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Hamiltonian singular value transformation and inverse block encoding

Authors :
Lloyd, Seth
Kiani, Bobak T.
Arvidsson-Shukur, David R. M.
Bosch, Samuel
De Palma, Giacomo
Kaminsky, William M.
Liu, Zi-Wen
Marvian, Milad
Publication Year :
2021

Abstract

The quantum singular value transformation is a powerful quantum algorithm that allows one to apply a polynomial transformation to the singular values of a matrix that is embedded as a block of a unitary transformation. This paper shows how to perform the quantum singular value transformation for a matrix that can be embedded as a block of a Hamiltonian. The transformation can be implemented in a purely Hamiltonian context by the alternating application of Hamiltonians for chosen intervals: it is an example of the Quantum Alternating Operator Ansatz (generalized QAOA). We also show how to use the Hamiltonian quantum singular value transformation to perform inverse block encoding to implement a unitary of which a given Hamiltonian is a block. Inverse block encoding leads to novel procedures for matrix multiplication and for solving differential equations on quantum information processors in a purely Hamiltonian fashion.<br />Comment: 11 pages, plain TeX

Subjects

Subjects :
Quantum Physics

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2104.01410
Document Type :
Working Paper