Boson sampling with Gaussian measurements

L. Chakhmakhchyan*, N. J. Cerf

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

21 Citations (Scopus)
214 Downloads (Pure)


We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a twofold version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states undergo parallel linear-optical transformations. This twofold scattershot model yields, as a corollary, an instance of boson sampling from Gaussian states where photon counting is hard to simulate. Then, a time-reversed setup is used to exhibit a boson sampling model in which the simulation of Gaussian measurements - namely the outcome of eight-port homodyne detection - is proven to be computationally hard. These results illustrate how the symmetry of quantum evolution under time reversal may serve as a tool for analyzing the computational complexity of novel physically motivated computational problems.

Original languageEnglish
Article number032326
Number of pages7
JournalPhysical Review A
Issue number3
Early online date14 Sep 2017
Publication statusPublished - Sep 2017


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