Affiliation:
1. School of Mathematics, University of Bristol, Bristol, United Kingdom
Abstract
Computing eigenvalues of matrices is ubiquitous in numerical linear algebra problems. Currently, fast quantum algorithms for estimating eigenvalues of Hermitian and unitary matrices are known. However, the general case is far from fully understood in the quantum case. Based on a quantum algorithm for solving linear ordinary differential equations, we show how to estimate the eigenvalues of diagonalizable matrices that only have real eigenvalues. The output is a superposition of the eigenpairs, and the overall complexity is polylog in the dimension for sparse matrices. Under an assumption, we extend the algorithm to diagonalizable matrices with complex eigenvalues.
Funder
QuantERA ERA-NET Cofund in Quantum Technologies implemented within the European Union’s Horizon 2020 Programme
EPSRC
Publisher
Association for Computing Machinery (ACM)
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