Quantum-Classical Solution Methods for Binary Compressive Sensing Problems.

Compressive sensing is a signal processing technique used to acquire and reconstruct sparse signals using significantly fewer measurement samples. Compressive sensing requires finding the most sparse solution to an underdetermined linear system, which is an NP-hard problem and as a consequence in practise is only solved approximately. In our work we restrict ourselves to the compressive sensing problem for the case of binary signals. For that case we have defined an equivalent formulation in terms of a quadratic binary optimisation (QUBO) problem, which we solve using classical and (hybrid-)quantum computing solving techniques based on quantum annealing. Phase transition diagrams show that this approach significantly improves the number of problem types that can be successfully reconstructed when compared to a more conventional Li optimisation method. A challenge that remain is how to select optimal penalty parameters in the QUBO formulation as was shown can heavily impact the quality of the solution.