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arXiv · 2009.04117

Hermitian Matrix Definiteness from Quantum Phase Estimation

Andrés Gómez·Javier Mas
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Abstract

An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a Hermitian matrix in one ancillary qubit. The signature of the matrix is extracted from the mean value of a spin operator in this single ancillary qubit. The algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits. The computational cost scales comparably to the classical one in the case of a generic matrix, but improves significantly for restricted classes of matrices like $k$-local or sparse hamiltonians.

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Andrés Gómez, Javier Mas. 2020-09-09. Hermitian Matrix Definiteness from Quantum Phase Estimation. https://doi.org/10.1007/s11128-022-03542-5

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