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.
Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove upper bounds on the number of queries to the input data required to compute these metrics. In the worst case, our quantum algorithms lead to polynomial reductions in query complexity relative to the corresponding classical algorithm. In certain cases, we show exponential or even super-exponential reductions over the classical analog. We study the performance of our quantum nearest-neighbor algorithms on several real-world binary classification tasks and find that the classification accuracy is competitive with classical methods.
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UNVERDICTED 3representative citing papers
VISTA achieves near-Heisenberg scaling in moderately noisy quantum magnetometry by passively evolving a probe, comparing it via swap test to a physics-informed quantum twin circuit, and optimizing only physical parameters with quasi-normalization.
Quantum algorithm for k-minima with O(sqrt(k N)) query complexity via threshold search and generalized amplitude amplification.
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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.
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GHZ is All You Need: Quantum Sensing with VISTA
VISTA achieves near-Heisenberg scaling in moderately noisy quantum magnetometry by passively evolving a probe, comparing it via swap test to a physics-informed quantum twin circuit, and optimizing only physical parameters with quasi-normalization.
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A Quantum Algorithm for Finding $k$-Minima
Quantum algorithm for k-minima with O(sqrt(k N)) query complexity via threshold search and generalized amplitude amplification.