Generalization of short coherent control pulses: extension to arbitrary rotations

TL;DR

This paper extends the theoretical framework for controlling quantum bits by generalizing the design of short coherent control pulses to arbitrary rotations, providing analytical corrections and identifying cases where complexity does not enhance performance.

Contribution

It introduces a systematic expansion for short control pulses acting as arbitrary rotations, extending prior work limited to fixed-axis rotations, with explicit correction calculations.

Findings

Leading and next-leading correction terms derived.

Certain pulses show no improvement with arbitrary rotations.

Framework applicable to advanced quantum control design.

Abstract

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.