Classically Simulating Quantum Supremacy IQP Circuits through a Random Graph Approach

TL;DR

This paper introduces improved classical algorithms for simulating random IQP quantum circuits, enabling simulation of larger circuits up to 50 qubits efficiently, which impacts the demonstration of quantum supremacy.

Contribution

The authors develop new algorithms that significantly enhance the classical simulation of IQP circuits, pushing the boundary of simulating larger quantum circuits.

Findings

Simulate up to 50-qubit circuits in minutes on a laptop.

Propose algorithms that simulate 70-qubit circuits on large clusters.

Achieve a theoretical simulation complexity reduction for dense circuits.

Abstract

Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to use random circuit sampling. It has been suggested that a good candidate for demonstrating quantum supremacy with random circuit sampling is to use \emph{IQP circuits}. These are quantum circuits where the unitary it implements is diagonal. In this paper we introduce improved techniques for classically simulating random IQP circuits. We find a simple algorithm to calculate an amplitude of an $n$-qubit IQP circuit with dense random two-qubit interactions in time $O(\frac{\log^2 n}{n} 2^n )$, which for sparse circuits (where each qubit interacts with $O(\log n)$ other qubits) runs in $o(2^n/\text{poly}(n))$ for any given polynomial. Using a more complicated stabiliser decomposition approach we improve the algorithm for dense circuits to $O\left(\frac{(\log n)^{4-\beta}}{n^{2-\beta}} 2^n \right)$ where $\beta \approx 0.396$. We benchmarked our algorithm and found that we can simulate up to 50-qubit circuits in a couple of minutes on a laptop. We estimate that 70-qubit circuits are within reach for a large computing cluster.