A Hybrid Quantum Solver for Gaussian Process Regression
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915559462928384 |
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| author | Bükrü, Kerem Leger, Steffen Hickmann, M. Lautaro Rieser, Hans-Martin Sturm, Ralf Siefkes, Tjark |
| author_facet | Bükrü, Kerem Leger, Steffen Hickmann, M. Lautaro Rieser, Hans-Martin Sturm, Ralf Siefkes, Tjark |
| contents | Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However, training a Gaussian process model using standard methods requires matrix inversions with a cubic time complexity, which poses significant computational challenges for inference on larger datasets. Quantum algorithms, such as the HHL algorithm, have been proposed as solutions that overcome the need for classical matrix inversions by efficiently solving linear systems of equations using quantum computers. However, to gain a computational advantage over classical algorithms, these algorithms require fault-tolerant quantum computers with a large number of qubits, which are not yet available. The Variational Quantum Linear Solver is a hybrid quantum-classical algorithm that solves linear systems of equations by optimizing the parameters of a variational quantum circuit using a classical computer. This method is especially suitable for noisy intermediate-scale quantum computers, as it does not require many qubits. It can be used to compute the posterior distribution of a Gaussian process by reformulating the matrix inversion into a set of linear systems of equations. We empirically demonstrate that using the Variational Quantum Linear Solver to perform inference for Gaussian process regression delivers regression quality comparable to that of classical methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hybrid Quantum Solver for Gaussian Process Regression Bükrü, Kerem Leger, Steffen Hickmann, M. Lautaro Rieser, Hans-Martin Sturm, Ralf Siefkes, Tjark Quantum Physics 68T05 (Primary) 65F10, 81P68 (Secondary) G.1.3; I.2.6 Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However, training a Gaussian process model using standard methods requires matrix inversions with a cubic time complexity, which poses significant computational challenges for inference on larger datasets. Quantum algorithms, such as the HHL algorithm, have been proposed as solutions that overcome the need for classical matrix inversions by efficiently solving linear systems of equations using quantum computers. However, to gain a computational advantage over classical algorithms, these algorithms require fault-tolerant quantum computers with a large number of qubits, which are not yet available. The Variational Quantum Linear Solver is a hybrid quantum-classical algorithm that solves linear systems of equations by optimizing the parameters of a variational quantum circuit using a classical computer. This method is especially suitable for noisy intermediate-scale quantum computers, as it does not require many qubits. It can be used to compute the posterior distribution of a Gaussian process by reformulating the matrix inversion into a set of linear systems of equations. We empirically demonstrate that using the Variational Quantum Linear Solver to perform inference for Gaussian process regression delivers regression quality comparable to that of classical methods. |
| title | A Hybrid Quantum Solver for Gaussian Process Regression |
| topic | Quantum Physics 68T05 (Primary) 65F10, 81P68 (Secondary) G.1.3; I.2.6 |
| url | https://arxiv.org/abs/2510.15486 |