What Can Quantum Optics Say about Computational Complexity Theory?

Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for c...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters Vol. 114; no. 6; p. 060501
Main Authors: Rahimi-Keshari, Saleh, Lund, Austin P., Ralph, Timothy C.
Format: Journal Article
Language:English
Published: United States 13.02.2015
Subjects:
Algorithms
Approximation
Complexity
Complexity theory
Computation
Gaussian
Probability distribution
Sampling
ISSN:0031-9007, 1079-7114, 1079-7114
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.114.060501