Solving the sampling problem of the Sycamore quantum circuits

TL;DR

This paper introduces an efficient classical method for sampling from the output distribution of Google's Sycamore quantum circuits, achieving results that challenge the presumed quantum advantage.

Contribution

A novel tensor network contraction approach that efficiently generates large numbers of uncorrelated samples from Sycamore circuits with high fidelity.

Findings

Generated one million samples in 15 hours on 512 GPUs

Achieved fidelity of approximately 0.0037 for the samples

Method potentially surpasses Google's quantum hardware in speed when scaled to ExaFLOPS

Abstract

We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a new method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in obtaining a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with $53$ qubits and $20$ cycles, we have generated one million uncorrelated bitstrings $\{\mathbf s\}$ which are sampled from a distribution $\hat P(\mathbf s)=|\hat \psi(\mathbf s)|^2$, where the approximate state $\hat \psi$ has fidelity $F\approx 0.0037$. The whole computation has cost about $15$ hours on a computational cluster with $512$ GPUs. The obtained one million samples, the contraction code and contraction order is made public. If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware.