arXiv subjects

Mingrui Jing

Publications and source records attributed to Mingrui Jing.

At least 19 recordsLinked to original sources

arXiv2026

An exchange-assisted entangling gate between 87Rb and 171Yb Rydberg atoms

Neutral-atom tweezer arrays support scalable quantum information processing. Dual-species $^{87}\mathrm{Rb}$--$^{171}\mathrm{Yb}$ arrays combine long-lived ytterbium nuclear-spin data qubits with fast, species-selective rubidium ancilla control and readout. However, realizing interspecies gates without inducing destructive Stark mixing in divalent atoms remains an outstanding problem. Here, we identify an optically accessible $S{+}S\leftrightarrow P{+}P$ F\"orster resonance at zero electric field, providing strong dipole-dipole exchange at array pitch. Using a shaped optical pulse under finite control response, we demonstrate a $0.36\,\mu\mathrm{s}$ exchange-assisted controlled-$Z$ gate with an intrinsic fidelity of $99.91\%$, remaining above $99.85\%$ under bounded perturbations. We also identify an auxiliary repulsive van der Waals channel, providing a comprehensive toolbox for hybrid quantum processors.

quant-ph↗

arXiv2026

Learning Quantum Matter through Attention in Complex Space

Magnetic many-electron wavefunctions require amplitude and phase to be optimized together. Whether a complex internal representation improves this variational search is a practical question for neural wavefunction design. We introduce Complex Psiformer for interacting electrons in a magnetic moir\'e continuum, combining complex hidden features and Hermitian-magnitude attention with magnetic boundary conditions and fermionic antisymmetry. After the same number of optimization steps, Complex Psiformer reaches lower energies than Real Psiformer in two finite supercells. Both Psiformers also improve on their respective neural Hartree-Fock references. Across five training seeds in the 25-cell system, the mean Complex advantage is 1.458 meV per electron, with a smaller observed spread. A separately trained two-electron Complex state has a smaller energy gap to a finite configuration interaction reference than its Real counterpart. In the Complex states, flux scans show nonmonotonic density correlations and weaker honeycomb mean-density modulation at higher flux, while connected fluctuations persist. Gauge invariant current maps provide a qualitative comparison of local circulation in the optimized states. These benchmarks support the combined architecture as a variational ansatz for studying energies and charge arrangements in finite magnetic systems.

cond-mat.str-el↗

arXiv2026

Exact Virtual Channel Programming with Vanishing Excess Overhead

A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels. We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state and its output observables are reconstructed by sampling physical channels and classically post-processing their measurement outcomes. For arbitrary $d$-dimensional channels, we construct a target-independent exact reconstruction protocol and prove the optimal one-copy sampling overhead, which grows quadratically with system dimension. We further prove the sharp fixed-$d$ law that the excess overhead vanishes inversely with the number of identical Choi programs. The upper bound combines deterministic port-based teleportation with a quasi-decomposition that corrects its depolarizing distortion. The converse maps any low-overhead reconstruction protocol to a physical learner of unknown unitaries and uses local quantum estimation to recover the same leading coefficient. These results recast the universal no-programming obstruction as a quantitative trade-off between quantum program memory and classical sampling, with a leading cost that reflects the locally learnable unitary degrees of freedom.

quant-ph↗

arXiv2026

Algebraic Speedups for Exact Inversion of Hamiltonian Evolutions

Deterministic exact inversion of an arbitrary $d$-dimensional unitary requires {$\Theta(d^2)$} coherent forward calls in the worst case. We ask how this cost changes for Hamiltonian evolution $U(x)=\exp(i\sum_j x_jH_j)$ when the generators are known but the parameters are hidden. For one-parameter families with a fixed eigenbasis, we show that additive relations among the distinct eigenvalues determine the optimal query number exactly, and we construct the corresponding inversion protocol. For general families, we prove that repeated symmetry sectors do not affect the exact query complexity and give an automatic construction for combining inverses from inequivalent active sectors. We also give a sufficient phase-alignment condition under which family-specific structure can reduce the query number. These results establish structure-dependent bounds for reversing the unknown dynamics arising in Tavis-Cummings out-of-time-order correlator protocols, collective-spin echo verification, and passive multimode links, without requiring prior knowledge or explicit estimation of the underlying coupling strengths.

quant-ph↗

arXiv2026

Benchmarking Agents for Proving Theorems in Quantum Algorithms and Quantum Information

