Efficient 2D Tensor Network Simulation of Quantum Systems

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.

to be published in SC 2020

References in corpus (12)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Algorithms for finite Projected Entangled Pair States
• Generic Construction of Efficient Matrix Product Operators
• Time evolution of projected entangled pair states in the single layer picture
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition