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Xiao Yuan

Publications and source records attributed to Xiao Yuan.

At least 37 records · Page 2Linked to original sources
arXiv2026

No Cloning of Quantum Ensembles

Modern quantum physics now enables control of quantum systems at the level of individual trajectories, opening a new frontier that links quantum information theory, quantum many-body physics, and quantum thermodynamics, and uncovers novel non-equilibrium phenomena such as deep thermalization and measurement-induced entanglement. However, a central challenge remains: their characterization relies on measuring nonlinear properties of individual quantum states, a task tantamount to fine-grained cloning of a quantum ensemble. Here, the fundamental laws governing the cloning of quantum ensembles are investigated. First, a general no-cloning theorem for arbitrary ensembles is established from an information-theoretic perspective, even assuming multiple copies of the ensemble's purification. It is then shown that this barrier can be unexpectedly circumvented for physical ensembles generated by finite-time evolutions. Nevertheless, these tasks are proven to remain computationally intractable, even when the full circuit description of state preparation is known. This stands in sharp contrast to the conventional no-cloning theorem, which relies on the state being unknown. Together, these results establish new fundamental principles of quantum mechanics, reveal intrinsic trade-offs among sample complexity, computational complexity, and quantum measurements, and highlight the necessity of problem-specific strategies for probing measurement-induced quantum phenomena.

quant-ph↗
arXiv2026

Efficient Noisy Quantum State and Process Tomography

Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system size. Here, we introduce a structure-agnostic learning framework for noisy $n$-qubit quantum circuits under~i.i.d.~single-qubit noise. We first prove that quantum states with unital noise channels admit an efficient learnable representation in the logarithmic-depth regime. We then extend this framework to quantum process tomography under constant noise, deriving a unified protocol that applies to both unital and non-unital noisy channels and retains efficient guarantees for logarithmic-depth circuits. This process-learning formulation is input-agnostic and imposes no distributional assumptions on the input quantum states. We further study a more general regime with arbitrary noise strength. In this setting, low-weight Pauli propagation induces a terminal truncation whose threshold depends logarithmically on the inverse accuracy, leading to quasi-polynomial complexity and near-unit success probability in the average case. In contrast to the preceding two results, this arbitrary-noise guarantee does not impose any restriction on the circuit depth, and therefore covers arbitrary-depth circuits, including both the noiseless limit ($γ= 0$) and the strong-decoherence regime ($γ= Θ(1)$). Numerical simulations of two-dimensional Hamiltonian dynamics further demonstrate the accuracy and robustness of the approach, including for structured circuits beyond the random-circuit setting assumed in the theoretical analysis. These results provide a scalable and practically relevant route toward characterizing large-scale noisy quantum devices, addressing a key bottleneck in the development of quantum technologies.

quant-ph↗
arXiv2026

A Three-Layer Architecture for Fault-Tolerant Quantum Computing

Fault tolerance is an indispensable prerequisite for constructing large-scale universal quantum computers. Drawing philosophies from classical computer architecture, this paper presents a hardware-agnostic three-layer high-level architectural framework for generic fault-tolerant quantum computation. Guided by the real execution workflows of fault-tolerant quantum algorithms, the proposed model is decoupled from specific physical qubit hardware platforms and quantum error correction codes, serving as a universal abstract standard rather than a platform-specific implementation scheme. Special attention is devoted to the intermediate Fault-Tolerance Layer, which serves as the architectural bridge between application-level logical programs and hardware-level execution. We systematically characterize its five internal components, the interfaces and data exchanged among them, and the execution, correction, and adaptation paths that together enable logical synthesis, fault-tolerant resources management, decoding, and runtime fault-tolerant control. An end-to-end example is further provided to illustrate the full-stack operating pipeline of fault-tolerant quantum algorithms under this framework. Given the increasing emphasis on modular, heterogeneous, and cross-layer fault-tolerant quantum systems, our architecture provides a unified foundational model for organizing such designs.

quant-ph↗
arXiv2026

Complexity-driven transitions in quantum observation

Observing the physical world is a foundational pursuit in science. In the quantum realm, however, observation necessitates a fundamental quantum-to-classical conversion: destructive measurements irreversibly project quantum states into classical data, inevitably incurring a loss of information. What physical principles govern this information loss, and how can we construct optimal measurements to maximize the readout? Here, we address these questions by establishing an intrinsic relationship between readout capability--quantified by the ratio of accessible classical Fisher information to the total quantum Fisher information (QFI), and measurement complexity--defined as the quantum circuit depth required prior to projection. Remarkably, we uncover a sudden emergence of observability: a sharp hidden-to-visible transition driven entirely by measurement complexity. We rigorously prove that below critical depth thresholds--$Θ((\log n)^{1/δ})$ for $δ$-dimensional architectures and $Θ(\log\log n)$ for all-to-all connectivity--readout capability decays exponentially with system size $n$, rendering the quantum information fundamentally inaccessible. Surprisingly, immediately above this threshold, the system enters a visible regime: we demonstrate that randomized measurements universally recover a constant fraction of the QFI using approximate unitary 3-designs, for which we explicitly develop optimal-depth circuit constructions tailored to finite-dimensional architectures. By unveiling the fundamental scaling laws and transitions that govern quantum observation, our results delineate definitive resource boundaries for quantum learning, state certification, and quantum metrology.

