The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
Quantum assisted Gaussian process regression
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regression (GPR), leading to an exponential reduction in computation time in some instances. We show that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs.
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quant-ph 2representative citing papers
Quantum data fitting algorithm for non-sparse N x N Hermitian matrices achieves O(κ² √N polylog(N) / (ε log κ)) runtime via QSVE, eigenvalue sign recovery, and regularization.
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A shortcut to an optimal quantum linear system solver
The paper gives a QLSS with query complexity (1+O(ε))κ ln(2√2/ε) using one kernel reflection when ||x|| is known, or O(κ log(1/ε)) overall, with explicit bound 56κ + 1.05κ ln(1/ε).
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Quantum Data Fitting Algorithm for Non-sparse Matrices
Quantum data fitting algorithm for non-sparse N x N Hermitian matrices achieves O(κ² √N polylog(N) / (ε log κ)) runtime via QSVE, eigenvalue sign recovery, and regularization.