Quantum Optimisation of Reconfigurable Surfaces in Complex Propagation Environments

The design and analysis of reconfigurable meta-surfaces operating within rich multi-path propagation fading is of crucial importance for the development of real-life programmable electromagnetic environments. We incorporate the effect of multi-path fading in an impedance-based model of wireless communication links assisted by reconfigurable surfaces. Previous work has shown that impedance-based channel models under rich multi-path propagation have an isomorphism with Sherrington-Kirkpatrick (SK) Hamiltonians. We focus on received power minimisation, which is equivalent to the hard-to-solve task task of finding the ground state of the SK Hamiltonian. It has been recently discovered that the Quantum Approximate Optimisation Algorithm (QAOA) predicts the ground state of SK Hamiltonians accurately. However, the landscape parameters of QAOA are dependent on the specific realisation of the random SK Hamiltonian, which hinders the full usage of quantum hardware to optimise reconfigurable surfaces dynamically. We show by Montecarlo simulations that a concentration property cures this impediment thus making QAOA an excellent candidate for surface optimisation under fast multi-path fading.