Papers

Quantum machine learning (QML) is expected to offer new opportunities to process high-dimensional data efficiently by exploiting the exponentially large state space of quantum systems. In this work, we apply quantum extreme reservoir computing (QERC) to the classification of microstructure images of polymer alloys generated using self-consistent field theory (SCFT). While previous QML efforts have primarily focused on benchmark datasets such as MNIST, our work demonstrates the applicability of QERC to engineering data with direct materials relevance. Through numerical experiments, we examine the influence of key computational parameters-including the number of qubits, sampling cost (the number of measurement shots), and reservoir configuration-on classification performance. The resulting phase classifications are depicted as phase diagrams that illustrate the phase transitions in polymer morphology, establishing an understandable connection between quantum model outputs and material behavior. These results illustrate QERC performance on realistic materials datasets and suggest practical guidelines for quantum encoder design and model generalization. This work establishes a foundation for integrating quantum learning techniques into materials informatics.

Where does what happens happen in a quantum system? The standard textbook formulation of quantum mechanics provides a strange, imprecise and yet successful-in-practice answer to this question. In the struggle to unify our understanding of gravity with quantum theory, though, the textbook answer no longer suffices, and an alternative approach is needed. The Feynman Sum Over Histories approach provides an alternative that is particularly suited to quantum gravity because the Sum Over Histories and General Relativity are built on the same fundamental concepts of `event' and `history'.

Frequency-tunable superconducting transmon qubits are a cornerstone of scalable quantum processors, yet their performance is often degraded by sensitivity to low-frequency flux noise. Here we present a doubly-connected gradiometric transmon (the “8-mon") that incorporates a nano-airbridge to link its two loops. This design preserves full electrical tunability and remains fully compatible with standard X-mon control and readout, requiring no additional measurement overhead. The airbridge interconnect eliminates dielectric loss, which enables the 8-mon to achieve both energy relaxation times $T_{\rm 1}$ comparable to reference X-mons and, in the small flux-bias regime, a nearly threefold enhancement in Ramsey coherence time $T_{\rm 2}^*$. This improved $T_{\rm 2}^*$ reaches the same order as $T_{\rm 1}$ without employing echo decoupling. The device also exhibits superior long-term frequency stability even without any magnetic field shielding. We develop a spatially correlated flux-noise model whose simulations quantitatively reproduce the experimental coherence trends, revealing the coexistence of short- and long-correlation-length magnetic noise in the superconducting chip environment. By unifying high tunability with intrinsic flux-noise suppression through a robust geometric design, the 8-mon provides a practical pathway toward more coherent and stable superconducting quantum processors.

The study of quantum and classical correlations between subsystems is fundamental to understanding many-body physics. In quantum information theory, the quantum mutual information, $I(A;B)$, is a measure of correlation between the subsystems $A,B$ in a quantum state, and is defined by the means of the von Neumann entropy: $I\left(A;B\right)=S\left(\rho_{A}\right)+S\left(\rho_{B}\right)-S\left(\rho_{AB}\right)$. However, such a computation requires an exponential amount of resources. This is a defining feature of quantum systems, the infamous “curse of dimensionality” . Other measures, which are based on Rényi divergences instead of von Neumann entropy, were suggested as alternatives in a recent paper showing them to possess important theoretical features, and making them leading candidates as mutual information measures. In this work, we concentrate on the maximal Rényi divergence. This measure can be shown to be the solution of a generalized eigenvalue problem. To calculate it efficiently for a 1D state represented as a matrix product state, we develop a generalized eigenvalue version of the density matrix renormalization group algorithm. We benchmark our method for the paradigmatic XXZ chain, and show that the maximal Rényi divergence may exhibit different trends than the von Neumann mutual information.

