-field Ising chain in the paramagnetic phase.

Understanding and quantifying entanglement entropy is crucial to characterize the quantum behaviors that drive phenomena in a variety of systems. Rare-earth spin complexes, with their unique magnetic properties, provide fertile ground for exploring these nonlocal correlations. In this work, we study Eu$^{2+}$ ions deposited on a Au(111) substrate, modeling finite clusters of large spin-moments using a Heisenberg Hamiltonian parameterized by first-principles calculations. Our analysis reveals a one-to-one correspondence between structures in the differential conductance profiles and changes in the von Neumann entanglement entropy of bipartite subsystems, influenced by probe-ion separation and applied magnetic fields. Distinct braiding patterns in the conductance profiles are shown to correspond to stepwise changes in the entanglement entropy, providing a new avenue for investigating quantum correlations. These results establish a foundation for experimentally probing and controlling entanglement in lanthanide-based systems, with potential applications in quantum technologies.

The thermalization of quark gluon plasma created in relativistic heavy-ion collisions is a crucial theoretical question in understanding the onset of hydrodynamics, and in a broad sense, a key step to the exploration of thermalization in isolated quantum systems. Addressing this problem theoretically, in a first principle manner, requires a real-time, non-perturbative method. To this end, we carry out a fully quantum simulation on a classical hardware, of a massive Schwinger model, which well mimics QCD as it shares the important properties such as confinement and chiral symmetry breaking. We focus on the real-time evolution of the Wigner function, namely, the two-point correlation function, which approximates quark momentum distribution. In the context of the eigenstate thermalization hypothesis and the evolution of entropy, our solution reveals the emergence of quantum thermalization in quark-gluon plasma with a strong coupling constant, while thermalization fails progressively as a consequence of the gradually increased significance of quantum many-body scar states in a more weakly coupled system. More importantly, we observe the non-trivial role of the topological vacuum in thermalization, as the thermalization properties differ dramatically in the parity-even and parity-odd components of the Wigner function.

Quantum phase transitions (QPTs) are investigated in biquadratic spin-$1$ XY chain with rhombic single-ion anisotropy by using the ground state energy (GE), the bipartite entanglement entropy (BEE), and the mutual information (MI). It turns out that there are three spin nematic phases and two Tomonaga-Luttinger (TL) liquid phases with the central charge $c = 1$. The TL Liquid phases emerge roughly for biquadratic interaction strength two times stronger than the absolute value of the single-ion anisotropy. The GE and the derivatives up to the second order reveal a first-order QPT between spin nematic ferroquarupole (FQ) phases but cannot capture an evident signal of QPTs between the spin nematic phases and the TL Liquid phases as well as QPT between the two TL liquid phases. The TL liquid-to-liquid transition point features a highly degenerate state and the spin-block entanglement entropy increases logarithmically with block size. The BEE exhibits a divergent or convergent behavior identifying the TL Liquid or spin nematic FQ phases, respectively. Similarly, the MI and the spin-spin correlation are shown to decay algebraically or exponentially with increasing the lattice distance in the TL Liquid or spin nematic FQ phases, respectively. In the TL liquid phase, the exponents $\eta_I$ and $\eta_z$ of the MI and the spin-spin correlation vary with the interaction parameter of the biquadratic interaction strength and the rhombic single-ion anisotropy and satisfy the relationship of $\eta_z <\eta_I$. Such changes of characteristic behavior of the BEE, the MI and the spin-spin correlation indicate an occurrence of the Berezinskii-Kosterlitz-Thouless (BKT)-type QPT between the TL Liquid phase and the spin nematic FQ phase. The staggered spin fluctuation $\langle S^x S^y \rangle$ is shown to play a significant role for the emergence of the TL liquid phase and thus give rise to the BKT-type QPT.

