https://doi.org/10.1140/epjb/s10051-021-00221-9
Regular Article - Mesoscopic and Nanoscale Systems
Implementation of one-qubit gates using optimal control theory for a dissipative system
, 13, Rue Saint Fulbert, 69008, Lyon, France
Received:
23
April
2021
Accepted:
5
October
2021
Published online:
27
October
2021
The main objective of this paper is optimal control of decoherence and dissipation in a system of single qubit. First, we use the Bloch–Redfield formalism to derive the master equation describing the evolution of the qubit state parameterized by vectors in the Bloch sphere. The dissipative effect is described by the driven spin-boson model. By use of the optimal control methodology, we determine the fields that generate Not gate and Hadamard gate. Our optimal control has two components. To solve our optimal control problem, we use the techniques of automatic differentiation (AD) as an alternative to the Pontryagin’s minimum principle (PMP). The later is less straightforward since the master equation is complex. According to our numerical results, we conjecture that in the regime of weak system–bath coupling and low temperature, the driven spin-boson model is quasi-controllable.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