The development of accurate tools to characterize Intramolecular Vibrational Redistribution (IVR) is of major interest in chemistry. In this context, surface-enhanced vibrational spectroscopies stand up as well-established techniques to study molecular vibrational lines and populations with a sensitivity that can reach the single-molecule level. However, to date, this possibility has not been fully developed to address IVR. Here, we establish a quantum mechanical framework based on molecular optomechanics that accounts for IVR, and we adopt it to analyze strategies to optimize IVR characterization by surface-enhanced vibrational spectroscopy. In particular, we model two different pump-and-probe configurations where the vibrational pumping is provided either by infrared laser illumination or by Stokes scattering processes in surface-enhanced Raman spectroscopy (SERS). We show for the two pumping configurations the existence of clear signatures on the anti-Stokes SERS spectra of population transfer between coupled vibrational modes in a molecule. Our calculations adopt realistic molecular and SERS parameters, suggesting that these signatures of IVR could be accessible at the single-molecule level within realistic experimental platforms.

We have developed an analytical framework for magnetically induced transparency-absorption (MITA) and normal-anomalous dispersion (MINAD) in a weakly driven ${}^{87}\text{Rb}$ vapor, or any J-type three-level system, under a vector magnetic field. By solving the Bloch equations in the stationary, quasi-stationary, and short-pulse regimes, we obtained closed-form expressions for the atomic populations and coherences and identified a bifurcation in the oscillatory dynamics at zero longitudinal Zeeman splitting. The Fourier-domain analysis reveals alternating transparency/absorption and normal/anomalous dispersion with frequency-dependent sign reversals, enabling spectrally selective filtering and group-delay effects. Slow oscillatory behavior in the radio-frequency range makes the system suitable for weak magnetic-field sensing, while fast oscillations at optical frequencies suggest applications in spectral filtering and frequency-comb-like signal shaping. The results provide a theoretical basis for experimental observation of MITA/MINAD and for optimizing atomic-vapor platforms for precision magnetometry and related photonic functionalities.

We consider the generation of photonic graph states in a linear optics setting where sequential non-deterministic fusion measurements are used to build large graph states out of small linear clusters and develop a framework to optimize the building process using graph theoretic characterizations of fusion networks. We present graph state generation protocols for linear cluster resource states and Type-I/Type-II fusions which are adaptive to fusion failure, that is, they reuse leftover graph states in the remaining building process. To estimate hardware costs, we interpret our protocols as finite Markov processes. This viewpoint allows to cast the expected number of fusion measurements until success as a first passage problem. We then deploy a pipeline of polynomial algorithms to optimize arbitrary graph states, extract fusion networks and find beneficial orderings of fusions with the goal of lowering the corresponding mean first passage times. We evaluate our pipeline for different initial resource states and fusion mechanisms with varying success probabilities. Results show reductions in the fusion overhead by several orders of magnitude when compared to simple repeat until success protocols and by up to 40% when compared to state-of-the-art graph state generation protocols, especially for realistic fusion success probabilities between 50-75%.

We optimize theoretically and experimentally the performances of the recently demonstrated modulation transfer protocol [D.-A. Trinh, K. V. Adwaith, M. Branco, A. Rouxel, S. Welinski, P. Berger, F. Goldfarb, and F. Bretenaker, Applied Physics Letters 125, 154001 (2024)] aiming at extending the bandwidth of quantum RF receivers based on hot Rydberg atoms. This optimization relies on tuning the parameters of the phase modulation of the coupling beam, which is converted by the nonlinear response of the atoms into an amplitude modulation of the probe beam. We develop a theoretical model to optimize both the modulation frequency and the modulation amplitude of the coupling beam, thereby maximizing the atomic response. Once optimized, the sensitivity to detuned RF fields of this modulation transfer protocol is measured and compared with that of the conventional protocol. This comparison shows that the new protocol permits a strong increase in the detection bandwidth. Indeed, it outperforms the usual one as soon as the RF signal to be measured is detuned by more than a few MHz. We illustrate the capability of this modulation transfer protocol to enhance the detection bandwidth by showing experimentally how it permits to bridge the gap between two Rydberg transitions separated by 166 MHz. In all cases, the experimental results are in good agreement with the simulations.

