density-matrix simulation

This work addresses the challenge of efficiently preparing quantum samples (qsamples)—coherent encodings of arbitrary probability distributions—on quantum computers. We establish a deep connection between classical continuous normalizing flows and quantum dynamics: the probabilistic transformation in flow models is mapped to unitary evolution governed by the Schrödinger equation, enabling explicit construction of the corresponding Hamiltonian. Leveraging this insight, we design a scalable quantum algorithm that integrates flow matching, diffusion modeling, and continuous-time Markov process principles to generate qsamples for broad distribution families—including non-Gaussian and multimodal distributions—with provable efficiency. This constitutes the first systematic framework translating classical generative models into quantum state preparation protocols. Our approach provides rigorous quantum advantage for statistical tasks such as mean estimation and property testing, overcoming longstanding limitations of oracle-dependent or distribution-restricted quantum sampling methods.

This work addresses quantum algorithms for solving linear and nonlinear ordinary differential equations (ODEs), overcoming prior limitations requiring matrix diagonalizability or normality. Methodologically, it introduces the matrix exponential norm as a key runtime criterion for linear ODE solvers—the first such formulation—and enhances the Carleman linearization framework by integrating quantum linear system algorithms (HHL-type), quantum matrix exponentiation, logarithmic norm analysis, and techniques for non-normal matrices. Contributions include: (1) exponential quantum speedup for sparse, invertible linear ODEs—even when non-diagonalizable or possessing negative logarithmic norms; and (2) a dramatic improvement in error scaling for nonlinear ODEs, reducing dependence from polynomial to logarithmic order. The algorithm significantly broadens applicability beyond Berry (2017) and Liu–Xue (2021), and is the first to support generalized dissipative structures.

This work addresses the accuracy–resource trade-off arising from high-dimensional encoding and bosonic mode truncation in fermion–boson coupled systems—such as those involving photons or phonons—for quantum simulation. We propose a compact, error-bound-driven adaptive truncation scheme for bosonic modes. Furthermore, we develop a hardware-aware and computationally efficient fermion–boson-to-qubit mapping method, integrating variants of the Jordan–Wigner and Bravyi–Kitaev encodings, combined with Hamiltonian downfolding and Trotter step optimization. Our approach enables high-fidelity approximation of both static observables and time-resolved dynamics, achieving significant reductions in qubit count and gate complexity while guaranteeing simulation accuracy within a rigorously bounded error tolerance. This provides a scalable theoretical framework and practical toolkit for quantum simulation of realistic physical systems with bosonic degrees of freedom.

This study addresses the long-standing challenge of efficiently computing local thermodynamic expectations for the Sachdev-Ye-Kitaev (SYK) model and classical spin glasses at arbitrary constant temperatures. To overcome the theoretical limitations inherent in conventional high-temperature approximations, this work proposes a rigorous quantum cavity method alongside polynomial-time classical simulation techniques. The primary contribution is the first proof establishing the polynomial-time computability of thermal-state observables in strongly interacting systems across all constant temperatures, with these results further extended to the domain of classical phase transitions. Additionally, a quantum algorithm for learning SYK Hamiltonians from Gibbs states is introduced, yielding significant improvements in sample complexity.

Quantum linear solvers (e.g., HHL) applied to discretized PDEs suffer from complexity scaling polynomially with the condition number κ, which typically grows polynomially with system size N—constituting a fundamental bottleneck. Method: We propose the first κ-independent quantum PDE solver framework, introducing wavelet bases as auxiliary coordinates and integrating diagonal preconditioning to render the preconditioned system’s condition number independent of N. Building upon this, we design a quantum algorithm with polylogarithmic complexity. Contribution/Results: We rigorously prove the overall query and gate complexity is poly(log N). Numerical experiments confirm substantial reduction in effective condition number across diverse PDEs—including elliptic, parabolic, and convection-diffusion equations—and demonstrate efficient extraction of solution features from the output quantum state. This work establishes the first theoretically sound and practically viable κ-independent quantum framework for PDE solving.

This work addresses bosonic quantum systems with Kerr nonlinearity—central to universal bosonic quantum computation and driven Bose-Hubbard models—and proposes a Schrödinger-picture simulation method based on sparse superpositions of coherent states. By introducing an error-controlled truncation scheme and approximation mechanism, the approach substantially reduces computational complexity under conditions of weak nonlinearity or a limited number of Kerr gates. The study establishes the first scalable classical simulation framework, demonstrating quasi-polynomial-time simulability for logarithmically many Kerr gates and delineating a polynomial-time simulable regime in the weak-nonlinearity limit. Numerical experiments on fully connected Bose-Hubbard models reproduce benchmark results obtained with Fock-state and matrix product state methods, confirming the method’s validity and practical potential.

Quantum computers, constrained by unitary evolution, struggle to directly simulate nonlinear dynamical systems. This work proposes a quantum Koopman approach that leverages data-driven learning of Koopman observables to embed nonlinear dynamics into a linear space, enabling their evolution via shallow, parallelized quantum circuits. The method is experimentally demonstrated on a superconducting quantum processor, achieving the first successful quantum simulations of reaction–diffusion systems, spherical fluid flows, and observational Gulf Stream data, accurately reproducing multiscale patterns and statistical properties. Validation across 32 parallel circuits, each comprising 10 qubits, confirms the efficacy of the approach while revealing fundamental limitations imposed by hardware noise and Koopman embedding dimensionality on simulation fidelity.

This work proposes an efficient digital quantum simulation method for time-dependent Hamiltonian evolution, under the assumption that the initial state is confined to a low-energy subspace. By integrating product formulas, adiabatic perturbation theory, and time-dependent commutator-based error analysis, the authors derive—for the first time—a rigorous error bound for simulating dynamics within this low-energy subspace. The analysis demonstrates a significant reduction in the required number of Trotter steps compared to full-space simulation and establishes a lower bound on the query complexity for general time-dependent quantum simulation. The approach exhibits superior resource efficiency and promising applicability in nonequilibrium many-body dynamics and adiabatic quantum state preparation.

This work addresses why macroscopic systems exhibit classical behavior and lack quantum interference by examining the role of computational complexity. It argues that if quantum systems cannot efficiently solve NP-complete problems, then certain formally valid quantum measurements are physically unrealizable, rendering the corresponding quantum states either unobservable or inaccessible. By integrating tools from quantum information theory, computational complexity, and linear algebra, the study establishes a direct link between computational constraints and phenomena such as quantum unobservability, state inaccessibility, and decoherence. The authors prove that specific Pauli operators in certain bases are unobservable, demonstrate the absence of physically realizable evolution paths between particular quantum states, and show that some superpositions are empirically indistinguishable from mixed states. These findings suggest that the emergence of classicality at macroscopic scales may stem fundamentally from computational complexity limitations, rather than solely from environmental decoherence.

PQLS是用于开放量子系统稳态模拟的高性能Python库，通过分层API设计和基于JAX、XLA的硬件加速计算方法，解决了大规模参数扫描效率低的问题。