Fourier-based quantum signal processing
- URL: http://arxiv.org/abs/2206.02826v1
- Date: Mon, 6 Jun 2022 18:02:30 GMT
- Title: Fourier-based quantum signal processing
- Authors: Thais de Lima Silva, Lucas Borges, Leandro Aolita
- Abstract summary: Implementing general functions of operators is a powerful tool in quantum computation.
Quantum signal processing is the state of the art for this aim.
We present an algorithm for Hermitian-operator function design from an oracle given by the unitary evolution.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Implementing general functions of operators is a powerful tool in quantum
computation. It can be used as the basis for a variety of quantum algorithms
including matrix inversion, real and imaginary-time evolution, and matrix
powers. Quantum signal processing is the state of the art for this aim,
assuming that the operator to be transformed is given as a block of a unitary
matrix acting on an enlarged Hilbert space. Here we present an algorithm for
Hermitian-operator function design from an oracle given by the unitary
evolution with respect to that operator at a fixed time. Our algorithm
implements a Fourier approximation of the target function based on the
iteration of a basic sequence of single-qubit gates, for which we prove the
expressibility. In addition, we present an efficient classical algorithm for
calculating its parameters from the Fourier series coefficients. Our algorithm
uses only one qubit ancilla regardless the degree of the approximating series.
This contrasts with previous proposals, which required an ancillary register of
size growing with the expansion degree. Our methods are compatible with
Trotterised Hamiltonian simulations schemes and hybrid digital-analog
approaches.
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