We extend quantum circuit cutting to heterogeneous registers comprising mixed-dimensional qudits. By decomposing non-local interactions into tensor products of local generalised Gell-Mann matrices, we enable the simulation and execution of high-dimensional circuits on disconnected hardware fragments. We validate this framework on qubit–qutrit ($2$–$3$) interfaces, achieving exact state reconstruction with a Total Variation Distance of 0 within single-precision floating-point tolerance. Furthermore, we demonstrate the memory advantage in an 8-particle, dimension-8 system, reducing memory usage from 128 MB to 64 KB per circuit.

Compilers transform code into action. They convert high-level programs into executable hardware instructions - a crucial step in enabling reliable and scalable quantum computation. However, quantum compilation is still in its infancy, and many existing solutions are ad hoc, often developed independently and from scratch. The resulting lack of interoperability leads to significant missed potential, as quantum software tools remain isolated and cannot be seamlessly integrated into cohesive toolchains. The Multi-Level Intermediate Representation (MLIR) has addressed analogous challenges in the classical domain. It was developed within the LLVM project, which has long powered robust software stacks and enabled compilation across diverse software and hardware components, with particular importance in high-performance computing environments. However, MLIR's steep learning curve poses a significant barrier to entry, particularly in quantum computing, where much of the software stack is still predominantly built by experimentalists out of necessity rather than by experienced software engineers. This paper provides a practical and hands-on guide for quantum software engineers to overcome this steep learning curve. Through a concrete case study linking Xanadu's PennyLane framework with the Munich Quantum Toolkit (MQT), we outline actionable integration steps, highlight best practices, and share hard-earned insights from real-world development. This work aims to support quantum tool developers in navigating MLIR's complexities and to foster its adoption as a unifying bridge across a rapidly growing ecosystem of quantum software tools, ultimately guiding the development of more modular, interoperable, and integrated quantum software stacks.

The foundational work by Bell led to an interest in understanding non-local correlations that arise from entangled states shared between distinct, spacelike-separated parties, which formed a foundation for the theory of quantum information processing. We investigate the question of maximal correlations analogous to the maximally entangled states defined in the entanglement theory of multipartite systems. In this work, we define the maximality of nonlocal correlation as being analogous to the absolutely maximally entangled state. To formalize this, we employ the sheaf-theoretic framework for contextuality, which generalizes non-locality. This provides a metric for correlations called contextual fraction (CF), which ranges from $0$ (non-contextual) to $1$ (maximally contextual). Using this, we have defined the absolutely maximal contextual correlations (AMCC), which are maximally contextual and have maximal marginals. The Popescu-Rohrlich (PR) box serves as the bipartite example, and we construct various extensions of such correlations in the tripartite case. An infinite family of various forms of AMCC is constructed using the parity check and the constraint satisfiability problem (CSP) construction. We also demonstrate the existence of maximally contextual correlations, which do not exhibit maximal marginals, and refer to them as non-AMCC. Furthermore, we showed that GHZ correlations in the $(n,2,2)$ setting give rise to AMCCs for the particular choice of measurement settings. The results are further applied to secret sharing and randomness extraction using AMCCs.

Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate fidelities and renders full Hilbert-space control optimization prohibitively difficult. Here, we overcome this challenge by reducing the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost. Our method effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates. Within this framework, we construct analytical pulse solutions for parallel single-qubit gates and numerical pulses for parallel multi-qubit operations. We validate the proposed approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and superconducting-qubit arrays with up to 200 qubits. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates. Moreover, our method does not require precise knowledge of crosstalk strengths and makes no assumption about the underlying qubit connectivity or lattice geometry, thereby establishing a scalable framework for parallel quantum control in large-scale quantum architectures.

Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused on discrete ensembles, despite that many physical processes, such as in quantum chaos, thermalization, and control, naturally involve continuous ensembles generated from continuous time-evolution. Here we initial the study of continuous unitary designs, addressing fundamental questions about their construction and practical utility. For single-qubit system, we construct explicit unitary 1-design paths from spherical 2-design curves and Hopf fibration theory. For arbitrary dimensions, we develop two systematic construction frameworks, one based on topological bundle theory of the unitary group and the other based on the Heisenberg-Weyl group. On the practical front, our unitary design paths provide analytical solutions to universally robust quantum control. Simulations show they outperform conventional pulse techniques in mitigating arbitrary unknown static noises, demonstrating immediate utility for quantum engineering. Extending unitary designs to the continuous domain not only introduces powerful geometric and topological tools that complement conventional combinatorial and group-theoretic methods, but also enhances experimental feasibility over discrete counterparts which usually involve instantaneous pulses. As an outlook, we anticipate that this work will pave the way for using continuous unitary designs to explore complex quantum dynamics and devise quantum information protocols.

