arXiv subjects

Zhao-Yun Chen

Publications and source records attributed to Zhao-Yun Chen.

At least 19 recordsLinked to original sources

arXiv2026

Spectator Leakage Suppression via Invariant Subspace Engineering for CZ Gates in Superconducting Quantum Circuits

Spectator leakage poses a fundamental challenge to scalable quantum computing, particularly as frequency collisions become unavoidable in multi-qubit processors. We introduce a leakage mitigation strategy based on dynamically reshaping the system Hamiltonian. Our technique utilizes a tunable coupler to enforce a block-diagonal structure on the effective Hamiltonian governing near-resonant spectator interactions, confining the gate dynamics to a two-dimensional invariant subspace and thus preventing leakage by construction. On a multi-qubit superconducting processor, we experimentally demonstrate that this dynamic control scheme suppresses leakage rates to the order of $10^{-4}$, across a wide near-resonant detuning range and with up to three simultaneous spectator qubits. These results demonstrate a robust and scalable method that resolves the critical trade-off between dense frequency packing and high-fidelity gate operation. Our work establishes dynamic Hamiltonian engineering as an essential technology for building fault-tolerant quantum computers.

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arXiv2026

Routing Codes: High-Rate Quantum LDPC Codes with Short, Parallel Non-Local Connectivity

Quantum low-density parity-check (qLDPC) codes are promising candidates for realizing large-scale fault-tolerant quantum computing. Although many codes with favorable theoretical parameters have been developed, their practical adoption must take hardware implementability into account. For mainstream quantum platforms such as superconductors and neutral atoms, the connectivity, the length of non-local couplings, and the complexity of wiring or atom rearrangement are key factors that dictate the difficulty of hardware realization. Here, we propose a new family of qLDPC codes, termed routing codes. Within this family, we find explicit instances whose encoding rates are competitive to those of bivariate bicycle (BB) codes, while systematically reducing qubit connectivity, shortening the length of non-local couplings, and, crucially, making all non-local couplings mutually parallel. This parallelism translates into quantifiable benefits, substantially reducing wiring crossings in superconducting multi-layer architectures and simplifying the scheduling of atom movement in neutral-atom arrays. The weight-7 routing codes maintain a high threshold of 0.7\% and reduce the physical qubit overhead by approximately a factor of 8, compared to surface codes achieving a same logical error rate. Further increasing the weight to 11 yields a [[200, 24, 14]] and [[200, 16, 17]] codes with an encoding rate over 23 times that of the surface code, at the cost of a higher logical error rate. These results establish routing codes as a hardware-centric qLDPC family that bridges the gap between theoretical optimality and near-term physical feasibility.

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arXiv2026

Poisson-Compiled Quantum Singular Value Transformation for Power-Exponential Dissipation

We study quantum implementations of the contraction $\exp(-T H^α)$ for $H=H^\dagger\succeq0$ and $α>0$. Poisson summation provides an exact target--alias--tail decomposition whose Fourier samples are compiled classically into a single Chebyshev polynomial, so the quantum circuit uses polynomial eigenvalue transformation rather than a frequency linear combination of unitaries. We compare block encodings of $H/\norm{H}$ and of the shifted signal $2H/\norm{H}-I$. Under ordinary single-sequence QSVT, parity forces the former to use an even extension, which is entire only for even positive integers. An exact quadratic lift for the shifted signal makes every positive integer entire and improves the fixed-scale approximation error for noninteger powers from $Θ(d^{-α})$ to $Θ(d^{-2α})$ within the stated access and parity classes. We derive matching degree bounds in the large-scale fixed-error and fixed-scale high-precision limits, including the output-normalization overhead $u_r$. Nearest-neighbor Laplacians give a unit-normalized shifted signal. We further establish a noncommutative Weyl--Poisson identity compatible with LCHS quadrature, and use the same polynomial construction to implement controlled dissipative families in amplitude--phase separation.

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arXiv2026

Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression

Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum $XY$ model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.

