矩阵乘积演化：一种用张量网络模拟量子电路的方法
Matrix Product Evolution: A Method for Simulating Quantum Circuits Using Tensor Networks
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中文总结 AI 辅助
针对量子电路经典模拟受希尔伯特空间指数增长限制的问题，提出沿电路深度构建的矩阵乘积演化（MPE）方法，开发拉链式收缩策略，经随机量子电路和多体态演化模拟验证，可作为MPS模拟的补充方法。
中文摘要 AI 辅助
量子电路的经典模拟是量子信息科学的重要工具，但其适用性受限于希尔伯特空间的指数增长和量子态的纠缠结构。本研究提出矩阵乘积演化（Matrix Product Evolution，MPE），这是一种沿电路深度而非量子比特索引构建的量子电路的张量列表示。在此框架内，量子电路的模拟被建模为多个MPE张量的收缩。我们开发了一种基于拉链过程的高效收缩策略，以在实践中实现这种收缩。我们通过随机量子电路的模拟以及量子多体态的时间演化，研究了这种基于MPE的收缩框架的数值行为。我们的结果表征了时间键维度的增长，阐明了后选择如何改变收缩成本和近似精度，并确定了深度导向的张量网络收缩可作为标准基于MPS的模拟方法的有用补充的区域。
英文摘要
Classical simulation of quantum circuits is an essential tool in quantum information science, but its applicability is constrained by the exponential growth of the Hilbert space and the entanglement structure of quantum states. In this work, we introduce Matrix Product Evolution (MPE), a tensor-train representation of quantum circuits constructed along the circuit depth rather than along the qubit index. Within this formulation, the simulation of a quantum circuit is modeled as the contraction of multiple MPE tensors. We develop an efficient contraction strategy based on a zip-up procedure to carry out this contraction in practice. We investigate the numerical behavior of this MPE-based contraction framework through simulations of random quantum circuits and the time evolution of a quantum many-body state. Our results characterize the growth of temporal bond dimensions, clarify how post-selection modifies the contraction cost and approximation accuracy, and identify regimes in which depth-oriented tensor-network contractions provide a useful complement to standard MPS-based simulation approaches.
