Solving graph problems with single photons and linear optics
Abstract
An important challenge for current and nearterm quantum devices is finding useful tasks that can be preformed on them. We first show how to efficiently encode a bounded n ×n matrix A into a linear optical circuit with 2 n modes. We then apply this encoding to the case where A is a matrix containing information about a graph G . We show that a photonic quantum processor consisting of singlephoton sources, a linear optical circuit encoding A , and singlephoton detectors can solve a range of graph problems including finding the number of perfect matchings of bipartite graphs, computing permanental polynomials, determining whether two graphs are isomorphic, and the k densest subgraph problem. We also propose preprocessing methods to boost the probabilities of observing the relevant detection events and thus improve performance. Finally we present both numerical simulations and implementations on Quandela's Ascella photonic quantum processor to validate our findings.
 Publication:

Physical Review A
 Pub Date:
 September 2023
 DOI:
 10.1103/PhysRevA.108.032405
 arXiv:
 arXiv:2301.09594
 Bibcode:
 2023PhRvA.108c2405M
 Keywords:

 Quantum Physics
 EPrint:
 9 pages + 9 pages appendix. To appear in Phys.Rev. A. Part of numerics section moved from appendix to main text. New experiments on photonic quantum hardware (Quandela's Ascella) added