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arXiv2026

Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition

Simulating non-Hermitian dynamics on quantum computers is often hindered by the decay of success probability and the instability of non-diagonalizable matrices. Here, we present contour-based matrix decomposition (CBMD), a rigorous and versatile quantum functional calculus framework for simulating non-Hermitian matrix functions. By generalizing the matrix Cauchy residue theorem, CBMD decomposes holomorphic non-Hermitian operators into an analytic infinite contour-residue identity, followed by finite truncation with controlled error to yield linear combinations of Hermitian components. For first-order dynamics, CBMD achieves optimal query complexity across all parameters, strictly matching the optimal performance bounds within the linear combination of Hamiltonian simulation (LCHS) paradigm. Beyond first-order systems, the framework naturally generalizes to complex operator functions, including second-order wave dynamics and non-Hermitian special functions such as Bessel and Airy evolutions. Furthermore, CBMD systematically suppresses the asymptotic growth of non-Hermitian components, yielding a significant reduction in the required number of amplitude amplifications compared to the naive scheme of combining monomials via linear combination of unitaries (LCU) after Taylor expansion. Notably, CBMD avoids explicit dependence on matrix diagonalizability, effectively mitigating the long-standing challenges associated with ill-conditioned eigenvectors and Jordan blocks. Our work establishes a systematic matrix calculus that bridges high-performance classical numerics and fault-tolerant quantum algorithms. It should be noted that CBMD inherits standard LCU overheads, and requires the target function to have a bounded growth order on the real axis.

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arXiv2026

QuantumQA: Enhancing Scientific Reasoning via Physics-Consistent Dataset and Verification-Aware Reinforcement Learning

Large language models (LLMs) show strong capabilities in general reasoning but typically lack reliability in scientific domains like quantum mechanics, which demand strict adherence to physical constraints. This limitation arises from the scarcity of verifiable training resources and the inadequacy of coarse feedback signals in standard alignment paradigms. To address the data challenge, we introduce QuantumQA, a large-scale dataset constructed via a task-adaptive strategy and a hybrid verification protocol that combines deterministic solvers with semantic auditing to guarantee scientific rigor. Building on this foundation, we propose the verification-aware reward model (VRM) tailored for Reinforcement Learning with Verifiable Rewards (RLVR), which employs an adaptive reward fusion (ARF) mechanism to dynamically integrate deterministic signals from a scientific execution suite (SES) with multidimensional semantic evaluations for precise supervision. Experimental results demonstrate that our method consistently outperforms baselines and general-purpose preference models. Notably, our optimized 8B model achieves performance competitive with proprietary models, validating that incorporating verifiable, rule-based feedback into the reinforcement learning loop offers a parameter-efficient alternative to pure scaling.

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arXiv2026

A Unified Poisson Summation Framework for Generalized Quantum Matrix Transformations

We present a unified algorithmic framework for quantum simulation of non-unitary dynamics and matrix functions, governed by the principle of spectral aliasing derived from the Poisson Summation Formula (PSF). By reinterpreting discretization errors as spectral folding in dual domains, we synthesize two distinct algorithmic paths: (i) the Fourier-PSF path, generalizing transmutation methods for time-domain filtering, which is optimal for singular and fractional dynamics $e^{-tH^α}$, here $H\succeq 0$; and (ii) the contour-PSF path, a novel discrete contour transform based on the resolvent formalism, which achieves exponential convergence for holomorphic matrix functions via radius optimization. This dual framework resolves the smoothness-sparsity trade-off: it utilizes the Fourier basis to handle branch-point singularities where analyticity fails, and the Resolvent basis to exploit complex-plane regularity where it exists. We demonstrate the versatility of this framework by efficiently simulating diverse phenomena, from fractional anomalous diffusion to high-precision solutions of stiff differential equations, outperforming existing methods in their respective optimal regimes.

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arXiv2026

Quantum Deep Learning: A Comprehensive Review

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

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arXiv2026

Experimental robustness benchmarking of quantum neural networks on a superconducting quantum processor

Quantum machine learning (QML) models, like their classical counterparts, are vulnerable to adversarial attacks, hindering their secure deployment. Here, we report the first systematic experimental robustness benchmark for 20-qubit quantum neural network (QNN) classifiers executed on a superconducting processor. Our benchmarking framework features an efficient adversarial attack algorithm designed for QNNs, enabling quantitative characterization of adversarial robustness and robustness bounds. From our analysis, we verify that adversarial training reduces sensitivity to targeted perturbations by regularizing input gradients, significantly enhancing QNN's robustness. Additionally, our analysis reveals that QNNs exhibit superior adversarial robustness compared to classical neural networks, an advantage attributed to inherent quantum noise. Furthermore, the empirical upper bound extracted from our attack experiments shows a minimal deviation ($3 \times 10^{-3}$) from the theoretical lower bound, providing strong experimental confirmation of the attack's effectiveness and the tightness of fidelity-based robustness bounds. This work establishes a critical experimental framework for assessing and improving quantum adversarial robustness, paving the way for secure and reliable QML applications.

