Optimal rotation of a qubit under dynamic measurement and velocity control

TL;DR

This paper investigates optimal control strategies for rotating a qubit in minimal time by leveraging weak measurements and control of measurement strength and angular velocity, demonstrating significant speedups over previous methods.

Contribution

It introduces a novel control approach that utilizes measurement backaction and control of measurement strength, improving the speed of qubit state transfer.

Findings

Significant speedup in state transfer time compared to previous methods

Effective use of measurement backaction in quantum control

Numerical validation on a single qubit example

Abstract

In this article we explore a modification in the problem of controlling the rotation of a two level quantum system from an initial state to a final state in minimum time. Specifically we consider the case where the qubit is being weakly monitored -- albeit with an assumption that both the measurement strength as well as the angular velocity are assumed to be control signals. This modification alters the dynamics significantly and enables the exploitation of the measurement backaction to assist in achieving the control objective. The proposed method yields a significant speedup in achieving the desired state transfer compared to previous approaches. These results are demonstrated via numerical solutions for an example problem on a single qubit.