Quantum Annealing Approaches to the Phase-Unwrapping Problem in Synthetic-Aperture Radar Imaging

TL;DR

This paper explores using quantum annealing to solve the phase-unwrapping problem in SAR imaging, formulating it as a QUBO problem and testing on both classical simulators and a real quantum annealer, showing promising results.

Contribution

It introduces a novel quantum annealing approach for phase unwrapping in SAR images, including problem decomposition and solution strategies for limited qubit quantum hardware.

Findings

Software solvers achieve high-quality solutions comparable to state-of-the-art.

Quantum annealer results are promising but require better mapping to hardware topology.

Decomposition approach enables handling larger images with limited qubits.

Abstract

The focus of this work is to explore the use of quantum annealing solvers for the problem of phase unwrapping of synthetic aperture radar (SAR) images. Although solutions to this problem exist based on network programming, these techniques do not scale well to larger-sized images. Our approach involves formulating the problem as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved using a quantum annealer. Given that present embodiments of quantum annealers remain limited in the number of qubits they possess, we decompose the problem into a set of subproblems that can be solved individually. These individual solutions are close to optimal up to an integer constant, with one constant per sub-image. In a second phase, these integer constants are determined as a solution to yet another QUBO problem. We test our approach with a variety of software-based QUBO solvers and on a variety of images, both synthetic and real. Additionally, we experiment using D-Wave Systems's quantum annealer, the D-Wave 2000Q. The software-based solvers obtain high-quality solutions comparable to state-of-the-art phase-unwrapping solvers. We are currently working on optimally mapping the problem onto the restricted topology of the quantum annealer to improve the quality of the solution.