Quantum Zeno dynamics (QZD), which restricts the system's evolution to a protected subspace, provides a promising approach for protecting quantum information from noise. Here, we explore a practical approach to harnessing QZD for robust quantum metrology. By introducing strong inter-particle interactions during the parameter encoding stage, we overcome the typical limitations of previous QZD studies, which have largely focused on single-particle systems and faced challenges where QZD could interfere with the encoding process. We experimentally validate the proposed scheme on a nuclear magnetic resonance platform, achieving near-optimal precision scaling under amplitude damping in both parallel and sequential settings. Numerical simulations further demonstrate the scalability of the approach and its compatibility with other control techniques for suppressing more general types of noise. These findings highlight QZD as a powerful strategy for noise-resilient quantum metrology.

We consider the nature of the wave function using the example of a harmonic oscillator. We show that the eigenfunctions $\psi_n{=}z^n$ of the quantum Hamiltonian in the complex Bargmann-Fock-Segal representation with $z\in\mathbb C$ are the coordinates of a classical oscillator with energy $E_n=\hbar\omega n$, $n=0,1,2,...\,$. They are defined on conical spaces ${\mathbb C}/{\mathbb Z}_n$ with cone angles $2\pi/n$, which are embedded as subspaces in the phase space $\mathbb C$ of the classical oscillator. Here ${\mathbb Z}_n$ is the finite cyclic group of rotations of the space $\mathbb C$ by an angle $2\pi/n$. The superposition $\psi =\sum_n c_n\psi_n$ of the eigenfunctions $\psi_n$ arises only with incomplete knowledge of the initial data for solving the Schrödinger equation, when the conditions of invariance with respect to the discrete groups ${\mathbb Z}_n$ are not imposed and the general solution takes into account all possible initial data parametrized by the numbers $n\in\mathbb N$.

In the years 1952 and 1965, H.-C. Wang and U. Hirzebruch showed that the two-point homogeneous compact spaces with convex metrics are isometric to the spheres, the real, complex, octonion projective spaces and the Moufang plane and as well to the sets of the minimal idempotents or pure states in the simple Euclidean Jordan algebras. Here we reveal the physical meaning of these mathematical achievements for the quantum mechanical transition probability. We show that this transition probability features a maximum degree of homogeneity in all simple Euclidean Jordan algebras, which includes common finite-dimensional Hilbert space quantum theory. The atomic parts of these algebras or, equivalently, the extreme boundaries of their state spaces can be characterized by purely topological means. This is an important difference to many other recent approaches that aim to distinguish the entire state spaces among the convex compact sets. An interesting case with non-homogeneous transition probability arises, when the $E_6$-symmetric bioctonionic projective plane is used as quantum logic.

We report rovibronic spectra of the A $^3\Sigma^+$($v'=0-2$) - X $^3\Pi_\Omega(v=0)$ rovibronic transitions ($|\Omega|=0, 1$ and 2) of the CO$^{2+}$ doubly-charged molecular ion. Spectra were recorded at high resolution ($\sim 5$~cm$^{-1}$) in a fast beam of CO$^{2+}$ molecules by detecting the Coulomb explosion of the molecules upon excitation to the A state. Measurements were guided by ab initio calculations which then assisted the assignment of the observed spectral features. Our results resolve the spin-orbit splittings of the ground vibronic state X $^3\Pi_\Omega(v=0)$, but not the rotational structure of the bands due to spectral congestion, and provide spectroscopic information on CO$^{2+}$ with unprecedented resolution. In doing so they expand our knowledge of this benchmark doubly charged molecular ion and expand the short list of doubly charged molecules studied at high resolution.

