Optimal rotation control for a qubit subject to continuous measurement

TL;DR

This paper investigates the optimal control of a monitored qubit's rotation to an orthogonal state in minimum time, using viscosity solutions to handle non-regular cost functions, and provides bounds for state preparation.

Contribution

It introduces a novel approach to quantum control problems with irregular cost functions by employing viscosity solutions, proving their existence and uniqueness.

Findings

Proved existence and uniqueness of viscosity solutions for the control problem.

Derived bounds on the minimum time to prepare pure states from mixed states.

Analyzed control strategies for qubit rotation under continuous measurement.

Abstract

In this article we analyze the optimal control strategy for rotating a monitored qubit from an initial pure state to an orthogonal state in minimum time. This strategy is described for two different cost functions of interest which do not have the usual regularity properties. Hence, as classically smooth cost functions may not exist, we interpret these functions as viscosity solutions to the optimal control problem. Specifically we prove their existence and uniqueness in this weak-solution setting. In addition, we also give bounds on the time optimal control to prepare any pure state from a mixed state.