Assessing Quantum Advantage for Gaussian Process Regression
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918080643334144 |
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| author | Lowe, Dominic Kim, M. S. Bondesan, Roberto |
| author_facet | Lowe, Dominic Kim, M. S. Bondesan, Roberto |
| contents | Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by rigorously proving that the condition number of a kernel matrix scales at least linearly with the matrix size under general assumptions on the data and kernel. We additionally prove that the sparsity and Frobenius norm of a kernel matrix scale linearly under similar assumptions. The implications for the quantum algorithms runtime are independent of the complexity of loading classical data on a quantum computer and also apply to dequantised algorithms. We supplement our theoretical analysis with numerical verification for popular kernels in machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Assessing Quantum Advantage for Gaussian Process Regression Lowe, Dominic Kim, M. S. Bondesan, Roberto Quantum Physics Machine Learning Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by rigorously proving that the condition number of a kernel matrix scales at least linearly with the matrix size under general assumptions on the data and kernel. We additionally prove that the sparsity and Frobenius norm of a kernel matrix scale linearly under similar assumptions. The implications for the quantum algorithms runtime are independent of the complexity of loading classical data on a quantum computer and also apply to dequantised algorithms. We supplement our theoretical analysis with numerical verification for popular kernels in machine learning. |
| title | Assessing Quantum Advantage for Gaussian Process Regression |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2505.22502 |