xploiting quantum interference remains a significant challenge in ultracold inelastic scattering. In this work, we propose a method to enable detectable quantum interference within the two-body loss rate resulting from various inelastic scattering channels. Our approach utilizes a ``ring-coupling" configuration, achieved by combining external radio-frequency and static electric fields during ultracold atomic collisions. We conduct close-coupling calculations for $^7$Li-$^{41}$K collisions at ultracold limit to validate our proposal. The results show that the interference profile displayed in two-body loss rate is unable to be observed with unoptimized external field parameters. Particularly, our findings demonstrate that the two-body loss rate coefficient exhibits distinct constructive and destructive interference patterns near the magnetically induced $p$-wave resonance in the incoming channel near which a rf-induced scattering resonance exists. These interference patterns become increasingly pronounced with greater intensities of the external fields. This work opens a new avenue for controlling inelastic scattering processes in ultracold collisions.

The explicit expression for the photon polarization operator in the presence of a single electron is found in the $in$-$in$ formalism in the one-loop approximation out of the photon mass-shell. This polarization operator describes the dielectric permittivity of a single electron wave packet in coherent scattering processes. The plasmons and plasmon-polaritons supported by a single electron wave packet are described. The two limiting cases are considered: the wavelength of the external electromagnetic field is much smaller than the typical scale of variations of the electron wave packet and the wavelength of the external electromagnetic field is much larger than the size of the electron wave packet. In the former case, there are eight independent plasmon-polariton modes. In the latter case, the plasmons boil down to the dynamical dipole moment attached to a point electron. Thus, in the infrared limit, the electron possesses a dynamical electric dipole moment manifesting itself in coherent scattering processes.

Polar polyatomic molecules provide an ideal but largely unexplored platform to encode qubits in rotational states. Here, we trap cold (100-600 mK) formaldehyde (H$_2$CO) inside an electric box and perform a Ramsey-type experiment to observe long-lived (~100 $\mu$s) coherences between symmetry-protected molecular states with opposite rotation but identical orientation, representing a quasi-hidden molecular degree of freedom. As a result, the observed qubit is insensitive to the magnitude of an external electric field, and depends only weakly on magnetic fields. Our findings provide a basis for future quantum and precision experiments with trapped cold molecules.

This work demonstrates a systematic implementation of hybrid quantum-classical computational methods for investigating corrosion inhibition mechanisms on aluminum surfaces. We present an integrated workflow combining density functional theory (DFT) with quantum algorithms through an active space embedding scheme, specifically applied to studying 1,2,4-Triazole and 1,2,4-Triazole-3-thiol inhibitors on Al111 surfaces. Our implementation leverages the ADAPT-VQE algorithm with benchmarking against classical DFT calculations, achieving binding energies of -0.386 eV and -1.279 eV for 1,2,4-Triazole and 1,2,4-Triazole-3-thiol, respectively. The enhanced binding energy of the thiol derivative aligns with experimental observations regarding sulfur-functionalized inhibitors' improved corrosion protection. The methodology employs the orb-d3-v2 machine learning potential for rapid geometry optimizations, followed by accurate DFT calculations using CP2K with PBE functional and Grimme's D3 dispersion corrections. Our benchmarking on smaller systems reveals that StatefulAdaptVQE implementation achieves a 5-6x computational speedup while maintaining accuracy. This work establishes a workflow for quantum-accelerated materials science studying periodic systems, demonstrating the viability of hybrid quantum-classical approaches for studying surface-adsorbate interactions in corrosion inhibition applications. In which, can be transferable to other applications such as carbon capture and battery materials studies.

Precision optical filters are key components for current and future photonic technologies. Here, we demonstrate a low loss spectral filter consisting of an ultrasteep bandpass feature with a maximum gradient of (90.6$\pm$0.7) dB/GHz, centred within a notch filter with (128$\pm$6) dB of suppression. The filter consists of a fiber Bragg grating with multiple $\pi$-phase discontinuities inscribed into a single mode photosensitive fiber. The measured performance closely matches the simulated spectrum calculated from the design parameters indicating a high degree of confidence in the repeatability and manufacture of such devices. These filters show great promise for applications reliant on high-frequency resolution noise suppression, such as quantum networking, and highlight the opportunities for the versatility, efficiency, and extreme suppression offered by high-performance fiber Bragg grating devices.

