发表机构
CY Cergy Paris Université; Collège de France; PSL Research University; Barcelona Supercomputing Center; Institute of Fundamental Physics IFF-CSIC; Quantum Advanced Research Center (QuARC), CSIC（塞吉巴黎大学; 法兰西公学院; 巴黎文理研究大学; 巴塞罗那超级计算中心; 西班牙国家科学研究委员会基础物理研究所; 西班牙国家科学研究委员会量子先进研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对一维混沌砖墙电路，提出基于约化转移矩阵的Sweeping RTM算法，实现指定输出概率的近似强模拟，数值表明所需键维次指数增长，为经典概率查询开辟新途径。
AI 中文摘要
张量网络是模拟量子多体系统的强大工具，但空间纠缠的增长严重限制了混沌幺正电路下纯态的直接演化。在此，我们考虑一个更具针对性的任务：在有限相对精度下，对一维混沌砖墙电路指定输出概率的近似强模拟。给定输入和输出比特串$\by$和$\bx$，我们使用Sweeping RTM算法（一种基于约化转移矩阵（RTMs）的横向张量网络收缩）评估$p(\bx|\by)=|\bra{\bx}U(T)\ket{\by}|^2$。该算法联合压缩左、右时间边界态，寻求在空间切割和键维增加时收敛的输出概率。对于混沌一维砖墙电路，在固定相对目标精度下，我们数值发现，在可访问的时间窗口内，获得稳定估计所需的键维呈次指数增长。我们的发现为混沌量子电路的经典概率查询开辟了直接途径，在基准测试和学习任务中具有潜在应用。
英文摘要
Tensor networks are powerful tools for simulating quantum many-body systems, but the growth of spatial entanglement severely limits the direct evolution of pure states under chaotic unitary circuits. Here we consider a more targeted task: the approximate strong simulation of a specified output probability of a 1D chaotic brick-wall circuit at finite relative precision. Given input and output bit strings $\by$ and $\bx$, we evaluate $p(\bx|\by)=|\bra{\bx}U(T)\ket{\by}|^2$ using the Sweeping RTM algorithm, a transverse tensor-network contraction based on reduced transition matrices (RTMs). The algorithm compresses the left and right temporal boundary states jointly, seeking an output probability that converges across spatial cuts and as the bond dimension is increased. For chaotic one-dimensional brick-wall circuits at a fixed relative target precision, we find numerical evidence that the bond dimension required to obtain stable estimates grows subexponentially over the accessible time window. Our findings open a direct route to classical probability queries for chaotic quantum circuits, with potential applications to benchmarking and learning tasks.
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