Formal verification is becoming increasingly practical for quantum computing, yet the ability of AI agents to construct machine-checkable proofs in this domain remains unmeasured. We introduce Lean-QuantumAlg-Bench and Lean-QIT-Bench, two Lean 4 benchmarks containing 36 and 40 theorem-completion tasks for quantum algorithms and quantum information theory, respectively. Every task compiles in a fixed environment and is evaluated by deterministic proof checking and targeted semantic review, with difficulty weights assigned before model execution. We evaluate four models-GPT-5.5, Kimi K3, DeepSeek V4-Pro, and MiniMax M3-within a common theorem-proving framework under two settings: a task-only baseline and library-augmented deduction (LAD), which additionally provides access to a verified domain library. The highest difficulty-weighted scores are 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark. LAD improves both score and completion rate in all eight model-benchmark comparisons, with gains of up to 15.9 points, providing evidence that verified libraries can strengthen domain-specific proof agents. The results reveal recurring weaknesses of agentic proving in areas such as quantum simulation, quantum learning, quantum information measures, and entanglement theory. Monetary and wall-clock costs per score point also vary substantially across models, highlighting important capability-efficiency trade-offs. We expect these benchmarks to establish a reproducible baseline for developing more capable and reliable proof agents, and to pave the way toward self-evolving AI scientists for advancing quantum information science.

quant-ph↗

arXiv2026

An Agentic Formalization for Certified Quantum Neural Network Design

A central model in quantum machine learning is the quantum neural network (QNN), whose design requires balancing expressivity and trainability. Technically, expressivity is studied through circuit-function analysis, such as quantum signal processing, while trainability is analyzed using dynamical-Lie-algebra (DLA) methods. To support certified QNN design, we formalize these major components of QNN theory in a connected lean 4 development checked by a proof kernel, where every analytic input is either proved or exposed as a named hypothesis. On the expressivity side, we prove exact if-and-only-if characterizations of single-qubit QNNs, a resource-counted quantum phase processing theorem, and an overparameterization ceiling that bounds the quantum Fisher information rank by the DLA dimension. On the trainability side, we derive the direct-sum loss-variance law through a de-circularized second-moment interface. A parameterized Casimir-uniqueness engine discharges the required inputs for fully controllable, orthogonal, and matchgate circuit families, while single-qubit and product-Clifford ensembles close the two-design assumptions directly. A capstone theorem pairs the conditional variance law with exact loss reconstruction in DLA coordinates. The development record identifies eight corrections and clarifications that were not explicit in the informal arguments. We expect this work to provide a machine-checkable foundation for QNN theory and a step toward AI-assisted or automated design of quantum machine learning algorithms.

quant-ph↗

arXiv2026

Thermal-Drift Sampling: Generating Thermal Ensembles for Learning Many-Body Systems

Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across different Hamiltonians remains costly with existing methods. We introduce a powerful operation, the quantum thermal-drift channel, to construct a measurement-controlled sampling algorithm that autonomously generates thermal states together with their system Hamiltonians as labels for general physical models. We prove that our algorithm is efficient: the total gate count scales polynomially with system size and quadratically with inverse temperature, providing the first polynomial resource bound for random thermal state generation. We characterize the distribution of sampled Hamiltonians as a normal distribution reweighted by partition functions, which quantifies a trade-off between sampling accuracy and effective label range. Level-spacing statistics computed from sampled thermal states of a 2D transverse-field Ising model show a crossover to Wigner-Dyson universality, confirming that the sampler captures nontrivial chaotic correlations. Finally, a variational quantum classifier trained on the generated dataset achieves near-optimal accuracy in predicting Hamiltonian properties of unseen states. These results establish a scalable, quantum-native route for thermodynamic simulation and labeled quantum data generation in many-body systems.

quant-ph↗

arXiv2025

Programmable Open Quantum Systems

Programmability is a unifying paradigm for enacting families of quantum transformations via fixed processors and program states, with a fundamental role and broad impact in quantum computation and control. While there has been a shift from viewing open systems solely as a source of error to treating them as a computational resource, their programmability remains largely unexplored. In this work, we develop a framework that characterizes and quantifies the programmability of Lindbladian semigroups by combining physically implementable retrieval maps with time varying program states. Within this framework, we identify quantum programmable classes enabled by symmetry and stochastic structure, including covariant semigroups and fully dissipative Pauli Lindbladians with finite program dimension. We further provide a necessary condition for physical programmability that rules out coherent generators and typical dissipators generating amplitude damping. For such nonphysically programmable cases, we construct explicit protocols with finite resources. Finally, we introduce an operational programming cost, defined via the number of samples required to program the Lindbladian, and establish its core structural properties, such as continuity and faithfulness. These results provide a notion of programming cost for Lindbladians, bridge programmable channel theory and open system dynamics, and yield symmetry driven compression schemes and actionable resource estimates for semigroup simulation and control in noisy quantum technologies.

