Machine Learning Science and Technology

Variational quantum principal component analysis for Hilbert space Gaussian process regression

Kerem Bükrü, Ralf Sturm, Tjark Siefkes

Published Oct 15, 2026• 0 citations

Abstract

Abstract Gaussian processes are widely used probabilistic models for regression and classification tasks. Their flexibility and ability to quantify uncertainties make them well-suited for many applications. However, their applicability to large datasets is limited by the cubic computational time complexity. While reduced-rank methods such as Hilbert space approximations reduce this complexity, scaling to very large datasets remains challenging. Quantum algorithms are promising candidates to further accelerate such computations. Quantum principal component analysis has previously been applied to Hilbert space Gaussian process regression to address this scaling limitation. However, its applicability is limited by the requirement for fault-tolerant quantum hardware. In this work, we present a hybrid quantum-classical model for reduced-rank Gaussian process regression, where we apply a quantum principal component analysis algorithm based on parameterized quantum circuits to Hilbert space Gaussian process regression. In noiseless simulations on a one-dimensional test function, the resulting model reaches a regression accuracy comparable to that of the exact Gaussian process and the classical Hilbert space Gaussian process. The framework uses shallow parameterized circuits and does not require fault-tolerant quantum hardware, which makes it a candidate for noisy intermediate-scale quantum devices.

DOI: 10.1088/2632-2153/aeb504

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