Assessing Quantum Advantage for Gaussian Process Regression

• URL: http://arxiv.org/abs/2505.22502v2
• Date: Thu, 03 Jul 2025 11:27:35 GMT
• Title: Assessing Quantum Advantage for Gaussian Process Regression
• Authors: Dominic Lowe, M. S. Kim, Roberto Bondesan,
• Abstract summary: We show that several quantum algorithms proposed for Gaussian Process Regression show no exponential speedup.<n>The implications for the quantum runtime algorithms are independent of the complexity of loading classical data on a quantum computer.<n>We supplement our theoretical analysis with numerical verification for popular kernels in machine learning.
• Score: 7.10052009802944
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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