标题： 利用正张量网络实现对含噪量子电路的大深度模拟 显示英文标题

标题： Enabling large-depth simulation of noisy quantum circuits with positive tensor networks

摘要： 矩阵乘积密度算符（MPDOs）是局域纯化密度矩阵的张量网络表示，其中每个物理自由度都关联到一个环境自由度。 MPDOs 在混合态表示中有有趣的性质：通过构造保证正定性、迹的高效守恒以及局域可观测量的计算效率。 然而，由于噪声的应用增加了环境希尔伯特空间的维度，导致键维数呈指数增长，因此它们在嘈杂量子电路模拟中的使用具有挑战性。 此外，由于环境希尔伯特空间基底选择的自由度，MPDOs 缺乏唯一的规范形式，这导致键维数出现巨大变化。 在这项工作中，我们提出了一种系统的方法，通过解纠缠纯化态来减少 MPDOs 的键维数。 我们通过对局部双量子比特基底优化执行类似于密度矩阵重正化群（DMRG）的扫描，从而优化环境希尔伯特空间的基底。 有趣的是，我们发现仅针对纯化态的解纠缠就可降低环境维度。 换句话说，紧凑的 MPDO 表示需要低纠缠的纯化态。 我们将我们的压缩方法应用于嘈杂随机量子电路的仿真。 与之前的 MPDO 相关工作不同，我们的技术允许保持有界的键维数和有限内存，同时保持合理的截断保真度。 显示英文摘要

摘要： Matrix product density operators (MPDOs) are tensor network representations of locally purified density matrices where each physical degree of freedom is associated to an environment degree of freedom. MPDOs have interesting properties for mixed state representations: guaranteed positivity by construction, efficient conservation of the trace and computation of local observables. However, they have been challenging to use for noisy quantum circuit simulation, as the application of noise increases the dimension of the environment Hilbert space, leading to an exponential growth of bond dimensions. MPDOs also lack a unique canonical form, due to the freedom in the choice of basis for the environment Hilbert space, which leads to a vast variation of bond dimensions. In this work, we present a systematic way to reduce the bond dimensions of MPDOs by disentangling the purified state. We optimize the basis for the environment Hilbert space by performing density matrix renormalization group (DMRG)-like sweeps of local 2-qubit basis optimization. Interestingly, we find that targeting only the disentanglement of the purified state leads to a reduction of the environment dimension. In other words, a compact MPDO representation requires a low-entanglement purified state. We apply our compression method to the emulation of noisy random quantum circuits. Our technique allows us to keep bounded bond dimensions, and thus bounded memory, contrary to previous works on MPDOs, while keeping reasonable truncation fidelities.