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High fidelity state reconstruction of a qubit via dynamics of a dissipative resonator | | G. Di Bello
; L. M. Cangemi
; V. Cataudella
; G. De Filippis
; A. Nocera
; C. A. Perroni
; | | Date: |
1 Aug 2022 | | Abstract: | Using a dissipative quantum Rabi model, we study the dynamics of a slow qubit
coupled to a fast quantum resonator embedded in a viscous fluid from weak to
strong and ultra-strong coupling regimes. Solving the quantum Heisenberg
equations of motion, perturbative in the internal coupling between qubit and
resonator, we derive functional relationships directly linking the qubit
coordinates on the Bloch sphere to resonator observables. We then perform
accurate Matrix Product State simulations using the time dependent variational
principle, and compare our results both with the analytical solutions obtained
via the Heisenberg equations of motion, and with numerical solutions of a
Lindblad master equation, perturbative in the external coupling between
resonator and environment. We demonstrate that a qubit state pointing to
generic coordinates on the Bloch sphere can be fully reconstructed, up to the
strong coupling regime with a damped resonator. Indeed, by monitoring the qubit
fidelity with respect to free limit, we point out that, up to the strong
coupling regime, the qubit state accurately fulfills the functional
relationships of the Heisenberg equations of motion. Interestingly, a weak to
intermediate resonator coupling to the bath is able to anticipate the state
reconstruction of the qubit with respect to the same procedure for the closed
system. Moreover, we find a parameter regime in which, even if the standard
qubit readout fails, the resonator is still able to monitor the qubit dynamics.
Finally, in the ultra-strong coupling regime, non-Markovian effects become
robust and the dynamics of qubit and resonator are inextricably entangled
making the qubit state reconstruction difficult. Our work is not only
interesting from a fundamental point of view, but also for quantum control
issues, aimed to provide information about system dynamics through
measurements. | | Source: | arXiv, 2208.00708 | | Services: | Forum | Review | PDF | Favorites | |
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