arXiv subjects

Xi-Ning Zhuang

Publications and source records attributed to Xi-Ning Zhuang.

At least 19 recordsLinked to original sources

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

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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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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arXiv2025

Simulation of open quantum systems on universal quantum computers

The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting non-unitary dynamics make quantum simulation challenging with only unitary quantum gates. In this work, we present an innovative and scalable method to simulate open quantum systems using quantum computers. We define an adjoint density matrix as a counterpart of the true density matrix, which reduces to a mixed-unitary quantum channel and thus can be effectively sampled using quantum computers. This method has several benefits, including no need for auxiliary qubits and noteworthy scalability. Moreover, some long-time properties like steady states and the thermal equilibrium can also be investigated as the adjoint density matrix and the true dissipated one converge to the same state. Finally, we present deployments of this theory in the dissipative quantum $XY$ model for the evolution of correlation and entropy with short-time dynamics and the disordered Heisenberg model for many-body localization with long-time dynamics. This work promotes the study of real-world many-body dynamics with quantum computers, highlighting the potential to demonstrate practical quantum advantages.

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arXiv2025

PolyQROM: Orthogonal-Polynomial-Based Quantum Reduced-Order Model for Flow Field Analysis

Quantum computing promises exponential acceleration for fluid flow simulations, yet the measurement overhead required to extract flow features from quantum-encoded flow field data fundamentally undermines this advantage--a critical challenge termed the ``output problem''. To address this, we propose an orthogonal-polynomial-based quantum reduced-order model (PolyQROM) that integrates orthogonal polynomial basis transformations with variational quantum circuits (VQCs). PolyQROM employs optimized polynomial-based quantum operations to compress flow field data into low-dimensional representations while preserving essential features, enabling efficient quantum or classical post-processing for tasks like reconstruction and classification. By leveraging the mathematical properties of orthogonal polynomials, the framework enhances circuit expressivity and stabilizes training compared to conventional hardware-efficient VQCs. Numerical experiments demonstrate PolyQROM's effectiveness in reconstructing flow fields with high fidelity and classifying flow patterns with accuracy surpassing classical methods and quantum benchmarks, all while reducing computational complexity and parameter counts. The work bridges quantum simulation outputs with practical fluid analysis, addressing the ``output problem'' through efficient reduced-order modeling tailored for quantum-encoded flow data, offering a scalable pathway to exploit quantum advantages in computational fluid dynamics.

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arXiv2025

SparQSim: Simulating Scalable Quantum Algorithms via Sparse Quantum State Representations

Efficient simulation of large-scale quantum algorithms is pivotal yet challenging due to the exponential growth of the state space inherent in both Schödinger-based and Feynman-based methods. While Feynman-based simulators can be highly efficient when the quantum state is sparse, these simulators often do not fully support the simulation of large-scale, complex quantum algorithms which rely on QRAM and other oracle-based operations. In this work, we present SparQSim, a quantum simulator implemented in C++ and inspired by the Feynman-based method. SparQSim operates at the register level by storing only the nonzero components of the quantum state, enabling flexible and resource-efficient simulation of basic quantum operations and integrated QRAM for advanced applications such as quantum linear system solvers. In particular, numerical experiments on benchmarks from QASMBench and MQTBench demonstrate that SparQSim outperforms conventional Schrödinger-based simulators in both execution time and memory usage for circuits with high sparsity. Moreover, full-process simulations of quantum linear system solvers based on a discrete adiabatic method yield results that are consistent with theoretical predictions. This work establishes SparQSim as a promising platform for the efficient simulation of scalable quantum algorithms.

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arXiv2025

Scalable Constant-Time Logical Gates for Large-Scale Quantum Computation Using Window-Based Correlated Decoding

Large-scale quantum computation requires to be performed in the fault-tolerant manner. One crucial challenge of fault-tolerant quantum computing (FTQC) is reducing the overhead of implementing logical gates. Recently work proposed correlated decoding and ``algorithmic fault tolerance" to achieve constant-time logical gates that enables universal quantum computation. However, for circuits involving mid-circuit measurements and feedback, the previous scheme for constant-time logical gates is incompatible with window-based decoding, which is a scalable approach for handling large-scale circuits. In this work, we propose an architecture that employs delayed fixup circuits and window-based correlated decoding, realizing scalable constant-time logical gates. This design significantly reduces both the frequency and duration of decoding, while maintaining support for constant-time and universal logical gates across a broad class of quantum codes. More importantly, by spatial parallelism of windows, this architecture well adapts to time-optimal FTQC, making it particularly useful for large-scale quantum computation. Using Shor's algorithm as an example, we explore the application of our architecture and reveals the promising potential of using constant-time logical gates to perform large-scale quantum computation with acceptable overhead on physical systems like ion traps.

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arXiv2024

Hardware-Efficient Quantum Random Access Memory Design with a Native Gate Set on Superconducting Platforms

Quantum Random Access Memory (QRAM) is a critical component for enabling data queries in superposition, which is the cornerstone of quantum algorithms. Among various QRAM architectures, the bucket-brigade model stands out due to its noise resilience. This paper presents a hardware-efficient native gate set {iSCZ, C-iSCZ} for implementing bucket-brigade QRAM on superconducting platforms. The experimental feasibility of the proposed gate set is demonstrated, showing high fidelity and reduced complexity. By leveraging the complementary control property in QRAM, our approach directly substitutes the conventional {SWAP, CSWAP} gates with the new gate set, eliminating decomposition overhead and significantly reducing circuit depth and gate count.

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