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arXiv2025

Quantum homotopy analysis method with quantum-compatible linearization for nonlinear partial differential equations

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the vast computational resources they demand, highlighting the pressing need for more efficient computational methods. Quantum computing offers a promising but technically challenging approach to solving nonlinear PDEs. Recently, Liao proposed a framework that leverages quantum computing to accelerate the solution of nonlinear PDEs based on the homotopy analysis method (HAM), a semi-analytical technique that transforms nonlinear PDEs into a series of linear PDEs. However, the no-cloning theorem in quantum computing poses a major limitation, where directly applying quantum simulation to each HAM step results in exponential complexity growth with the HAM truncation order. This study introduces a ``quantum-compatible linearization'' approach that maps the whole HAM process into a system of linear PDEs, allowing for a one-time solution using established quantum PDE solvers. Our method preserves the exponential speedup of quantum linear PDE solvers while ensuring that computational complexity increases only polynomially with the HAM truncation order. We demonstrate the efficacy of our approach by applying it to the Burgers' equation and the Korteweg-de Vries (KdV) equation. Our approach provides a novel pathway for transforming nonlinear PDEs into linear PDEs, with potential applications to fluid dynamics. This work thus lays the foundation for developing quantum algorithms capable of solving the Navier-Stokes equations, ultimately offering a promising route to accelerate their solutions using quantum computing.

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arXiv2025

Variational quantum simulation of many-body dissipative dynamics on a superconducting quantum processor

Open quantum systems host a wide range of intriguing phenomena, yet their simulation on well-controlled quantum devices is challenging, owing to the exponential growth of the Hilbert space and the inherently non-unitary nature of the dynamics. Here we propose and experimentally demonstrate a variational quantum algorithm capable of scalable simulation of non-unitary many-body dissipative dynamics. The algorithm builds on the framework of linear combination of Hamiltonian simulation, which converts non-unitary dynamics into a weighted sum of unitary evolutions. With the further introduction of a simplified quantum circuit for loss-function evaluation, our scheme is suitable for near-term quantum hardware, with the circuit depth independent of the simulation time. We illustrate our scheme by simulating the collective dynamics of a dissipative transverse Ising model, as well as an interacting Hatano-Nelson model, on the superconducting quantum processor Wukong. Our work underlines the capability of noisy intermediate-scale quantum devices in simulating dissipative many-body dynamics and represents a step forward in exploiting their potential for solving outstanding physical problems.

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arXiv2025

Data-driven Quantum Dynamical Embedding Method for Long-term Prediction on Near-term Quantum Computers

The increasing focus on long-term time series prediction across various fields has been significantly strengthened by advancements in quantum computation. In this paper, we introduce a data-driven method designed for time series prediction with quantum dynamical embedding (QDE). This approach enables a trainable embedding of the data space into an extended state space, allowing for the recursive retrieval of time series information. Based on its independence of time series length, this method achieves depth-efficient quantum circuits that are crucial for near-term quantum computers. Numerical simulations demonstrate the model's capability to predict not only wave signals but also more complex signals such as NARMA. Prediction accuracy improves with model scaling, and notably, the model achieves better accuracy on wave signal tasks with fewer parameters compared to QRC. Additionally, the model shows promising potential for denoising classical noise in wave signals, and when combined with error mitigation techniques for typical quantum noise, it enables reliable long-term prediction of wave signals. We implement this model, restricted to 2 qubits, on the Origin ``Wukong" superconducting quantum processor as a simple proof-of-concept on NISQ devices. Furthermore, we provide theoretical analysis of the QDE's dynamical properties for the 2-qubit case and discuss its potential universality. Overall, this study represents our first step towards leveraging near-term quantum devices for time series forecasting, offering insights into integrating data-driven learning with quantum dynamical embeddings.

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arXiv2025

Low-Overhead and High-Fidelity Preparation of Logical Non-Clifford States with Multi-Level Transversal Injection

Rotation gates are widely used in various quantum algorithms. To implement fault-tolerant rotation gates, state distillation or gate synthesis is typically employed. However, the overhead of these schemes scales rapidly with increasing Clifford hierarchy levels and required fidelity, limiting their use in large-scale quantum algorithms. In this letter, we propose a method termed multi-level transversal injection (MLTI) for preparing rotation states at arbitrary Clifford hierarchy levels, which achieves high fidelity while significantly reducing overhead compared to previous methods. Unlike the linear cost scaling of state distillation, the overhead of MLTI drops with Clifford hierarchy levels and then plateaus at higher levels, slashing the required space-time volume by up to several orders of magnitude. Additionally, we introduce a method for eliminating the off-diagonal terms of rotation states without extra overhead, unifying the metrics of infidelity and trace distance. These results render the overhead for high-precision rotation gates no longer prohibitive, and thus bring the broad adoption of large-scale quantum algorithms a critical step closer to reality.

