Resources for bosonic quantum computational advantage

TL;DR

This paper demonstrates that bosonic quantum computations can be represented as continuous-variable sampling problems, and introduces a classical simulation method based on the non-Gaussian stellar rank, clarifying the role of resources like squeezing, non-Gaussianity, and entanglement.

Contribution

It provides a reduction of bosonic quantum computations to a classical simulation framework based on stellar rank, and clarifies the resource interplay in quantum advantage.

Findings

Classical simulation complexity scales with stellar rank.

Operational notion of non-Gaussian entanglement identified.

Conditions for efficient classical simulation analyzed.

Abstract

Quantum computers promise to dramatically outperform their classical counterparts. However, the non-classical resources enabling such computational advantages are challenging to pinpoint, as it is not a single resource but the subtle interplay of many that can be held responsible for these potential advantages. In this work, we show that every bosonic quantum computation can be recast into a continuous-variable sampling computation where all computational resources are contained in the input state. Using this reduction, we derive a general classical algorithm for the strong simulation of bosonic computations, whose complexity scales with the non-Gaussian stellar rank of both the input state and the measurement setup. We further study the conditions for an efficient classical simulation of the associated continuous-variable sampling computations and identify an operational notion of non-Gaussian entanglement based on the lack of passive separability, thus clarifying the interplay of bosonic quantum computational resources such as squeezing, non-Gaussianity and entanglement.