quant-ph↗
arXiv2026

A Resource Comparison of Logical T-State Preparation

Logical T state preparation is a major overhead source in fault tolerant architectures built from stabilizer operations. Existing protocols, however, are reported under different code families, noise models, postselection rules, and cost conventions, making direct comparison difficult. We compare three representative preparation routes: magic state distillation, magic state cultivation, and code switching, using currently available results. Rather than reducing heterogeneous data to a single cost metric, we retain source native cost units and record output error, single attempt cost, expected cost per accepted output, footprint, latency, and reporting completeness for each configuration. Within the current dataset, distillation reaches the lowest output error regime; code switching achieves the lowest reported single attempt cost and the smallest explicit footprint among the compatible rows; and recent RP2 cultivation results add low cost cultivation points with output errors between 1e-6 and 1e-9. As a simple algorithm level case study, we also examine the reported preparation routes under an error budget motivated by Shor factoring algorithm, in order to relate single state preparation costs to full workload requirements. The resulting comparison clarifies the trade offs currently supported across the literature, while remaining bounded by the conventions and coverage of the underlying papers.

quant-ph↗
arXiv2026

A Variational Dissipative Framework for Quantum Algorithms

Dissipation engineering has attracted growing interest as an approach to controlling open quantum systems through engineered system-environment interactions. Standard variational quantum circuits are usually built from unitary operations and therefore explore only a restricted family of states. To go beyond this limitation, we introduce a variational dissipative framework in which ancilla-assisted engineered dissipation is incorporated into parameterized quantum algorithms. In this framework, system-only variational layers are combined with trainable dissipative modules, so that the circuit can prepare a broader class of mixed states through ancilla-assisted nonunitary transformations. Within this framework, the same ancilla-assisted dissipative block is used in two representative settings with different objectives. For ground-state search, it is integrated into a dissipative variational quantum eigensolver to improve the convergence toward low-energy states. For state recovery, it is trained as a recovery channel to suppress preparation noise and enhance fidelity with the target state. In both cases, the block is realized through parameterized system-ancilla couplings followed by ancilla reset and trace-out. Our results show that engineered dissipation can be incorporated into variational quantum circuits as a reusable trainable primitive rather than treated only as a source of noise. In this sense, the proposed framework identifies ancilla-assisted dissipative channels as a concrete variational resource that can support both optimization and recovery tasks within a unified design.

quant-ph↗
arXiv2026

Geometric encoding of turbulence for end-to-end quantum simulation

Multiscale organization is a hallmark of fluid turbulence in aerospace, energy, and transport systems. While quantum computing promises exponential speedups for solving the evolution equations governing flow fields, this potential is fundamentally hindered by the quantum state preparation bottleneck, the prohibitive cost of loading classical complex data into quantum states. Here, we overcome this barrier by introducing a physics-informed, three-stage geometric encoding method "turbuloscope", which efficiently generates turbulent fields relevant to high-Reynolds-number engineering flows. Rather than brute-force data loading, our approach acts as a kaleidoscope, leveraging the multiscale structures of turbulence. We capture scale-invariant self-similarity via a hyperplane approximation in high-dimensional feature space, and utilize the Hopf fibration to map quantum observables directly onto vortex tubes, the fundamental building blocks of turbulence that control mixing, drag, and heat transfer in mechanical systems. Remarkably, the algorithm requires no ancillary qubits, utilizes a linear-depth quantum circuit, and scales logarithmically with the Reynolds number, an exponential speedup compared to classical methods. We demonstrate the power of this method by generating an instantaneous turbulent field at a high Reynolds number of 35,000 across over one billion grid points using only 30 qubits, reproducing Kolmogorov's 5/3 energy spectrum, tangled vortex structures, and strong intermittency. This asymptotically optimal approach not only signals a near-term pathway to practical quantum advantage in engineering simulation, but establishes a scalable foundation for the quantum simulation of broad multiscale systems.