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arXiv2025

Quantum Computational Insurance and Actuarial Science

In recent years, quantum computation has been rapidly advancing, driving a technological revolution with significant potential across various sectors, particularly in finance. Despite this, the insurance industry, an essential tool for mitigating unforeseen risks and losses, has received limited attention. This paper provides an initial exploration into the realm of quantum computational insurance and actuarial science. After introducing key insurance models and challenges, we discuss quantum algorithms that can address insurance problems based on their mathematical nature. Our study includes experimental and numerical demonstrations of quantum applications in non-life insurance, life insurance, and reinsurance. Additionally, we explore the timeline for quantum insurance, the development of quantum-enhanced insurance products, and the challenges posed by quantum computational advancements. This work systematically constructs the connection between quantum computation and the insurance industry, enhancing the development of insurance while promoting the application of quantum computation to more realistic problems.

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arXiv2025

A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations

The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing.

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arXiv2025

Refined Criteria for QRAM Error Suppression via Efficient Large-Scale QRAM Simulator

Quantum random access memory (QRAM) is a critical primitive for quantum algorithms that require data lookup in superposition, but its lack of fault tolerance poses a major obstacle to practical deployment. Error filtration (EF) has been proposed as a hardware-efficient alternative to error correction, capable of suppressing incoherent noise without encoding overhead. However, its performance in realistic QRAM systems with moderate fidelity has remained unclear, as existing analyses rely on asymptotic approximations and numerical simulations have been limited to small sizes. We address this gap using a new simulator for bucket-brigade (BB) QRAM that combines sparse state encoding with a noise-aware pruning algorithm. This framework provides full quantum state access and scales efficiently, enabling us to probe EF performance in size and noise regimes far beyond previous studies. Our simulations reveal suppression anomalies at high noise levels or large address sizes, where post-selection probability fundamentally constrains EF scaling. Incorporating this effect, we refine EF theory into near-deterministic criteria linking base infidelity to achievable suppression, thereby delineating the regime in which EF yields progressive improvement. Beyond refining EF, we quantitatively characterize the runtime and memory costs of our noisy BB QRAM simulator, achieving simulations of systems with 20 layers using less than 1 GB of memory. This efficiency is what enables us to probe parameter regimes beyond previous work and to establish the simulator as a practical, ``fine-print'' analysis tool for assessing QRAM as a quantum resource.

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arXiv2025

Quantum State Preparation by Improved MPS Method

Efficient encoding of classical information plays a fundamental role in numerous practical quantum algorithms. However, the preparation of an arbitrary amplitude-encoded state has been proven to be time-consuming, and its deployment on current noisy devices can be challenging. In this work, we propose an improved Matrix Product State(MPS) method preparation protocol with an exponential reduction on the circuit depth, as well as topological adaptability. By refined utilization of the disentangling principle, we also reduce approximately 33% two-qubit gate count. To validate our method, we study various families of functions and distributions with provably bounded MPS rank. Numerical experiments show that our method significantly reduces circuit depth while achieving higher fidelity for states arising in financial and other applications.

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arXiv2025

Towards Fault-Tolerant Quantum Deep Learning: Designing and Analyzing Quantum ResNet and Transformer with Quantum Arithmetic and Linear Algebra Primitives

Achieving a practical quantum speedup for deep neural networks (DNNs) remains a central yet elusive goal, hindered by the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement. We introduce a framework to overcome these barriers, specifically targeting an asymptotic speedup with respect to the large input dimensions of modern DNNs (e.g., sequence length or image size). Our framework enables the design of multi-layer Quantum ResNet and Quantum Transformer models by strategically decomposing tasks: computationally intensive operations on the large input dimension are assigned to quantum linear algebra subroutines, while operations on the smaller, fixed feature dimension are handled by efficient quantum arithmetic. A cornerstone of our approach is a novel data transfer protocol, Discrete Chebyshev Decomposition (DCD), which facilitates this modularity. Numerical validation reveals a pivotal insight: the measurement cost required to maintain a target accuracy scales sublinearly with the input dimension. This sublinear scaling is the key to preserving the quantum advantage, ensuring that I/O overhead does not nullify the computational gains. A rigorous resource analysis further corroborates the superiority of our models in both efficiency and flexibility. Powered by this targeted acceleration strategy and the efficiency of DCD, our framework establishes a viable path toward scalable quantum deep learning.

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