More Optimal Simulation of Universal Quantum Computers

TL;DR

This paper introduces a method to significantly improve the classical simulation efficiency of universal quantum computers by reducing the sampling cost through correlated sampling, surpassing previous state-of-the-art techniques.

Contribution

It presents a novel correlated sampling approach that reduces the worst-case sampling cost for $L_1$-norm simulation of quantum devices, achieving a 68-fold improvement.

Findings

Reduced the simulation cost prefactor by 68 times

Surpassed average-case performance of prior methods

Validated results with numerical demonstrations

Abstract

Validating whether a quantum device confers a computational advantage often requires classical simulation of its outcomes. The worst-case sampling cost of $L_1$-norm based simulation has plateaued at $\le(2+\sqrt{2})\xi_t \delta^{-1}$ in the limit that $t \rightarrow \infty$, where $\delta$ is the additive error and $\xi_t$ is the stabilizer extent of a $t$-qubit magic state. We reduce this prefactor 68-fold by a leading-order reduction in $t$ through correlated sampling. The result exceeds even the average-case of the prior state-of-the-art and current simulators accurate to multiplicative error. Numerical demonstrations support our proofs. The technique can be applied broadly to reduce the cost of $L_1$ minimization.