Phase shift rule with the optimal parameter selection
- URL: http://arxiv.org/abs/2309.07655v1
- Date: Thu, 14 Sep 2023 12:20:28 GMT
- Title: Phase shift rule with the optimal parameter selection
- Authors: L.A. Markovich, S. Malikis, S. Polla and J.T. Brugu\'es
- Abstract summary: We provide insights about the optimal design of a parameter shift rule, tailored to various sorts of spectral information.
The proposed method lets derivatives be calculated for any system, regardless of how close the eigenvalues are to each other.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The phase shift rules enable the estimation of the derivative of a quantum
state with respect to phase parameters, providing valuable insights into the
behavior and dynamics of quantum systems. This capability is essential in
quantum simulation tasks where understanding the behavior of complex quantum
systems is of interest, such as simulating chemical reactions or condensed
matter systems. However, parameter shift rules are typically designed for
Hamiltonian systems with equidistant eigenvalues. For systems with closely
spaced eigenvalues, effective rules have not been established. We provide
insights about the optimal design of a parameter shift rule, tailored to
various sorts of spectral information that may be available. The proposed
method lets derivatives be calculated for any system, regardless of how close
the eigenvalues are to each other. It also optimizes the number of phase
shifts, which reduces the amount of gate resources needed.
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