Bayesian estimation for collisional thermometry and time-optimal
holonomic quantum computation
- URL: http://arxiv.org/abs/2307.10175v1
- Date: Sun, 16 Jul 2023 17:46:13 GMT
- Title: Bayesian estimation for collisional thermometry and time-optimal
holonomic quantum computation
- Authors: Gabriel O. Alves
- Abstract summary: In the first half we investigate how the Bayesian formalism can be introduced into the problem of quantum thermometry.
In the last part of the thesis we approach the problem of non-adiabatic holonomic computation.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this thesis we deal with two different topics. In the first half we
investigate how the Bayesian formalism can be introduced into the problem of
quantum thermometry -- a field which exploits the high level of control in
coherent devices to offer enhanced precision for temperature estimation. In
particular, we investigate concrete estimation strategies, with focus on
collisional thermometry, a protocol where a series of ancillae are sent
sequentially to probe the system's temperature. We put forth a complete
framework for analyzing collisional thermometry using Bayesian inference. The
approach is easily implementable and experimentally friendly. Moreover, it is
guaranteed to always saturate the Cram\'er-Rao bound in the long-time limit.
Subtleties concerning the prior information about the system's temperature are
also discussed and analyzed in terms of a modified Cram\'er-Rao bound
associated with Van Trees and Sch\"utzenberger.
Meanwhile, in the last part of the thesis we approach the problem of
non-adiabatic holonomic computation. Namely, we investigate the implementation
based on $\Lambda$-systems. It is known that a three-level system can be used
in a $\Lambda$-type configuration in order to construct a universal set of
quantum gates through the use of non-Abelian nonadiabatic geometrical phases.
Such construction allows for high-speed operation times which diminish the
effects of decoherence. This might be, however, accompanied by a breakdown of
the validity of the rotating-wave approximation (RWA) due to the comparable
timescale between counter-rotating terms and the pulse length, which greatly
affects the dynamics. Here, we investigate the trade-off between dissipative
effects and the RWA validity, obtaining the optimal regime for the operation of
the holonomic quantum gates.
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