标题： 用二维张量网络对量子电路进行模拟和采样 显示英文标题

标题： Simulating and Sampling from Quantum Circuits with 2D Tensor Networks

摘要： 经典量子电路模拟在量子计算机的发展以及对领域进行温度检测中起着至关重要的作用。 在这里，我们使用二维张量网络假设对多种物理动机电路进行经典模拟，这些假设与底层量子处理器的几何结构相匹配。 然后，我们采用边界矩阵乘积态收缩算法的广义版本，以可控的方式从结果张量网络状态中生成样本。 我们的方法使我们能够系统地将最终状态的质量以及从中抽取的样本收敛到由电路定义的真实分布。 通过这些方法，我们以数值精度模拟了最近IBM实验中最大的局部单位Jastrow假设电路。 我们还研究了在大heavy-hex和旋转正方形晶格上的二维离散时间海森堡模型中的域壁淬火，这些晶格分别反映了IBM和Google最新的量子处理器。 我们在Google Willow几何结构上观察到复杂环状关联的快速积累，这对系统的局部性质产生了显著影响。 同时，我们在heavy-hex处理器上发现环状关联积累极其缓慢，并且即使在大的电路深度下，对系统局部性质的影响也几乎可以忽略不计。 我们的结果强调了量子处理器几何结构在经典可模拟性中的作用。 显示英文摘要

摘要： Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network ans\"atze for the many-body wavefunction which match the geometry of the underlying quantum processor. We then employ a generalized version of the boundary Matrix Product State contraction algorithm to controllably generate samples from the resultant tensor network states. Our approach allows us to systematically converge both the quality of the final state and the samples drawn from it to the true distribution defined by the circuit. With these methods, we simulate the largest local unitary Jastrow ansatz circuit taken from recent IBM experiments to numerical precision. We also study a domain-wall quench in a two-dimensional discrete-time Heisenberg model on large heavy-hex and rotated square lattices, which reflect IBM's and Google's latest quantum processors respectively. We observe a rapid buildup of complex loop correlations on the Google Willow geometry which significantly impact the local properties of the system. Meanwhile, we find loop correlations build up extremely slowly on heavy-hex processors and have almost negligible impact on the local properties of the system, even at large circuit depths. Our results underscore the role the geometry of the quantum processor plays in classical simulability.