We report a self-supervised deep learning framework for Rydberg sensors that enables single-shot noise suppression matching the accuracy of multi-measurement averaging. The framework eliminates the need for clean reference signals (hardly required in quantum sensing) by training on two sets of noisy signals with identical statistical distributions. When evaluated on Rydberg sensing datasets, the framework outperforms wavelet transform and Kalman filtering, achieving a denoising effect equivalent to 10,000-set averaging while reducing computation time by three orders of magnitude. We further validate performance across diverse noise profiles and quantify the complexity-performance trade-off of U-Net and Transformer architectures, providing actionable guidance for optimizing deep learning-based denoising in Rydberg sensor systems.

In applications where multiple optimal solutions are needed, transverse-field quantum annealing (QA) is known to sample degenerate ground states in a strongly biased manner. Despite extensive empirical observations, it remains unclear which features of degenerate ground states are preferentially sampled and why by QA. Here we analyze the final states using degenerate perturbation theory to characterize the preference among them. In this analysis, the adjacency matrix of the graph composed by the ground states naturally emerges, and we can predict the eigenvector centralities (one of the node centralities) are related to the probabilities of these states. We verify this prediction on toy models where degeneracy is lifted at first and second order, and we show that second-order weights encode local barrier information, relating sampling fairness to the flatness of the local energy landscape. Finally, this perspective suggests two practical routes toward fair sampling – promoting connectivity of the graph and reducing heterogeneity of centralities – and we illustrate consistency with higher-order drivers and minor-embedding transformations.

Quantum Private Query (QPQ) based on Quantum Key Distribution (QKD) is among the most practically viable quantum communication protocols, with application value second only to QKD itself. However, prevalent security vulnerabilities in the post-processing stages of most existing QKD-based QPQ protocols have been severely overlooked. This study focuses on hidden information extraction under undetermined signal bits, revealing that most such QPQ protocols face severe security threats even without complex quantum resources. Specifically, direct observation attack causes incremental information leakage, while the minimum error discrimination attack efficiently steals additional database inforamtion. To address these critical flaws, the proposed multi-encryption defense scheme is compatible with existing QPQ protocols. The study demonstrates the necessity of the multi-encryption strategy for the security of databases in QPQ, providing key theoretical and technical support for constructing practical QPQ protocols resistant to real-world attacks.

Over-parameterization is commonly used to increase the expressivity of variational quantum circuits (VQCs), yet deeper and more highly parameterized circuits often exhibit poor trainability and limited generalization. In this work, we provide a theoretical explanation for this phenomenon from a function-class perspective. We show that sufficiently expressive, unstructured variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size. As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions, a phenomenon we term simplicity bias, with barren plateaus arising as a consequence rather than the root cause. Using tools from random matrix theory and concentration of measure, we rigorously characterize this universality class and establish uniform hypothesis-class collapse over finite datasets. We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class. By restricting the accessible unitary ensemble through bounded tensor rank or bond dimension, these architectures prevent concentration of measure, preserve output variability for local observables, and retain non-degenerate gradient signals even in over-parameterized regimes. Together, our results unify barren plateaus, expressivity limits, and generalization collapse under a single structural mechanism rooted in random-matrix universality, highlighting the central role of architectural inductive bias in variational quantum algorithms.

Detecting high-order epistasis is a fundamental challenge in genetic association studies due to the combinatorial explosion of candidate locus combinations. Although multifactor dimensionality reduction (MDR) is a widely used method for evaluating epistasis, exhaustive MDR-based searches become computationally infeasible as the number of loci or the interaction order increases. In this paper, we define the epistasis detection problem as a black-box optimization problem and solve it with a factorization machine with quadratic-optimization annealing (FMQA). We propose an efficient epistasis detection method based on FMQA, in which the classification error rate (CER) computed by MDR is used as a black-box objective function. Experimental evaluations were conducted using simulated case-control datasets with predefined high-order epistasis. The results demonstrate that the proposed method successfully identified ground-truth epistasis across various interaction orders and the numbers of genetic loci within a limited number of iterations. These results indicate that the proposed method is effective and computationally efficient for high-order epistasis detection.

