Machine Learning Framework for Quantum Sampling of Highly-Constrained, Continuous Optimization Problems

Abstract

In recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine. The factorization machine is trained as a low-dimensional, binary surrogate model for the continuous design space and sampled using various QUBO samplers. Using the D-Wave Advantage hybrid sampler and simulated annealing, we demonstrate that by repeated resampling and retraining of the factorization machine, our framework finds designs that exhibit figures of merit exceeding those of its training set. We showcase the framework's performance on two inverse design problems by optimizing (i) thermal emitter topologies for thermophotovoltaic applications and (ii) diffractive meta-gratings for highly efficient beam steering. This technique can be further scaled to leverage future developments in quantum optimization to solve advanced inverse design problems for science and engineering applications.

References in corpus (19)

• Quantum Computing in the NISQ era and beyond
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• Outlook for inverse design in nanophotonics
• Quantum Annealing and Analog Quantum Computation
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Deep neural networks for the evaluation and design of photonic devices
• Global optimization of dielectric metasurfaces using a physics-driven neural network
• Freeform Diffractive Metagrating Design Based on Generative Adversarial Networks
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Machine-Learning-Assisted Metasurface Design for High-Efficiency Thermal Emitter Optimization
• Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures
• Expanding the horizon of automated metamaterials discovery via quantum annealing
• Topology optimization of freeform large-area metasurfaces
• Scaling advantage in quantum simulation of geometrically frustrated magnets
• Quantum Machine Learning for Electronic Structure Calculations
• Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics vs quantum approaches
• Knowledge Discovery In Nanophotonics Using Geometric Deep Learning
• Simulating the Shastry-Sutherland Ising Model using Quantum Annealing

Cited by in corpus (9)

• Quantum Annealing for Industry Applications: Introduction and Review
• Artificial Neural Networks for Photonic Applications: From Algorithms to Implementation
• Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine
• Application of QUBO solver using black-box optimization to structural design for resonance avoidance
• Machine-Learning-Assisted Photonic Device Development: A Multiscale Approach from Theory to Characterization
• Tutorial: AI-assisted exploration and active design of polymers with high intrinsic thermal conductivity
• A Universal Quantum Circuit Design for Periodical Functions
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Subsampling Factorization Machine Annealing