Hamiltonian singular value transformation and inverse block encoding
- URL: http://arxiv.org/abs/2104.01410v2
- Date: Sun, 30 May 2021 19:50:09 GMT
- Title: Hamiltonian singular value transformation and inverse block encoding
- Authors: Seth Lloyd, Bobak T. Kiani, David R.M. Arvidsson-Shukur, Samuel Bosch,
Giacomo De Palma, William M. Kaminsky, Zi-Wen Liu, Milad Marvian
- Abstract summary: We show how to perform the quantum singular value transformation for a matrix embedded as a block of a Hamiltonian.
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.
- Score: 12.386348820609626
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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