We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions are in fact linked in multiple ways, and can be seen as different aspects of the same research programme. This research programme has two main physical goals and one general conceptual aim. The physical goals are to move beyond the two idealizations/approximations of asymptotic or closed boundary conditions in gravitational physics and of ideal reference frames (coded in coordinate frames or gauge fixings), thus achieving a more realistic modeling of (quantum) gravitational physical phenomena. The conceptual aim is to gain a better understanding of the influence of observers in physics and the ensuing limits of objectivity.

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework" and provides a new perspective for understanding the Hawking effect of the black hole.

In this study, we propose a novel architecture, the Quantum Pointwise Convolution, which incorporates pointwise convolution within a quantum neural network framework. Our approach leverages the strengths of pointwise convolution to efficiently integrate information across feature channels while adjusting channel outputs. By using quantum circuits, we map data to a higher-dimensional space, capturing more complex feature relationships. To address the current limitations of quantum machine learning in the Noisy Intermediate-Scale Quantum (NISQ) era, we implement several design optimizations. These include amplitude encoding for data embedding, allowing more information to be processed with fewer qubits, and a weight-sharing mechanism that accelerates quantum pointwise convolution operations, reducing the need to retrain for each input pixels. In our experiments, we applied the quantum pointwise convolution layer to classification tasks on the FashionMNIST and CIFAR10 datasets, where our model demonstrated competitive performance compared to its classical counterpart. Furthermore, these optimizations not only improve the efficiency of the quantum pointwise convolutional layer but also make it more readily deployable in various CNN-based or deep learning models, broadening its potential applications across different architectures.

Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder. Here, we investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr\'e model with quasiperiodic disorder. We uncover counter-intuitive transport behaviors: subdiffusion with a spreading exponent $\delta=1/3$ in the localized regime and diffusion with $\delta=1/2$ in the delocalized regime, in stark contrast to their Hermitian counterparts (halted vs. ballistic). We then establish a unified framework from random-variable perspective to determine the universal scaling relations in both regimes for generic disordered non-Hermitian systems. An efficient method is presented to extract the spreading exponents from Lyapunov exponents. The observed subdiffusive or diffusive transport in our model stems from Van Hove singularities at the tail of imaginary density of states, as corroborated by Lyapunov-exponent analysis.

Bright sources of quantum microwave light are an important building block for various quantum technological applications. Josephson junctions coupled to microwave cavities are a particularly versatile and simple source for microwaves with quantum characteristics, such as different types of squeezing. Due to the inherent nonlinearity of the system, a pure dc-voltage bias can lead to the emission of correlated pairs of photons into a stripline resonator. However, a drawback of this method is that it suffers from bias voltage noise, which disturbs the phase of the junction and consequently destroys the coherence of the photons, severely limiting its applications. Here we describe how adding a small ac reference signal either to the dc-bias or directly into the cavity can stabilize the system and counteract the sensitivity to noise. We first consider the injection locking of a single-mode device, before turning to the more technologically relevant locking of two-mode squeezed states, where phase locking preserves the entanglement between photons. Finally, we describe locking by directly injecting a microwave into the cavity, which breaks the symmetry of the squeezing ellipse. In all cases, locking can mitigate the effects of voltage noise, and enable the use of squeezed states in quantum technological applications.

The quantum loop model (QLM), along with the quantum dimer model (QDM), are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, these models are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg quantum simulators. However, the effect of finite temperature fluctuations on these quantum constrained models has been barely explored. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite temperature phase diagram of the QLM on the triangular lattice. We discover that the vison plaquette (VP) crystal experiences a finite temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and $\mathbb{Z}_{2}$ quantum spin liquid phases. This finite temperature phase transition acquires a unique property of {\it thermal fractionalization}, in that, both the cubic order parameter -- the plaquette loop resonance -- and its constituent -- the vison field -- exhibit independent criticality signatures. This phase transition is connected to a 3-state Potts transition between the lattice nematic phase and the high-temperature disordered phase.

