# Quantum-Classical Solution Methods for Binary Compressive Sensing Problems

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 L1 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.

SubjectBinary compressive sensing

Quadratic unconstrained binary optimisation

Quantum annealing

Computational complexity

Linear systems

Optimization

Quantum computers

Quantum optics

Binary compressive sensing

Binary optimization

Classical solutions

Compressive sensing

Quadratic unconstrained binary optimization

Quantum annealing

Quantum-classical

Sensing problems

Signal processing technique

Solution methods

Compressed sensing

http://resolver.tudelft.nl/uuid:3f852361-6a30-434b-a972-f32b258c0fe6

TNO identifier973205

9783031087592

0302-9743

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 22nd Annual International Conference on Computational Science, ICCS 2022, 21 June 2022 through 23 June 2022, 107-121

Document typeconference paper

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