Sparse quantum Gaussian processes to counter the curse of dimensionality

Abstract 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 different method to achieve better scalability and higher accuracy using quantum computing, outperforming classical neural networks for large datasets significantly. Unlike other approaches learning, computationally expensive linear algebra operations not just replaced their counterparts. Instead, start from recent study that proposed circuit implementing then use phase estimation induce approximation analogous in sparse processes. We provide evidence numerical tests, mathematical error bound estimation, complexity analysis can “curse dimensionality,” where each additional input parameter no longer leads an exponential growth computational cost. This is also demonstrated applying algorithm practical setting it data-driven design recently metamaterial. The algorithm, however, requires computing hardware improvements before advantage be achieved.