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arXiv · 1607.05404

Quantum singular value decomposition of non-sparse low-rank matrices

Patrick Rebentrost·Adrian Steffens·Seth Lloyd
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Abstract

In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors to be found quantum mechanically in a time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and non-square matrices via embedding matrices. In the context of the generic singular value decomposition of a matrix, we discuss the Procrustes problem of finding a closest isometry to a given matrix.

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Patrick Rebentrost, Adrian Steffens, Seth Lloyd. 2016-07-19. Quantum singular value decomposition of non-sparse low-rank matrices. https://doi.org/10.1103/physreva.97.012327

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