标题： 基于动态簇的张量网络算法优化方法用于量子电路模拟 显示英文标题

标题： Dynamical cluster-based optimization of tensor network algorithms for quantum circuit simulations

摘要： 我们通过利用电路中纠缠操作的不规则排列，优化了基于矩阵乘积态（MPS）的算法，用于模拟具有有限保真度的量子电路，特别是时间演化块消去（TEBD）和密度矩阵重正则化群（DMRG）算法。我们引入了一种标准TEBD算法的变化形式，我们称之为“簇-TEBD”，它动态地将量子比特分组为纠缠簇，从而在单个时间步内精确收缩多个电路层。此外，我们通过引入一种自适应协议来增强DMRG算法，该协议分析每个待收缩电路部分中的纠缠分布，并在每次迭代中动态调整量子比特分组。我们分析了这些增强算法在模拟稳定子和非稳定子随机电路中的性能，最多达到$1000$个量子比特和$100$层克利福德和非克利福德门，并在模拟Shor量子算法时涉及数万个层次。我们的研究结果表明，即使每个任务的计算资源合理，基于簇的方法也可以显著加快大规模量子电路的模拟，并提高最终状态的保真度。 显示英文摘要

摘要： We optimize Matrix-Product State (MPS)-based algorithms for simulating quantum circuits with finite fidelity, specifically the Time-Evolving Block Decimation (TEBD) and the Density-Matrix Renormalization Group (DMRG) algorithms, by exploiting the irregular arrangement of entangling operations in circuits. We introduce a variation of the standard TEBD algorithm, we termed "cluster-TEBD", which dynamically arranges qubits into entanglement clusters, enabling the exact contraction of multiple circuit layers in a single time step. Moreover, we enhance the DMRG algorithm by introducing an adaptive protocol which analyzes the entanglement distribution within each circuit section to be contracted, dynamically adjusting the qubit grouping at each iteration. We analyze the performances of these enhanced algorithms in simulating both stabilizer and non-stabilizer random circuits, with up to $1000$ qubits and $100$ layers of Clifford and non-Clifford gates, and in simulating Shor's quantum algorithm with tens of thousands of layers. Our findings show that, even with reasonable computational resources per task, cluster-based approaches can significantly speed up simulations of large-sized quantum circuits and improve the fidelity of the final states.