quant-ph↗
arXiv2026

Universal Analog Quantum Simulation

Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying hardware, restricting the Hamiltonians that can be realized and limiting programmability. Here we introduce universal analog quantum simulation (UAQS), a hybrid framework that systematically expands the range of accessible quantum evolutions within a given analog platform. UAQS employs optimized continuous-time control fields to engineer target dynamics directly, avoiding decomposition into discrete gate sequences. By preserving native analog evolution while extending the set of achievable Hamiltonians, UAQS transforms fixed-interaction analog devices into programmable simulators. Numerical studies on representative architectures, including superconducting circuits and Rydberg-atom arrays, show that UAQS accurately reproduces non-trivial many-body dynamics beyond the intrinsic interaction structure of the hardware. These results establish UAQS as a practical route toward programmable analog quantum simulation.

quant-ph↗
arXiv2026

Theory of Quantum Imaginary-Time Mpemba Effect

Quantum imaginary-time evolution (QITE) is a fundamental framework for preparing ground and thermal states, yet its computational cost scales significantly with the evolution duration $τ$. Reducing this duration is critical for practical quantum advantage. Here, we establish a unified theoretical framework for the Mpemba effect in QITE -- a counterintuitive phenomenon where a state initially farther from the ground state relaxes to it faster than one initially closer. We derive a remarkably simple necessary and sufficient condition for the occurrence of this effect, showing it is uniquely determined by the population ratios of excited states to the ground state. For practical state preparation, we introduce a rigorous sufficient condition for the finite-time Mpemba effect, ensuring the crossing occurs before reaching a prescribed proximity threshold. Furthermore, we unveil unique dynamical features, including a multiple-crossing phenomenon in multi-level systems and simultaneous intersections for collinear initial states. Our results provide criteria for identifying favorable initial states in QITE and offer deep insights into the speed limit of quantum state preparation.

quant-ph↗
arXiv2026

A unified framework for efficient quantum simulation of nonlinear spectroscopy

Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is fundamentally limited by the exponential growth of the Hilbert space, and practical quantum algorithms for the nonlinear regime have remained largely unexplored. Here, we present a unified quantum algorithmic framework for computing $n$-th order nonlinear spectroscopies. By reformulating multi-time responses as a weighted sum of expectation values at finite pump amplitudes via a generalized parameter shift rule, our approach bypasses the costly evaluation of high-order commutators and time-dependent operator expansions. This reformulation enables efficient execution via real-time evolution on current quantum hardware, ensuring inherent noise resilience. We validate the framework on IBM's superconducting quantum processors, successfully obtain higher-order response functions of a 12-qubit XXZ spin-chain. Furthermore, the versatility of our method is demonstrated by resolving quasi-particle excitation spectra in spin-liquids and identifying interaction-induced cross-peaks in atomic systems. Our results establish a practical and scalable pathway for probing complex quantum dynamics on near-term quantum devices, extending the reach of quantum simulation into the nonlinear domain.

quant-ph↗
arXiv2026

A Review of Variational Quantum Algorithms: Insights into Fault-Tolerant Quantum Computing

Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers an insightful analysis of VQAs and their progression toward the fault-tolerant regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.

quant-ph↗
arXiv2026

Efficient Preparation of Quantum States via Randomized Truncation

While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a small number of large components alongside a vast number of small but non-negligible ones. Standard approaches deterministically truncate the small amplitude would incur an approximation error that scales linearly with the discarded amplitude mass, enforcing a rigid trade-off between precision and circuit depth. Here, we circumvent the challenge by introducing a randomized state-preparation protocol with probabilistic amplification of small amplitudes using ensembles of low-complexity circuits. Analytically, we prove that this approach significantly reduces the number of encoded amplitudes, halving the requirement for exponentially decaying states and offering asymptotically larger gains for heavy-tailed power-law decays. Numerical simulations on LiH molecular wavefunctions and deep-learning-derived states demonstrate reductions of up to 99 percent in CNOT and T-gate counts compared with deterministic methods. These results establish a resource-efficient paradigm for initializing complex states, relaxing gate-synthesis precision requirements for both near-term and fault-tolerant hardware, and improving the end-to-end feasibility of quantum computing.

quant-ph↗
arXiv2026

Constraint-Aware Quantum Optimization via Hamming Weight Operators

Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales. The Quantum Approximate Optimization Algorithm (QAOA) offers a promising quantum framework, but conventional penalty-based formulations distort optimization landscapes and demand deep circuits, undermining scalability on near-term hardware. In this work, we introduce Hamming Weight Operators, a new class of constraint-aware operators that confine quantum evolution strictly within the feasible subspace. Building on this idea, we develop Adaptive Hamming Weight Operator QAOA, which dynamically selects the most effective operators to construct shallow, problem-tailored circuits. We validate our approach on benchmark tasks from both finance and high-energy physics, specifically portfolio optimization and two-jet clustering with energy balance. Across these problems, our method inherently satisfies all constraints by construction, converges faster, and achieves higher Approximation Ratios than penalty-based QAOA, while requiring roughly half as many gates. By embedding constraint-aware operators into an adaptive variational framework, our approach establishes a scalable and hardware-efficient pathway for solving practical constrained optimization problems on near-term quantum devices.

