Quantum Inverse Scattering – A Proof-of-Concept

The potentialities offered by the Quantum Computing framework in the solution of microwave imaging problems are discussed and validated in a proof-of-concept fashion in this work. Towards this end, a tomographic inverse problem is firstly formulated within the first-order Born approximation under transverse-magnetic illumination. The resulting linear system of equations is solved by a customized version of the Harrow-Hassidim-Lloyd (HHL) quantum algorithm. Preliminary numerical results are shown to illustrate the possibility to dramatically decrease the retrieval time by leveraging on the exponential computational improvement made possible by quantum algorithms.