quant-ph↗

arXiv2025

Structure, Optimality, and Symmetry in Shadow Unitary Inversion

Reversing unitary operations is a key task in quantum computing and quantum control. In this work, we introduce and develop the framework of shadow unitary inversion, a relaxed variant of unitary inversion in which the goal is to reproduce the action of the inverse unitary only at the level of the expectation value of a fixed observable. This task captures an operational setting in which only shadow information is required and allows query complexities significantly below those of full unitary inversion. We establish a dimension-dependent lower bound showing that any $t$-query scheme requires $t$ to scale at least linearly with the system dimension, with the constant determined by the spectral properties of the target observable. In the qubit case, we construct a deterministic three-query sequential protocol that achieves exact shadow inversion, and we provide a complete characterization of all admissible qubit channels satisfying the shadow constraint. Numerical evidence suggests that three queries are optimal. For higher-dimensional systems, we develop a semidefinite-programming formulation for optimizing shadow-inversion combs and introduce a representation-theoretic symmetry reduction that decomposes the problem into invariant blocks, substantially reducing the problem size. These results provide the first systematic study for shadow unitary inversion and establish its resource requirements and symmetry structure across dimensions.

quant-ph↗

arXiv2025

LCQNN: Linear Combination of Quantum Neural Networks

Quantum neural networks combine quantum computing with advanced data-driven methods, offering promising applications in quantum machine learning. However, the optimal paradigm for balancing trainability and expressivity in QNNs remains an open question. To address this, we introduce the Linear Combination of Quantum Neural Networks (LCQNN) framework, which uses the linear combination of unitaries concept to create a tunable design that mitigates vanishing gradients without incurring excessive classical simulability. We show how specific structural choices, such as adopting $k$-local control unitaries or restricting the model to certain group-theoretic subspaces, prevent gradients from collapsing while maintaining sufficient expressivity for complex tasks. We further employ the LCQNN model to handle supervised learning tasks, demonstrating its effectiveness on real datasets. In group action scenarios, we show that by exploiting symmetry and excluding exponentially large irreducible subspaces, the model circumvents barren plateaus. Overall, LCQNN provides a novel framework for focusing quantum resources into architectures that are practically trainable yet expressive enough to tackle challenging machine learning applications.

quant-ph↗

arXiv2025

Implementation of a quantum sequence alignment algorithm for quantum bioinformatics

This paper presents the implementation of a quantum sequence alignment (QSA) algorithm on biological data in environments simulating noisy intermediate-scale quantum (NISQ) computers. The approach to quantum bioinformatics adapts the original QSA algorithm proposed in 2000 to current capabilities and limitations of NISQ-era quantum computers and uses a genetic algorithm for state preparation (GASP) to create encoding circuits to load both database and target sequences into the quantum data registers. The implementation is tested in a simulated quantum computer environment to validate the approach and refine the GASP data-loading circuit designs. The results demonstrate the practicalities of deploying the QSA algorithm and exemplify the potential of GASP for data encoding in the realm of quantum circuit design, particularly for complex algorithms in quantum bioinformatics and other data-rich problems.

quant-ph↗

arXiv2025

Quantum Recurrent Embedding Neural Network

Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, previous studies have demonstrated inevitable trainability issues that severely limit their capabilities in the large-scale regime. In this work, we propose a quantum recurrent embedding neural network (QRENN) inspired by fast-track information pathways in ResNet and general quantum circuit architectures in quantum information theory. By employing dynamical Lie algebras, we provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus. Notably, the general QRENN architecture resists classical simulation as it encompasses powerful quantum circuits such as QSP, QSVT, and DQC1, which are widely believed to be classically intractable. Building on this theoretical foundation, we apply our QRENN to accurately classify quantum Hamiltonians and detect symmetry-protected topological phases, demonstrating its applicability in quantum supervised learning. Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning in predicting physical properties and solving complex problems.

quant-ph↗

arXiv2025

Exploring Large Language Models in Healthcare: Insights into Corpora Sources, Customization Strategies, and Evaluation Metrics

This study reviewed the use of Large Language Models (LLMs) in healthcare, focusing on their training corpora, customization techniques, and evaluation metrics. A systematic search of studies from 2021 to 2024 identified 61 articles. Four types of corpora were used: clinical resources, literature, open-source datasets, and web-crawled data. Common construction techniques included pre-training, prompt engineering, and retrieval-augmented generation, with 44 studies combining multiple methods. Evaluation metrics were categorized into process, usability, and outcome metrics, with outcome metrics divided into model-based and expert-assessed outcomes. The study identified critical gaps in corpus fairness, which contributed to biases from geographic, cultural, and socio-economic factors. The reliance on unverified or unstructured data highlighted the need for better integration of evidence-based clinical guidelines. Future research should focus on developing a tiered corpus architecture with vetted sources and dynamic weighting, while ensuring model transparency. Additionally, the lack of standardized evaluation frameworks for domain-specific models called for comprehensive validation of LLMs in real-world healthcare settings.

