par Chakhmakhchyan, Levon ;Cerf, Nicolas
Référence Physical Review A, 96, 3, 032326
Publication Publié, 2017
Article révisé par les pairs
Résumé : 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-outcome measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a time-symmetric 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 time-symmetric 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 develop a boson sampling model in which the simulation of Gaussian measurements − namely the outcome of unbalanced heterodyne detection − is proven to be computationally hard. These results illustrate how time symmetry may serve as a tool for analyzing the computational complexity of novel physically-motivated computational problems.