A detailed study of Gaussian Boson Sampling

TL;DR

This paper advances Gaussian Boson Sampling by deriving a hafnian-based probability expression, proposing a new protocol, and analyzing its advantages and experimental feasibility compared to existing methods.

Contribution

It introduces a hafnian-based formulation for Gaussian Boson Sampling and proposes a new, more efficient protocol with improved experimental prospects.

Findings

Derived a hafnian-based probability expression for Gaussian states.

Designed a Gaussian Boson Sampling protocol with advantages over previous methods.

Discussed experimental requirements and relations to Scattershot Boson Sampling.

Abstract

Since the development of Boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper we interpret and extend the results presented in [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the \textit{hafnian} matrix function and us it to design a Gaussian Boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian Boson Sampling. Finally, we relate it to the previously most general protocol, Scattershot Boson Sampling [Phys. Rev. Lett. 113, 100502 (2014)]