Simulation of low-depth quantum circuits as complex undirected graphical models

TL;DR

This paper presents a classical simulation algorithm for low-depth quantum circuits, demonstrating its efficiency on certain large circuits and analyzing its scalability and parallelizability.

Contribution

It introduces a Feynman path-based classical simulation method for quantum circuits, extending the size and depth of circuits that can be simulated on a single workstation.

Findings

Simulated larger quantum circuits than previously possible.

Identified the depth and size limits for efficient classical simulation.

Analyzed the parallelization potential of the simulation process.

Abstract

Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical algorithms on state-of-the-art computers, achieving the first milestone of so-called quantum supremacy. This has stimulated recent progress in classical algorithms to simulate quantum circuits. Classical simulations are also necessary to approximate the fidelity of multiqubit quantum computers using cross entropy benchmarking. Here we present numerical results of a classical simulation algorithm to sample universal random circuits, on a single workstation, with more qubits and depth than previously reported. For example, circuits with $5 \times 9$ qubits of depth 37, $7 \times 8$ qubits of depth 27, and $10 \times (\kappa > 10)$) qubits of depth 19 are all easy to sample. We also show up to what depth the sampling, or estimation of observables, is trivially parallelizable. The algorithm is related to the "Feynmann path" method to simulate quantum circuits. For low-depth circuits, the algorithm scales exponentially in the depth times the smaller lateral dimension, or the treewidth, as explained in Boixo et. al., and therefore confirms the bounds in that paper. In particular, circuits with $7 \times 7$ qubits and depth 40 remain currently out of reach. Follow up work on a supercomputer environment will tighten this bound.