Quantum Topology Optimization via Quantum Annealing

TL;DR

This paper introduces a quantum annealing approach for continuum topology optimization, enabling the solution of complex structural design problems on current quantum hardware by splitting the problem into classical and quantum parts.

Contribution

It formulates continuum topology optimization as a mixed-integer nonlinear program suitable for quantum annealing and develops a splitting method to adapt to current quantum hardware limitations.

Findings

Quantum annealing can effectively solve continuum TO problems.

The splitting approach enables handling larger problems on existing quantum hardware.

Compared to classical heuristics, the method shows promising solution quality and efficiency.

Abstract

We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate sub-problems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting sub-problems small enough to be solved on quantum computers currently accessible with small numbers of quits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the state-of-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.