Classically Simulating Quantum Supremacy IQP Circuits trough a Random Graph Approach

• URL: http://arxiv.org/abs/2212.08609v1
• Date: Fri, 16 Dec 2022 17:38:42 GMT
• Title: Classically Simulating Quantum Supremacy IQP Circuits trough a Random Graph Approach
• Authors: Julien Codsi, John van de Wetering
• Abstract summary: A good candidate for demonstrating quantum supremacy with random circuit sampling is to use emphIQP circuits. We introduce improved techniques for classically simulating random IQP circuits. We estimate that 70-qubit circuits are within reach for a large computing cluster.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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