Gaussian Boson Sampling

TL;DR

Gaussian Boson Sampling introduces a new classically hard problem using squeezed states, enhancing photonic quantum sampling efficiency and addressing the challenge of sampling from Gaussian states.

Contribution

It presents the first formulation of Gaussian Boson Sampling, relating measurement probabilities to the hafnian, and demonstrates a more efficient photonic boson sampler.

Findings

Relates measurement probabilities to the hafnian function.

Designs a #P hard Gaussian Boson Sampling problem.

Achieves more efficient sampling with advantages in probability and measurement time.

Abstract

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms.Here, we introduce Gaussian Boson Sampling, a classically hard-to-solve problem that uses squeezed states as a non-classical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson Sampling, a #P hard problem, using squeezed states. This approach leads to a more efficient photonic boson sampler with significant advantages in generation probability and measurement time over currently existing protocols.