quant-ph↗
arXiv2025

Computing n-time correlation functions without ancilla qubits

The $n$-time correlation function is pivotal for establishing connections between theoretical predictions and experimental observations of a quantum system. Conventional methods for computing $n$-time correlation functions on quantum computers, such as the Hadamard test, generally require an ancilla qubit that controls the entire system -- an approach that poses challenges for digital quantum devices with limited qubit connectivity, as well as for analog quantum platforms lacking controlled operations. Here, we introduce a method to compute $n$-time correlation functions using only unitary evolutions on the system of interest, thereby eliminating the need for ancillas and the control operations. This approach substantially relaxes hardware connectivity requirements for digital processors and enables more practical measurements of $n$-time correlation functions on analog platforms. We demonstrate our protocol on IBM quantum hardware up to 12 qubits to measure the single-particle spectrum of the Schwinger model and the out-of-time-order correlator in the transverse-field Ising model. In the demonstration, we further introduce an error mitigation procedure based on signal processing that integrates signal filtering and correlation analysis, and successfully reproduces the noiseless simulation results from the noisy hardware. Our work highlights a route to exploring complex quantum many-body correlation functions in practice, even in the presence of realistic hardware limitations and noise.

quant-ph↗
arXiv2025

Estimating Local Observables via Cluster-Level Light-Cone Decomposition

Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work, we introduce a framework based on Cluster-level Light-cone analysis that leverages the natural locality of quantum workloads. We propose two complementary algorithms: the Causal Decoupling Algorithm, which exploits geometric disconnections in the light cone for sampling efficiency, and the Algebraic Decomposition Algorithm, which utilizes algebraic expansion to minimize hardware requirements. These methods allow simulation costs to depend on circuit depth and connectivity rather than system size. Together, our results generalize Lieb-Robinson-inspired locality to modular architectures and establish a quantitative framework for probing local physics on near-term quantum devices by decoupling the simulation cost from the global system size.

quant-ph↗
arXiv2025

Efficient Quantum Simulation of Non-Adiabatic Molecular Dynamics with Precise Electronic Structure

In the study of non-adiabatic chemical processes such as photocatalysis and photosynthesis, non-adiabatic molecular dynamics (NAMD) is an indispensable theoretical tool, which requires precise potential energy surfaces (PESs) of ground and excited states. Quantum computing offers promising potential for calculating PESs that are intractable for classical computers. However, its realistic application poses significant challenges to the development of quantum algorithms that are sufficiently general to enable efficient and precise PES calculations across chemical systems with diverse properties, as well as to seamlessly adapt existing NAMD theories to quantum computing. In this work, we introduce a quantum-adapted extension to the Landau-Zener-Surface-Hopping (LZSH) NAMD. This extension incorporates curvature-driven hopping corrections that protect the population evolution while maintaining the efficiency gained from avoiding the computation of non-adiabatic couplings (NACs), as well as preserving the trajectory independence that enables parallelization. Furthermore, to ensure the high-precision PESs required for surface hopping dynamics, we develop a sub-microhartree-accurate PES calculation protocol. This protocol supports active space selection, enables parallel acceleration either on quantum or classical clusters, and demonstrates adaptability to diverse chemical systems - including the charged H3+ ion and the C2H4 molecule, a prototypical multi-reference benchmark. This work paves the way for practical application of quantum computing in NAMD, showcasing the potential of parallel simulation on quantum-classical heterogeneous clusters for ab-initio computational chemistry.

physics.chem-ph↗
arXiv2025

BeeTLe: An Imbalance-Aware Deep Sequence Model for Linear B-Cell Epitope Prediction and Classification with Logit-Adjusted Losses

The process of identifying and characterizing B-cell epitopes, which are the portions of antigens recognized by antibodies, is important for our understanding of the immune system, and for many applications including vaccine development, therapeutics, and diagnostics. Computational epitope prediction is challenging yet rewarding as it significantly reduces the time and cost of laboratory work. Most of the existing tools do not have satisfactory performance and only discriminate epitopes from non-epitopes. This paper presents a new deep learning-based multi-task framework for linear B-cell epitope prediction as well as antibody type-specific epitope classification. Specifically, a sequenced-based neural network model using recurrent layers and Transformer blocks is developed. We propose an amino acid encoding method based on eigen decomposition to help the model learn the representations of epitopes. We introduce modifications to standard cross-entropy loss functions by extending a logit adjustment technique to cope with the class imbalance. Experimental results on data curated from the largest public epitope database demonstrate the validity of the proposed methods and the superior performance compared to competing ones.

q-bio.QM↗
arXiv2025

Quantum computing quantum Monte Carlo algorithm

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.

quant-ph↗