Estimating outcome probabilities of quantum circuits using quasiprobabilities

TL;DR

This paper introduces a Monte Carlo sampling method using quasiprobability representations to estimate quantum circuit outcome probabilities, with efficiency linked to the circuit's negativity measure, emphasizing negativity's role as a non-classical resource.

Contribution

The paper proposes a novel quasiprobability-based Monte Carlo method for estimating quantum outcomes, connecting convergence rate to negativity, and highlighting its significance in quantum computation.

Findings

Estimator converges efficiently if negativity grows polynomially.

Negativity measured by the 1-norm influences convergence rate.

Negativity serves as a resource indicator in quantum computation.

Abstract

We present a method for estimating the probabilities of outcomes of a quantum circuit using Monte Carlo sampling techniques applied to a quasiprobability representation. Our estimate converges to the true quantum probability at a rate determined by the total negativity in the circuit, using a measure of negativity based on the 1-norm of the quasiprobability. If the negativity grows at most polynomially in the size of the circuit, our estimator converges efficiently. These results highlight the role of negativity as a measure of non-classical resources in quantum computation.