量子动力学模拟的加速通常需要幺正时间演化，而现实中物理模型中遇到的大型ODE/PDE系统通常是非幺正的。我们提出了一种通用动量满足的扩张，将任意线性、非厄米特流\dot x = Lx（其中L=-iH+K）嵌入到一个扩展的希尔伯特空间中的严格幺正演化中：$$ ( (l| \otimes I ) \mathcal T e^{-i \int ( I_A\otimes H +i F\otimes K) dt} ( |r) \otimes I ) = \mathcal T e^{\int L dt}, $$ 提供三元组（F, (l|, |r)）满足在辅助空间中的紧动量恒等式（l| F^{k}|r）=1对于所有k≥0。这个代数条件恢复了Schrödingerization [Phys. Rev. Lett. 133, 230602 (2024)] 和线性-组合-哈密顿量（LCHS）方案 [Phys. Rev. Lett. 131, 150603 (2023)]，同时揭示了由微分、积分、伪微分和差分生成器构建的整个新的扩张家族。每个家族都带有连续调节参数，并且在保持动量不变的相似变换下闭合，从而产生了一个庞大的设计空间，允许量子扩张与特定应用、算法和硬件共同优化。作为具体演示，我们证明了在有限区间内简单的有限差分扩张在 oracle 复杂度上达到近最优。Maxwell粘弹性波传播的数值实验证实了该方法的准确性和鲁棒性。
英文摘要：
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that embeds any linear, non-Hermitian flow $\dot x = L x$ with $L=-iH+K$ into a strictly unitary evolution on an enlarged Hilbert space: \[
( (l| \otimes I )
\mathcal T e^{-i \int ( I_A\otimes H +i F\otimes K) dt}
( |r) \otimes I )
= \mathcal T e^{\int L dt}, \] provided the triple $( F, (l|, |r) )$ satisfies the compact moment identities $(l| F^{k}|r) =1$ for all $k\ge 0$ in the ancilla space. This algebraic criterion recovers both \emph{Schrödingerization} [Phys. Rev. Lett. 133, 230602 (2024)] and the linear-combination-of-Hamiltonians (LCHS) scheme [Phys. Rev. Lett. 131, 150603 (2023)], while also unveiling whole families of new dilations built from differential, integral, pseudo-differential, and difference generators. Each family comes with a continuous tuning parameter \emph{and} is closed under similarity transformations that leave the moments invariant, giving rise to an overwhelming landscape of design space that allows quantum dilations to be co-optimized for specific applications, algorithms, and hardware.
As concrete demonstrations, we prove that a simple finite-difference dilation in a finite interval attains near-optimal oracle complexity. Numerical experiments on Maxwell viscoelastic wave propagation confirm the accuracy and robustness of the approach.
Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京国家实验室）；Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机科学与技术学院前沿计算研究中心）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技研究院）；Dahlem Center for Complex Quantum Systems, Department of Physics, Freie Universität Berlin（达勒姆复杂量子系统中心，柏林自由大学物理系）
Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
Origin Quantum Computing Technology (Hefei) Co., Ltd.（本源量子计算技术（合肥）有限公司）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）
University of Edinburgh（爱丁堡大学）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；State Key Laboratory for Novel Software Technology, Nanjing University（南京大学软件新技术国家重点实验室）；Hefei National Laboratory（合肥国家实验室）
