Minimum time generation of a uniform superposition in a qubit with only transverse field control

Abstract

We consider a two-level system with a fixed energy spacing (detuning) between the two levels and a single transverse control field which can take values between zero and a maximum amplitude. Using Pontryagin's maximum principle, we completely solve the problem of generating in minimum time a uniform superposition of the two quantum states when starting from one of them, for all the values of the ratio between the maximum control amplitude and the detuning. For each value of this ratio we find the optimal pulse sequence to have the bang-bang form, and calculate the durations of the pulses composing it. The suggested framework is not only restricted to the problem at hand, but it can be also exploited in the problem of fast charging a quantum battery based on a two-level system, as well as for the optimization of pulse-sequences used for the controlled preparation of the excited state in a quantum emitter, which is a prerequisite for its usage as a single-photon source.

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• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Analytically solvable many-body Rosen-Zener quantum battery
• Fast charging of an Ising spin pair quantum battery using optimal control
• Noncompletely Positive Quantum Maps Enable Efficient Local Energy Extraction in Batteries
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• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Fast chiral resolution with optimal control
• Binary Quantum Control Optimization with Uncertain Hamiltonians
• Time-optimal single-scalar control on a qubit of unitary dynamics