Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios

TL;DR

This paper presents a classical simulation algorithm for measurement-based quantum computation using multipartite Bell scenarios, highlighting the roles of non-stabilizerness and entanglement in quantum speedup.

Contribution

It introduces a novel simulation method leveraging non-signaling polytopes, expanding the class of quantum states that can be efficiently simulated classically.

Findings

Efficient simulation of certain quantum states including the Bell polytope.

Non-stabilizerness and entanglement are necessary for quantum speedup.

Simulation extends beyond phase space sampling methods.

Abstract

We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computation with single-qubit Pauli measurements. In our model, the simultaneous presence of non-stabilizerness and entanglement is necessary for quantum speedup. The region of quantum states that can be efficiently simulated includes the Bell polytope and extends beyond what is currently achievable by sampling algorithms based on phase space methods.