Related papers: Quantum polar decomposition algorithm

Quantum polar decomposition algorithm

URL: http://arxiv.org/abs/2006.00841v1
Date: Mon, 1 Jun 2020 10:34:24 GMT
Title: Quantum polar decomposition algorithm
Authors: Seth Lloyd, Samuel Bosch, Giacomo De Palma, Bobak Kiani, Zi-Wen Liu, Milad Marvian, Patrick Rebentrost, David M. Arvidsson-Shukur
Abstract summary: This paper shows that the ability to apply a Hamiltonian $pmatrix 0 & Adagger cr A & 0 cr $ translates into the ability to perform the transformations $e-iBt$ and $U$ in a deterministic fashion.
Score: 12.386348820609626
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The polar decomposition for a matrix $A$ is $A=UB$, where $B$ is a positive Hermitian matrix and $U$ is unitary (or, if $A$ is not square, an isometry). This paper shows that the ability to apply a Hamiltonian $\pmatrix{ 0 & A^\dagger \cr A & 0 \cr} $ translates into the ability to perform the transformations $e^{-iBt}$ and $U$ in a deterministic fashion. We show how to use the quantum polar decomposition algorithm to solve the quantum Procrustes problem, to perform pretty good measurements, to find the positive Hamiltonian closest to any Hamiltonian, and to perform a Hamiltonian version of the quantum singular value transformation.

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