Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound

TL;DR

This paper establishes a subexponential classical simulation method for certain quantum circuits using tensor network contraction algorithms, providing significant practical speedups over existing techniques.

Contribution

It introduces a rigorous upper bound on classical simulation time and presents an efficient algorithm that outperforms standard methods for simulating various quantum circuits.

Findings

Subexponential simulation time for 2D quantum circuits.

Algorithm achieves several orders of magnitude speedup.

Effective for Google's Sycamore and random quantum circuits.

Abstract

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be classically simulated in subexponential time in the number of gates. Moreover, we present and implement an algorithm guaranteed to meet our bound and which finds contraction orders with vastly lower computational times in practice. In many practically relevant cases this beats standard simulation schemes and, for certain quantum circuits, also a state-of-the-art method. Specifically, our algorithm leads to speedups of several orders of magnitude over naive contraction schemes for two-dimensional quantum circuits on as little as an $8 \times 8$ lattice. We obtain similarly efficient contraction schemes for Google's Sycamore-type quantum circuits, instantaneous quantum polynomial-time circuits, and non-homogeneous (2+1)-dimensional random quantum circuits.