The vacuum provides quantum advantage to otherwise simulatable architectures

TL;DR

This paper demonstrates that a computational model using Gottesman-Kitaev-Preskill states, Gaussian operations, and homodyne measurement is classically simulatable, showing the vacuum state as the key resource for quantum advantage.

Contribution

It extends the Gottesman-Knill theorem to a continuous-variable setting, explicitly providing a classical simulation algorithm for this quantum architecture.

Findings

The architecture is classically efficiently simulatable.

The vacuum state is the resource enabling quantum advantage.

An explicit algorithm for probability density function calculation.

Abstract

We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states, Gaussian operations - including all rational symplectic operations and all real displacements -, and homodyne measurement. We prove that such architecture is classically efficiently simulatable, by explicitly providing an algorithm to calculate the probability density function of the measurement outcomes of the computation. We also provide a method to sample when the circuits contain conditional operations. This result is based on an extension of the celebrated Gottesman-Knill theorem, via introducing proper stabilizer operators for the code at hand. We conclude that the resource enabling quantum advantage in the universal computational model considered by B.Q. Baragiola et al. [Phys. Rev. Lett. 123, 200502 (2019)], composed of a subset of the elements given above augmented with a provision of vacuum states, is indeed the vacuum state.