Quantuminspired algorithm for estimating the permanent of positive semidefinite matrices
Abstract
We construct a quantuminspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the permanent of a Hermitian positive semidefinite matrix can be expressed in terms of the expected value of a random variable, which stands for a specific photoncounting probability when measuring a linearoptically evolved random multimode coherent state. Our algorithm then approximates the matrix permanent from the corresponding sample mean and is shown to run in polynomial time for various sets of Hermitian positive semidefinite matrices, achieving a precision that improves over known techniques. This work illustrates how quantum optics may benefit algorithm development.
 Publication:

Physical Review A
 Pub Date:
 August 2017
 DOI:
 10.1103/PhysRevA.96.022329
 arXiv:
 arXiv:1609.02416
 Bibcode:
 2017PhRvA..96b2329C
 Keywords:

 Quantum Physics
 EPrint:
 9 pages, 1 figure. Updated version for publication