Enhanced Quantum Search via Partial Diffusion and Entanglement with Linear Optics

Searching for specific items in an unstructured database presents a vital computational problem. While the best-known classical search algorithm in a database of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> has a complexity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{O}(N)$</tex>, Grover's quantum search algorithm exhibits a complexity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{O}(\sqrt{N})$</tex>, featuring a quadratic speed-up. In this paper, we present an optical system that implements an enhanced version of the search algorithm proposed by Younis et al. The system uses linear optical components such as beam splitters, phase shifters, and wave plates, along with a single-photon source and photodetectors.