Chiral symmetry is broken by typical interactions in lattice models, but the statistical interactions embodied in the anyon-Hubbard model are an exception. It is an example of a correlated hopping model in which chiral symmetry protects a degenerate zero-energy subspace. Complementary to the traditional approach of anyon braiding in real space, we adiabatically evolve the statistical parameter in the anyon-Hubbard model and we find non-trivial Berry phases and holonomies in this chiral subspace. The corresponding states possess stationary checkerboard pattern in their $N$-particle densities which are preserved under adiabatic manipulation. We give an explicit protocol for how these chirally-protected zero energy states can be prepared, observed, validated, and controlled.

We employ the quasiparticle picture of entanglement evolution to obtain an effective description for the out-of-equilibrium Entanglement Hamiltonian at the hydrodynamical scale following quantum quenches in free fermionic systems in two or more spatial dimensions. Specifically, we begin by applying dimensional reduction techniques in cases where the geometry permits, building directly on established results from one-dimensional systems. Subsequently, we generalize the analysis to encompass a wider range of geometries. We obtain analytical expressions for the entanglement Hamiltonian valid at the ballistic scale, which reproduce the known quasiparticle picture predictions for the Renyi entropies and full counting statistics. We also numerically validate the results with excellent precision by considering quantum quenches from several initial configurations.

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as $1/r^\alpha$ using exact large scale Quantum Monte-Carlo simulations. For all $1<\alpha\leq 3$ the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in a way incompatible with the Berezinskii-Kosterlitz-Thouless (BKT) scenario, which is recovered for $\alpha>3$. We characterise the new universality class by providing the critical exponents by means of data collapse analysis near the critical point for each $\alpha$ and from careful analysis of the spectrum. Large-scale simulations of the grand canonical phase diagram and of the decay of correlation functions demonstrate an overall behavior akin to higher dimensional systems with long-range order in the ground state for $\alpha \leq 2$ and intermediate between one and higher dimensions for $2<\alpha \leq 3$. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.

Gauged Gaussian fermionic projected entangled pair states (GGFPEPS) form a novel type of Ansatz state for the groundstate of lattice gauge theories. The advantage of these states is that they allow efficient calculation of observables by combining Monte-Carlo integration over gauge fields configurations with Gaussian tensor network machinery for the fermionic part. Remarkably, for GGFPEPS the probability distribution for the gauge field configurations is positive definite and real so that there is no sign problem. In this work we will demonstrate that gauged (non-Gaussian) fermionic projected pair states (GFPEPS) exactly capture the groundstate of generic lattice gauge theories. Additionally, we will present a framework for the efficient computation of observables in the case where the non-Gaussianity of the PEPS follows from the superposition of (few) Gaussian PEPS. Finally, we present a new graphical notation for Gaussian tensor and their contractions into Gaussian tensor network states.

We investigate Riemannian quantum-geometric structures in semiclassical transport features of two-dimensional multigap topological phases. In particular, we study nonlinear Hall-like bulk electric current responses and, accordingly, semiclassical equations of motion induced by the presence of a topological Euler invariant. We provide analytic understanding of these quantities by phrasing them in terms of momentum-space geodesics and geodesic deviation equations and further corroborate these insights with numerical solutions. Within this framework, we moreover uncover anomalous bulk dynamics associated with the second- and third-order nonlinear Hall conductivities induced by a patch Euler invariant. As a main finding, our results show how one can reconstruct the Euler invariant on coupling to electric fields at nonlinear order and from the gradients of the electric fields. Furthermore, we comment on the possibility of deducing the non-trivial non-Abelian Euler class invariant specifically in second-order nonlinear ballistic conductance measurements within a triple-contact setup, which was recently proposed to probe the Euler characteristics of more general Fermi surfaces. Generally, our results provide a route for deducing the topology in real materials that exhibit the Euler invariant by analyzing bulk electrical currents.