Pontryagin-Optimal Control of a non-Hermitian Qubit
- URL: http://arxiv.org/abs/2208.02882v1
- Date: Thu, 4 Aug 2022 20:51:29 GMT
- Title: Pontryagin-Optimal Control of a non-Hermitian Qubit
- Authors: Philippe Lewalle, K. Birgitta Whaley
- Abstract summary: We study the control of a single non-Hermitian qubit.
We show how to realize any continuous and differentiable pure-state trajectory in the dynamics of a qubit conditioned on no emission.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Open-system quantum dynamics described by non-Hermitian effective
Hamiltonians have become a subject of considerable interest. Studies of
non-Hermitian physics have revealed general principles, including relationships
between the topology of the complex eigenvalue space and the breakdown of
adiabatic control strategies. We study here the control of a single
non-Hermitian qubit, similar to recently realized experimental systems in which
the non-Hermiticity arises from an open spontaneous emission channel. We review
the topological features of the resulting non-Hermitian Hamiltonian and then
present two distinct results. First, we illustrate how to realize any
continuous and differentiable pure-state trajectory in the dynamics of a qubit
that are conditioned on no emission. This result implicitly provides a
workaround for the breakdown of standard adiabatic following in such
non-Hermitian systems. Second, we use Pontryagin's maximum principle to derive
optimal trajectories connecting boundary states on the Bloch sphere, using a
cost function which balances the desired dynamics against the controller energy
used to realize them. We demonstrate that the latter approach can effectively
find trajectories which maintain high state purity even in the case of
inefficient detection.
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