Pontryagin-Optimal Control of a non-Hermitian Qubit

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.

8 + 8 Pages, 7 Figures

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• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Enhancement of vibrationally assisted energy transfer by proximity to exceptional points, probed by fluorescence-detected vibrational spectroscopy
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Chiral and non-chiral swift mode conversion near an exception point with dynamic adiabaticity engineering
• Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging
• Quantum state-preparation control in noisy environment via most-likely paths
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation
• CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems