Abstract
Despite its wide scope of applications, topology optimization faces a major challenge, which is its high computational expenses caused by the large number of design variables and the underlying physics. Because the number of possible material layouts increases exponentially, the search for the optimum becomes computationally intractable. Recently, quantum computing emerged as an alternative paradigm for solving optimization problems with potentially much higher efficiency than classical computing. The quantum superposition phenomenon allows quantum computer to perform a parallel search of many possible solutions. In this work, a two-mixer quantum approximate Bayesian optimization algorithm (TM-QABOA) is developed as a hybrid quantum-classical optimization algorithm, where Pauli-X mixers and generalized Grover mixers are applied in an alternating fashion. TM-QABOA enables a dynamic exploration-exploitation balance to improve searching efficiency. The exploration is done with the Pauli-X mixers, whereas the exploitation is enhanced by the generalized Grover mixers through amplitude amplification. Surrogate-based Bayesian optimization is used to optimize the hyperparameters of the quantum circuit, i.e., rotation angles. The algorithm can also be used to solve mixed-integer optimization problems. The feasibility of TM-QABOA to solve optimization problems is demonstrated with two simple examples. One is two-dimensional truss design, and the other is metamaterials design.
