论文标题
量子系统的高效2D张量网络模拟
Efficient 2D Tensor Network Simulation of Quantum Systems
论文作者
论文摘要
由于状态空间的指数尺寸，量子系统的模拟是具有挑战性的。张量网络为量子状态提供了系统改进的近似值。 2D张量网络（例如预测的纠缠对状态（PEP））非常适合物理系统和量子电路的关键类别。但是，PEPS网络的直接收缩具有指数成本，而近似算法则需要大量张量的计算。我们为基于PEPS的方法提出了新的可扩展算法和软件摘要，从而加速了收缩的瓶颈操作以及张量子子网的重构。我们使用具有隐式矩阵的随机SVD来渐近地降低成本和内存足迹。此外，我们开发了一个分布式内存PEPS库，并研究了PEPS收缩和Stampede2 SuperCuputer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，变异量子本量（VQE）和基准假想时间演化（ITE），该算法（ITE）计算了汉密尔顿人的基础状态。
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.
