Quantum Gaussian Processes for Data-Driven Design of Metamaterials

Abstract

The data-driven approach shows great potential for designing new materials with unprecedented properties by using machine learning and optimization. Recently, a data-driven framework was successfully applied to design a unit cell of metamaterial achieving super-compressibility, despite being built out of brittle base material. The key element of the framework is the algorithm called Gaussian processes regression (GPs) – a unique machine learning method that provides with the uncertainty of the prediction, which can be used during the design process to account for inherent material imperfections, ensuring the robustness of the design. Despite their superior predictive performance, however, GPs suffer from scalability issues, which limit their application to relatively small design problems. In the future, those limitations could be surpassed by quantum computing.

This research aims at demonstrating how quantum computing could enhance the computational design of materials, specifically by replacing the expensive machine learning step of the data-driven design framework with an exponentially faster quantum algorithm for Gaussian processes (QGP). This objective is achieved in two steps. First, the QGP algorithm was Implementation and simulated within a quantum computing framework (Qiskit), which allowed to understand and control its performance (in particular its accuracy), proving the feasibility for practical applications. Furthermore, the numerical tests exposed a mechanism for inducing a low-rank approximation, which allows for additional speed-up, making the QGP algorithm similar to classical sparse Gaussian processes, which rely on low-rank approximations to improve the scalability of full GPs. In the second part of this research, the implemented QGP algorithm was integrated within a computational framework for the data-driven design of materials and applied to two example design problems of optimization a unit cell for a super-compressible metamaterial. The results obtained with the QGP were comparable to those obtained with classical methods (also from literature), which proved the feasibility of the concept.