Verifying Random Quantum Circuits with Arbitrary Geometry Using Tensor Network States Algorithm

TL;DR

This paper introduces a tensor network algorithm capable of efficiently simulating random quantum circuits with arbitrary geometries, significantly improving classical verification of quantum devices.

Contribution

The authors develop a tensor network-based algorithm with SVD compression and optimized contraction paths, enabling faster simulation of random quantum circuits with arbitrary geometry.

Findings

Up to 100x faster than previous algorithms for 53-qubit circuits

Successfully simulated 104-qubit circuits with shallow depths

Effective verification tool for near-term quantum computers

Abstract

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically designed to compute amplitudes for random quantum circuits with arbitrary geometry. Singular value decomposition based compression together with a two-sided circuit evolution algorithm are used to further compress the resulting tensor network. To further accelerate the simulation, we also propose a heuristic algorithm to compute the optimal tensor contraction path. We demonstrate that our algorithm is up to $2$ orders of magnitudes faster than the Sch$\ddot{\text{o}}$dinger-Feynman algorithm for verifying random quantum circuits on the $53$-qubit Sycamore processor, with circuit depths below $12$. We also simulate larger random quantum circuits up to $104$ qubits, showing that this algorithm is an ideal tool to verify relatively shallow quantum circuits on near-term quantum computers.