cs.CL↗

arXiv2024

Retrieving non-linear features from noisy quantum states

Accurately estimating high-order moments of quantum states is an elementary precondition for many crucial tasks in quantum computing, such as entanglement spectroscopy, entropy estimation, spectrum estimation, and predicting non-linear features from quantum states. But in reality, inevitable quantum noise prevents us from accessing the desired value. In this paper, we address this issue by systematically analyzing the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. We then establish a method for deriving protocols that attain optimal sample complexity using quantum operations and classical post-processing only. Our protocols, in contrast to conventional ones, incur lower overheads and avoid sampling different quantum operations due to a novel technique called observable shift, making the protocols strong candidates for practical usage on current quantum devices. The proposed method also indicates the power of entangled protocols in retrieving high-order information, whereas in the existing methods, entanglement does not help. We further construct the protocol for large quantum systems to retrieve the depolarizing channels, making the proposed method scalable. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.

quant-ph↗

arXiv2024

Circuit Knitting Faces Exponential Sampling Overhead Scaling Bounded by Entanglement Cost

Circuit knitting, a method for connecting quantum circuits across multiple processors to simulate nonlocal quantum operations, is a promising approach for distributed quantum computing. While various techniques have been developed for circuit knitting, we uncover fundamental limitations to the scalability of this technology. We prove that the sampling overhead of circuit knitting is exponentially lower bounded by the exact entanglement cost of the target bipartite dynamic, even for asymptotic overhead in the parallel cut regime. Specifically, we prove that the regularized sampling overhead assisted with local operations and classical communication (LOCC), of any bipartite quantum channel is lower bounded by the exponential of its exact entanglement cost under separable preserving operations. Furthermore, we show that the regularized sampling overhead for simulating a general bipartite channel via LOCC is lower bounded by $\kappa$-entanglement and max-Rains information, providing efficiently computable benchmarks. Our work reveals a profound connection between virtual quantum information processing via quasi-probability decomposition and quantum Shannon theory, highlighting the critical role of entanglement in distributed quantum computing.

quant-ph↗

arXiv2023

Virtual Quantum Markov Chains

Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept of virtual quantum Markov chains (VQMCs), focusing on scenarios where subsystems retain classical information about global systems from measurement statistics. As a generalization of quantum Markov chains, VQMCs characterize states where arbitrary global shadow information can be recovered from subsystems through local quantum operations and measurements. We present an algebraic characterization for virtual quantum Markov chains and show that the virtual quantum recovery is fully determined by the block matrices of a quantum state on its subsystems. Notably, we find a distinction between two classes of tripartite entanglement by showing that the W state is a VQMC while the GHZ state is not. Furthermore, we introduce the virtual non-Markovianity to quantify the non-Markovianity of a given quantum state, which also assesses the optimal sampling overhead for virtually recovering this state. Our findings elucidate distinctions between quantum Markov chains and virtual quantum Markov chains, extending our understanding of quantum recovery to scenarios prioritizing classical information from measurement statistics.

quant-ph↗

arXiv2023

Enhancement of non-Stabilizerness within Indefinite Causal Order

In quantum computing, the nonstabilizerness of quantum operations is crucial for understanding and quantifying quantum speedups. In this study, we explore the phenomena of nonstabilizerness of the quantum SWITCH, a novel structure that allows quantum states to pass through operations in a superposition of different orders, outperforming traditional circuits in numerous tasks. To assess its nonstabilizerness, we propose the magic resource capacity of a quantum process to quantitatively examine the nonstabilizerness of general quantum transformations. We find that the completely stabilizer-preserving operations, which cannot generate magic states under standard conditions, can be transformed to do so when processed by the quantum SWITCH. Furthermore, when considering the impact of noise, although the nonstabilizerness of each path may be annihilated, their superposition could still preserve the overall nonstabilizerness. These findings reveal the unique properties of the quantum SWITCH and open avenues in research on nonstabilizer resources of general quantum architecture.

quant-ph↗

arXiv2023

Computable and Faithful Lower Bound on Entanglement Cost

Quantifying the minimum entanglement needed to prepare quantum states and implement quantum processes is a key challenge in quantum information theory. In this work, we develop computable and faithful lower bounds on the entanglement cost under quantum operations that completely preserve the positivity of partial transpose (PPT operations), by introducing the generalized divergence of $k$-negativity, a generalization of logarithmic negativity. Our bounds are efficiently computable via semidefinite programming and provide non-trivial values for all states that are non-PPT (NPT), establishing their faithfulness for the resource theory of NPT entanglement. Notably, we find and affirm the irreversibility of asymptotic entanglement manipulation under PPT operations for full-rank entangled states. Furthermore, we extend our methodology to derive lower bounds on the entanglement cost of both point-to-point and bipartite quantum channels. Our bound demonstrates improvements over previously known computable bounds for a wide range of quantum states and channels. These findings push the boundaries of understanding the structure of entanglement and the fundamental limits of entanglement manipulation.

quant-ph↗