Bargmann invariants, a class of unitary-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the relative geometry of the projective Hilbert space. This survey offers a comprehensive overview of their theoretical characterization and practical applications, with particular emphasis on recent progress in determining the full structure of their admissible set. The core of this review demonstrates how these invariants serve as a powerful tool for characterizing the intrinsic geometry of the space of quantum states, leading to applications in determining local unitary equivalence and constructing a complete set of polynomial invariants for mixed states. On the operational side, we review the cycle-test quantum circuit for the direct estimation of Bargmann invariants without full state tomography, and demonstrate their utility in witnessing quantum imaginary, discriminating local unitary equivalence, and detecting entanglement via partial-transpose moments—with explicit complete invariant sets provided for two-qubit systems. By connecting fundamental geometric classification with experimentally feasible estimation protocols,this survey establishes Bargmann invariants as indispensable probes of the relational, noncommutative, and geometric structure of quantum states, and identifies key open problems for multipartite high-dimensional systems and for quantum resource theories.

Photon-induced Near-field Electron Microscopy (PINEM) effect has revealed the quantum interaction between free electrons and optical near filed, which demonstrated plenty of novel phenomena of manipulating free electron wave packet and detecting/shaping quantum photonic states. However, free electrons generally only absorb/emit one photon at a time, while the physical mechanism and phenomena of free electron-two-photon interaction have not been studied yet. Moreover, the relationship between PINEM and Kapitza-Dirac (KD) effect and nonlinear Compton scattering is still unclear. Here we develop the full quantum theory of electron-photon interaction considering the two-photon process. It is revealed that the emission/absorption of two photons by electrons can be greatly enhanced by manipulating the electric field component of optical near field, and the quantum interference between single-photon and two-photon processes can occur in some circumstances, which affects the photon number state, electron energy states and electron-photon entanglement. Meanwhile, it is found that the KD effect (elastic electron-photon scattering) and nonlinear Compton scattering (inelastic electron-photon scattering) are also a kind of two-photon process and the distribution of electrons can be deduced analytically based on the full quantum theory. Our work uncovers the possible abundant phenomena when free electron interacting with two photons, paves the way for more in-depth studies of nonlinear processes in electron-photon quantum interactions in the future.

We propose and experimentally demonstrate a global parametric gate that generates multi-qubit entangled states in a single step. By applying a parametric drive to a common qubit at precise detunings relative to computational qubits, we directly produce two-, three-, and four-qubit entanglement with state fidelities of 99.4%\pm0.2%, 93.4%\pm0.3%, and 91.4%\pm0.3%, respectively. This scheme enables efficient, reconfigurable control using only microwave drives and is compatible with fixed-frequency qubits. Error analyses indicate that infidelity stems primarily from decoherence and coherent control errors, with negligible contributions from static ZZ coupling and flux noise. Furthermore, simulations with state-of-the-art parameters predict this global gate can generate high-fidelity (99.70%) entanglement in systems of up to six qubits.

Theoretical proposals to reach the Heisenberg scaling of the measurement precision typically require carefully engineered interactions or initial entanglement. In studying optical magnetometry, we show that the continuous collective measurement process itself can generate the necessary many-body quantum correlations to achieve the elusive Heisenberg scaling of the quantum Fisher information in a dissipative, steady-state system without direct inter-atomic interactions. By contrasting a correlation-neglecting but otherwise consistent semiclassical model, which can violate the quantum Cramér-Rao bound (QCRB) by several orders of magnitude, with a collective quantum model, we isolate measurement-induced correlations as the essential mechanism. The violation of the QCRB serves thereby as a fundamental sanity check for semiclassical spectroscopic theories. This work reveals measurement-induced correlations as a widely unexplored quantum resource for quantum-enhanced sensing, establishes a new paradigm for achieving Heisenberg scaling in open quantum systems, and provides a direct path to test the foundations of quantum mechanics using macroscopic atom ensembles.

