发表机构
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出将受等距约束的变分PEPS映射到受监控量子电路，以高效计算二维量子多体系统的可观测量，其$J_1$-$J_2$模型相图与DMRG结果定性一致，且兼容近期量子硬件。
AI 中文摘要
投影纠缠对态（PEPS）为二维量子相提供了高效的变分近似，但计算可观测量仍具挑战性，因为PEPS收缩通常成本高昂。本文中，我们利用受等距约束的变分PEPS参数化二维量子态，并将所得近似映射到受监控量子电路，用电路采样替代张量网络收缩。对于无限圆柱，转移矩阵在虚拟边界上定义了一个量子通道，我们采用定点处理和该通道的受监控电路展开来高效评估可观测量。我们的方法使用固定数量的变分参数和仅随圆柱宽度缩放的量子比特数，得到的$J_1$-$J_2$模型相图与密度矩阵重整化群（DMRG）结果定性一致。由于受监控电路兼容近期量子硬件，该方法为模拟二维量子多体系统提供了一种混合量子-经典框架。
英文摘要
Projected entangled pair states (PEPS) provide an efficient variational ansatz for two-dimensional quantum phases, but computing observables remains challenging because PEPS contraction is generally costly. Here, we parameterize two-dimensional quantum states using variational PEPS subject to isometric constraints and map the resulting ansatz onto monitored quantum circuits, replacing tensor-network contraction with circuit sampling. For infinite cylinders, the transfer matrix defines a quantum channel on the virtual boundary. We use a fixed-point treatment and a monitored-circuit unraveling of this channel to evaluate observables efficiently. Using a constant number of variational parameters and a number of qubits that scales only with the cylinder width, our method yields a phase diagram for the $J_1$-$J_2$ model in qualitative agreement with DMRG results. Because the monitored circuits are compatible with near-term quantum hardware, this approach provides a hybrid quantum-classical framework for simulating two-dimensional quantum many-body systems.
Comments21 pages, 12 figures
