Boson sampling with Gaussian measurements
Abstract
We develop an alternative boson sampling model operating on singlephoton states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuousvariable 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 twomode squeezed vacuum states undergo parallel linearoptical 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 timereversed setup is used to exhibit a boson sampling model in which the simulation of Gaussian measurements—namely the outcome of eightport 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.
 Publication:

Physical Review A
 Pub Date:
 September 2017
 DOI:
 10.1103/PhysRevA.96.032326
 arXiv:
 arXiv:1705.05299
 Bibcode:
 2017PhRvA..96c2326C
 Keywords:

 Quantum Physics
 EPrint:
 8 pages, 3 figures. Updated version for publication