This work investigates photon blockade control in a hybrid quantum system containing a Kerr-nonlinear cavity coupled to an optical parametric amplifier (OPA). The dynamics are governed by a master equation derived from an effective Hamiltonian that includes cavity decay. To obtain analytical solutions, the system's quantum state is expanded in the Fock basis up to the two-photon level. Solving the steady-state Schrodinger equation yields probability amplitudes and the analytical conditions for optimal photon blockade. Results confirm that photon blockade is achievable with suitable parameters. Excellent agreement is found between the analytical solutions and numerical simulations for the steady-state, equal-time second-order correlation function, validating both the analytical method and the blockade effect. Numerically, the average intracavity photon number increases significantly under resonance, providing a theoretical pathway for enhancing single-photon source brightness. Furthermore, the driving phase is shown to regulate the optimal blockade region: it shifts the parabolic region within the two-dimensional parameter space of driving strength and OPA nonlinearity and can even reverse its opening direction. The influence of Kerr nonlinearity is also examined. Photon blockade remains robust across a wide range of Kerr strengths. Physical analysis attributes the effect to destructive quantum interference between two distinct excitation pathways that suppress two-photon states. While Kerr nonlinearity shifts the system's energy levels, it does not disrupt this interference mechanism, explaining the effect's stability over a broad parameter range.

In open quantum systems, a basic question at the interface of quantum information, statistical physics, and many-body dynamics is how well can one infer the structure of noise and dissipation generators from finite-time measurement statistics alone. Motivated by this question, we study the learnability and cryptographic applications of random open-system dynamics generated by Lindblad-Gorini-Kossakowski-Sudarshan (GKSL) master equations. Working in the affine hull of the GKSL cone, we introduce physically motivated ensembles of random local Lindbladians via a linear parametrisation around a reference generator. On top of this geometric structure, we extend statistical query (SQ) and quantum-process statistical query (QPStat) frameworks to the open-system setting and prove exponential (in the parameter dimension $M$) lower bounds on the number of queries required to learn random Lindbladian dynamics. In particular, we establish average-case SQ-hardness for learning output distributions in total variation distance and average-case QPStat-hardness for learning Lindbladian channels in diamond norm. To support these results physically, we derive a linear-response expression for the ensemble-averaged total variation distance and verify the required nonvanishing scaling in a random local amplitude-damping chain. Finally, we design two Lindbladian physically unclonable function (Lindbladian-PUF) protocols based on random Lindbladian ensembles with distribution-level and tomography-based verification, thereby providing open-system examples where learning hardness can be translated into cryptographic security guarantees.

Unit Commitment (UC) is a core optimization problem in power system operation and electricity market scheduling. It determines the optimal on/off status and dispatch of generating units while satisfying system, operational, and market constraints. Traditionally, UC has been solved using mixed-integer programming, dynamic programming, or metaheuristic methods, all of which face scalability challenges as systems grow in size and uncertainty. Recent advances in quantum computing, spanning quantum annealing, variational algorithms, and hybrid quantum classical optimization, have opened new opportunities to accelerate UC solution processes by exploiting quantum parallelism and entanglement. This paper presents a comprehensive survey of existing research on the applications of quantum computing for solving the UC problem. The reviewed works are categorized based on the employed quantum paradigms, including annealing-based, variational hybrid, quantum machine learning, and quantum-inspired methods. Key modeling strategies, hardware implementations, and computational trade-offs are discussed, highlighting the current progress, limitations, and potential future directions for large-scale quantum-enabled UC.

Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such as operation precision, circuit depth and connectivity. With improved hardware efficiency by using superconducting qutrits (three-level systems), we experimentally demonstrate a scalable DTQW in a superconducting circuit, observing the ballistic spreading of quantum walk in a qutrit chain. The usage of qutrits in our implementation allows hardware efficiently encoding of the walker position and the coin degree of freedom. By exploiting the flexibility and intrinsic symmetries of qutrit-based DTQWs, we successfully prepare two topological phases in the chain. For the first time, particle-hole-symmetry-protected edge states, bounded at the interface between these two topological phases, are observed in the superconducting platform. Measured parameter dependencies further validate the properties of edge states. The scalability and gate-control compatibility of the demonstrated DTQWs enable a versatile tool for superconducting quantum computing and quantum simulation.