quandela / matrix-encoding-problems

Matrix encoding and graph problems

An important challenge for current and near-term quantum devices is finding useful tasks which can be performed on these devices. In this Solving graph problems with single-photons and linear optics paper, we take a photonic quantum computing platform consisting of single-photon sources, a linear optical circuit encoding $A$, and single-photon detectors being by demonstrating how to efficiently encode a bounded $n \times n$ matrix $A$ onto a linear optical circuit acting on $2n$ modes. We then apply this encoding to the case where $A$ is a matrix containing information about a graph $G$.

The notebooks presented here can be used to reproduce the results from the paper and to develop further applications. From the theoretical demonstrations, with these notebooks you can also solve the following graph problems:

1. Finding the number of perfect matchings in bipartite graphs;
2. Computing permanent polynomials;
3. Determining whether two graphs are isomorphic;
4. $k$-densest subgraph problem.

It contains 4 notebooks arranged the following way:

1. Matrix encoding into linear optical circuits and permanent estimation of these matrices with the optical device.
2. Graph isomorphism problem (including computing permanent polynomials, Laplacians and many others) and results.
3. $k$-densest subgraph problem and results.
4. Boosting methods.