Sparse quantum Gaussian processes to counter the curse of dimensionality

Sparse quantum Gaussian processes to counter the curse of dimensionality

Kuś, G.I. (TU Delft Novel Aerospace Materials)
van der Zwaag, S. (TU Delft Novel Aerospace Materials)
Bessa, M.A. (TU Delft Team Georgy Filonenko)

2021

Gaussian processes are well-established Bayesian machine learning algorithms with significant merits, despite a strong limitation: lack of scalability. Clever solutions address this issue by inducing sparsity through low-rank approximations, often based on the Nystrom method. Here, we propose a different method to achieve better scalability and higher accuracy using quantum computing, outperforming classical Bayesian neural networks for large datasets significantly. Unlike other approaches to quantum machine learning, the computationally expensive linear algebra operations are not just replaced with their quantum counterparts. Instead, we start from a recent study that proposed a quantum circuit for implementing quantum Gaussian processes and then we use quantum phase estimation to induce a low-rank approximation analogous to that in classical sparse Gaussian processes. We provide evidence through numerical tests, mathematical error bound estimation, and complexity analysis that the method can address the “curse of dimensionality,” where each additional input parameter no longer leads to an exponential growth of the computational cost. This is also demonstrated by applying the algorithm in a practical setting and using it in the data-driven design of a recently proposed metamaterial. The algorithm, however, requires significant quantum computing hardware improvements before quantum advantage can be achieved.

Data-driven design
Design of materials
Gaussian processes
Low-rank approximation

http://resolver.tudelft.nl/uuid:e0f7cd3e-8b47-4e3a-8cc2-9e1a302049fa

https://doi.org/10.1007/s42484-020-00032-8

2524-4906

Quantum Machine Intelligence, 3 (1)

Institutional Repository

journal article

© 2021 G.I. Kuś, S. van der Zwaag, M.A. Bessa