Engineering Reflective Metasurfaces With Ising Hamiltonian and Quantum Annealing

Charles Ross,Zhen Peng,Gabriele Gradoni,Qi Jian Lim

doi:10.1109/tap.2021.3137424

Abstract

We present a novel and flexible method to optimize the phase response of reflective metasurfaces (MSs) toward the desired scattering profile. The scattering power is expressed as a spin-chain Hamiltonian using the radar cross section (RCS) formalism. For MSs reflecting an oblique plane wave, an Ising Hamiltonian is obtained. Thereby, the problem of achieving the scattering profile is recast into finding the ground-state solution of the associated Ising Hamiltonian. To rapidly explore the configuration states, we encode the Ising coefficients with quantum annealing (QA) algorithms, taking advantage of the fact that the adiabatic evolution efficiently performs energy minimization in the Ising model. Finally, the optimization problem is solved on the D-Wave 2048-qubit quantum adiabatic optimizer machine for binary phase as well as quadriphase reflective MSs. Even though the work is focused on the phase modulation of MSs, we believe this approach paves the way to fast optimization of reconfigurable intelligent surfaces (RISs) that are modulated in both amplitude and phase for multi-beam generation in and beyond 5G/6G mobile networks.

Highlights

T HE study of wave propagation mediated by metamaterials and metasurfaces (MSs) has been a longstanding topic in applied physics and modern engineering [1]–[8]
We propose to find the optimal phase configuration by a physics-based approach inspired by the quantum mechanical physics of spins
One key question arises on how efficiently to select the phase configuration that produces a scattered field matching the desired scattering profile. This is of paramount importance when a solution to the optimization problem is not available in closed-form, and constitutes a substantial computational task

Summary

Introduction

T HE study of wave propagation mediated by metamaterials and metasurfaces (MSs) has been a longstanding topic in applied physics and modern engineering [1]–[8]. Due to the enormous design space, 2MN for M × N Ising spins, finding the optimal solution with classical computational algorithms can be very challenging. This is where the quantum annealing becomes an appealing way forward. “Intelligent reflecting surfaces: Physics, propagation, and pathloss modeling,” IEEE Wireless Communications Letters, vol 9, pp. “Quantum annealing in the transverse ising model,” Physical Review E, vol 58, pp. “High-fidelity, highperformance computational algorithms for intrasystem electromagnetic interference analysis of IC and electronics,” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol 7, pp. 653– 668, 2017

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