Efficient 2D Tensor Network Simulation of Quantum Systems

TL;DR

This paper introduces scalable algorithms and software for efficient 2D tensor network simulations of quantum systems, significantly improving contraction and evolution computations on supercomputers.

Contribution

It presents novel algorithms and a distributed-memory library for PEPS tensor networks, reducing computational costs and enabling large-scale quantum system simulations.

Findings

Accelerated tensor contraction and refactorization using randomized SVD.

Achieved efficient simulation of quantum algorithms like VQE and ITE.

Demonstrated scalability on the Stampede2 supercomputer.

Abstract

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.