Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.

中文翻译：

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量子系统的高效二维张量网络仿真

由于状态空间的指数大小，量子系统的模拟具有挑战性。张量网络为量子态提供了系统可改进的近似。诸如投影纠缠对状态 (PEPS) 之类的 2D 张量网络非常适合物理系统和量子电路的关键类别。然而，PEPS 网络的直接收缩具有指数级成本，而近似算法需要使用大张量进行计算。我们为基于 PEPS 的方法提出了新的可扩展算法和软件抽象，加速了张量子网络收缩和重构的瓶颈操作。我们采用带有隐式矩阵的随机 SVD 来渐近地降低成本和内存占用。更多，我们开发了一个分布式内存 PEPS 库，并研究了 Stampede2 超级计算机上 PEPS 收缩和进化的替代算法的准确性和效率。我们还模拟了一种流行的近期量子算法、变分量子特征求解器 (VQE) 和基准虚时间演化 (ITE)，它们计算哈密顿量的基态。