Nonadiabatic holonomic quantum computation based on commutation relation
- URL: http://arxiv.org/abs/2308.06674v1
- Date: Sun, 13 Aug 2023 03:30:13 GMT
- Title: Nonadiabatic holonomic quantum computation based on commutation relation
- Authors: P. Z. Zhao, D. M. Tong
- Abstract summary: A crucial step in realizing nonadiabatic holonomic quantum computation is to remove the dynamical phase from the total phase.
In this paper, we put forward a strategy to design nonadiabatic holonomic quantum computation based on a commutation relation rather than the parallel transport condition.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Nonadiabatic holonomic quantum computation has received increasing attention
due to the merits of both robustness against control errors and high-speed
implementation. A crucial step in realizing nonadiabatic holonomic quantum
computation is to remove the dynamical phase from the total phase. For this
reason, previous schemes of nonadiabatic holonomic quantum computation have to
resort to the parallel transport condition, i.e., requiring the instantaneous
dynamical phase to be always zero. In this paper, we put forward a strategy to
design nonadiabatic holonomic quantum computation, which is based on a
commutation relation rather than the parallel transport condition. Instead of
requiring the instantaneous dynamical phase to be always zero, the dynamical
part of the total phase is separated from the geometric part and then removed
by properly choosing evolution parameters. This strategy enhances the
flexibility to realize nonadiabatic holonomic quantum computation as the
commutation relation is more relaxed than the parallel transport condition. It
provides more options for realizing nonadiabatic holonomic quantum computation
and hence allows us to optimize realizations such as the evolution time and
evolution paths.
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