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...

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Vydáno v:Physical review letters Ročník 114; číslo 6; s. 060501
Hlavní autoři: Rahimi-Keshari, Saleh, Lund, Austin P., Ralph, Timothy C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 13.02.2015
Témata:
Algorithms
Approximation
Complexity
Complexity theory
Computation
Gaussian
Probability distribution
Sampling
ISSN:0031-9007, 1079-7114, 1079-7114
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0031-9007
1079-7114
1079-7114
DOI:10.1103/PhysRevLett.114.060501