强关联系统中 Trotter 化 MERA 的收敛性与量子优势
Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
AI总结：
本文分析 Trotter 化 MERA VQE 模拟临界自旋链的成本标度，证明其相对经典方法具有多项式量子优势，并提出逐层初始化、相图扫描及小角度电路改进收敛与实验可行性。
摘要：
强关联量子多体系统难以用经典方法研究和模拟。我们最近提出了一种基于多尺度纠缠重整化拟设（MERA）的变分量子本征求解器（VQE），其中张量被约束为特定的 Trotter 电路。本文中，我们确定了各种临界自旋链的计算成本标度，这证实了与基于精确能量梯度或变分蒙特卡洛的经典 MERA 模拟相比，该方法具有多项式量子优势。算法相图表明，对于更高维系统，分离程度甚至更大。因此，Trotter 化 MERA VQE 是在量子计算机上高效研究强关联量子多体系统的一条有前景的途径。此外，我们展示了如何通过在初始化阶段逐层构建 MERA，并在优化过程中扫描相图，从而显著改善收敛性。由于 Trotter 电路由单量子比特和双量子比特旋转组成，较小的旋转角度在实验上具有优势。我们发现，平均角度幅度可以大幅减小，而对能量精度的影响可以忽略。基准模拟表明，TMERA 张量的 Trotter 电路结构并非决定性因素；具体而言，brick-wall 电路和 parallel random-pair 电路产生了非常相似的能量精度。
英文摘要：
Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
