In recent years, there is 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.
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Machine learning framework for quantum sampling of highly constrained, continuous optimization problems
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December 2021
Research Article|
December 29 2021
Machine learning framework for quantum sampling of highly constrained, continuous optimization problems

Blake A. Wilson
;
Blake A. Wilson
1
School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University
, West Lafayette, Indiana 47907, USA
2
The Quantum Science Center (QSC), National Quantum Information Science Research Center of the U.S. Department of Energy (DOE)
, Oak Ridge, Tennessee 37931, USA
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Zhaxylyk A. Kudyshev
;
Zhaxylyk A. Kudyshev
1
School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University
, West Lafayette, Indiana 47907, USA
2
The Quantum Science Center (QSC), National Quantum Information Science Research Center of the U.S. Department of Energy (DOE)
, Oak Ridge, Tennessee 37931, USA
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Alexander V. Kildishev
;
Alexander V. Kildishev
1
School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University
, West Lafayette, Indiana 47907, USA
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Sabre Kais
;
Sabre Kais
2
The Quantum Science Center (QSC), National Quantum Information Science Research Center of the U.S. Department of Energy (DOE)
, Oak Ridge, Tennessee 37931, USA
3
School of Chemistry, Purdue University
, West Lafayette, Indiana 47907, USA
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Vladimir M. Shalaev
;
Vladimir M. Shalaev
1
School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University
, West Lafayette, Indiana 47907, USA
2
The Quantum Science Center (QSC), National Quantum Information Science Research Center of the U.S. Department of Energy (DOE)
, Oak Ridge, Tennessee 37931, USA
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Alexandra Boltasseva
Alexandra Boltasseva
a)
1
School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University
, West Lafayette, Indiana 47907, USA
2
The Quantum Science Center (QSC), National Quantum Information Science Research Center of the U.S. Department of Energy (DOE)
, Oak Ridge, Tennessee 37931, USA
a)Author to whom correspondence should be addressed: [email protected]
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a)Author to whom correspondence should be addressed: [email protected]
Appl. Phys. Rev. 8, 041418 (2021)
Article history
Received:
June 18 2021
Accepted:
November 24 2021
Connected Content
A companion article has been published:
Framework maps continuous-space inverse design problems for compression
Citation
Blake A. Wilson, Zhaxylyk A. Kudyshev, Alexander V. Kildishev, Sabre Kais, Vladimir M. Shalaev, Alexandra Boltasseva; Machine learning framework for quantum sampling of highly constrained, continuous optimization problems. Appl. Phys. Rev. 1 December 2021; 8 (4): 041418. https://doi.org/10.1063/5.0060481
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