A simple encoding of a quantum circuit amplitude as a matrix permanent

TL;DR

This paper introduces a straightforward method to encode quantum circuit transition amplitudes as matrix permanents, enabling classical approximation algorithms for quantum computations.

Contribution

It presents a simple construction linking quantum amplitudes to matrix permanents, facilitating classical Monte Carlo algorithms for quantum circuit simulation.

Findings

Transition amplitudes encoded as matrix permanents.

Enables classical approximation of quantum circuits.

Matrix size proportional to number of gates.

Abstract

A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This opens up some interesting classical monte-carlo algorithms for approximating quantum circuits.