Framework maps continuous-space inverse design problems for compression

Advances continue to push the fields of quantum hardware and quantum algorithms closer to applications. When solving combinatorial optimization problems, most current methods are hampered by their mapping into the quantum annealer without compression. New work looks to expand the types of problems that the quantum annealer can optimize.

Wilson et al. developed a generic, machine learning-based framework that can map continuous-space inverse design problems. By employing a binary variational autoencoder and a factorization machine, the group’s framework maps continuous-space inverse design problems into a surrogate quadratic unconstrained binary optimization problem.

It learns to compress optimization problems into smaller surrogate problems, which are then optimized with a quantum annealer.

“Oftentimes solutions to engineering problems have symmetries and fabrication constraints which heavily restrict the number of possible solutions,” said author Alexandra Boltasseva. “By using machine learning, we can implicitly include these symmetries and constraints into the surrogate model and perform the optimization within this surrogate space.”

The group demonstrated the framework’s performance by first optimizing thermal emitter topologies for thermophotovoltaic applications. They then optimized diffractive meta-gratings for highly efficient beam steering.

The technique can scale to solve advanced inverse design problems for science and engineering applications.

“Something that surprised us is that we only need about three times the number of qubits currently available to use our framework to solve useful engineering problems with a pure quantum annealer,” Boltasseva said.

The researchers aim to implement a similar algorithm on a gate model quantum computer and to improve the accuracy of the surrogate model while its dataset grows using data science techniques.

Source: “Machine learning framework for quantum sampling of highly-constrained, continuous optimization problems,” by Blake Anthony Wilson, Zhaxylyk A. Kudyshev, Alexander V. Kildishev, Sabre Kais, Vladimir M. Shalaev, and Alexandra Boltasseva, Applied Physics Reviews (2021). The article can be accessed at https://doi.org/10.1063/5.0060481 .