Hermitian Matrix Definiteness from Quantum Phase Estimation

• URL: http://arxiv.org/abs/2009.04117v2
• Date: Thu, 24 Nov 2022 19:00:13 GMT
• Title: Hermitian Matrix Definiteness from Quantum Phase Estimation
• Authors: Andr\'es G\'omez and Javier Mas
• Abstract summary: An algorithm to classify a general Hermitian matrix according to its signature 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 algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits.
• Score: 3.04585143845864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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