Quantum Topology Optimization via Quantum Annealing

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 qubits 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 stateof-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.

Warm and Cold Start Quantum Annealing for Metaverse Resource Optimization

“…Quantum Annealing (QA) [16] has the strength of a magnetic transverse field to avoid getting stuck into local optimal, unlike the classical counterpart. Quantum tunnelling [17] al-lows waveforms to overcome barriers by exploiting quantum mechanical phenomena. The potentials of quantum fluctuations and quantum dynamics in combination with quantum entanglement and superposition properties can be considered to overcome the shortcomings of classical approaches [15].…”

“…The solution found out by QA is stored as a starting solution in the variable state 0 . Considering this initial feasible solution, we either choose SA or GA as the classical optimization algorithm and further improve upon the quantum solution (line number [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The process of classical SA and GA has already been elaboratively discussed in the Subsection IV.A and IV.B, respectively.…”

A Formulation of Structural Design Optimization Problems for Quantum Annealing

“…In another study [11], the authors performed a topology optimization for a minimum compliance problem in which they considered a rectangular domain with a unit point force acting on it. To that end, they transform the original mixed integer nonlinear programming (MINLP) problem into a sequence of mixed integer linear programming (MILP) problems by separating field and design variables that are updated in an iterative manner.…”

A Symbolic Approach to Discrete Structural Optimization Using Quantum Annealing

“…Both quantum computing technologies are still in their infancy as compared to the advanced state of classical computing technologies. However, some recent studies on quantum(-inspired) computing applications have already shown promising results [9][10][11][12][13][14][15][16].…”