Simulation of quantum computation with magic states via Jordan-Wigner transformations

TL;DR

This paper introduces a new quasiprobability representation based on Jordan-Wigner transformations that enables efficient classical simulation of certain quantum circuits in the magic state model, highlighting the role of negativity.

Contribution

It develops a novel quasiprobability representation connected to Jordan-Wigner transformations, improving classical simulation of magic state quantum circuits.

Findings

Efficient classical simulation algorithm for specific magic state circuits.

Representation outperforms previous models in positive state representation.

Connection established between quasiprobability negativity and quantum advantage.

Abstract

Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the magic state model. It is based on generalized Jordan-Wigner transformations, and it has a close connection to the probability representation of universal quantum computation based on the $\Lambda$ polytopes. For each number of qubits, it defines a polytope contained in the $\Lambda$ polytope with some shared vertices. It leads to an efficient classical simulation algorithm for magic state quantum circuits for which the input state is positively represented, and it outperforms previous representations in terms of the states that can be positively represented.