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.
@article{arxiv.1612.01199,
title = {Gaussian Boson Sampling},
author = {Craig S. Hamilton and Regina Kruse and Linda Sansoni and Sonja Barkhofen and Christine Silberhorn and Igor Jex},
journal= {arXiv preprint arXiv:1612.01199},
year = {2017}
}