Hamiltonian singular value transformation and inverse block encoding
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.
Cite
@article{arxiv.2104.01410,
title = {Hamiltonian singular value transformation and inverse block encoding},
author = {Seth Lloyd and Bobak T. Kiani and David R. M. Arvidsson-Shukur and Samuel Bosch and Giacomo De Palma and William M. Kaminsky and Zi-Wen Liu and Milad Marvian},
journal= {arXiv preprint arXiv:2104.01410},
year = {2021}
}
Comments
11 pages, plain TeX