How to simulate a quantum computer using negative probabilities

TL;DR

This paper introduces a method to simulate quantum computers using negative probabilities, decomposing quantum gates into classically implementable operations, and analyzing the computational speed-up through probabilistic simulation.

Contribution

It presents a novel approach to simulate quantum gates with negative probabilities, enabling classical simulation of quantum computation.

Findings

Decomposition of quantum gates into classical operations with negative probabilities.

Simulation of quantum circuits using probabilistic methods with negative weights.

Evaluation of quantum speed-up in terms of increased simulation complexity.

Abstract

The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1, and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate and assigning a negative statistical weight to the outcomes of sequences with an odd number of negative probability operations. The exponential speed-up of a quantum computer can then be evaluated in terms of the increase in the number of sequences needed to simulate a single operation of the quantum circuit.