Frequency modulated pulses for quantum bits coupled to time-dependent baths

TL;DR

This paper develops frequency modulated pulse techniques for controlling quantum bits coupled to time-dependent baths, enabling robust quantum gates by decoupling bath dynamics during finite-duration pulses.

Contribution

It introduces frequency modulated pulses and extends the analysis to time-dependent baths, providing analytical solutions for robust quantum control.

Findings

Frequency modulated pulses effectively decouple bath and qubit dynamics.

Analytical solutions for nd -pulses are derived.

Methods are suitable for experimental setups with amplitude modulation constraints.

Abstract

We consider the coherent control of a quantum bit by the use of short pulses with finite duration \tau_p. By shaping the pulse, we perturbatively decouple the dynamics of the bath from the dynamics of the quantum bit during the pulse. Such shaped pulses provide single quantum bit gates robust against decoherence which are useful for quantum information processing. We extend previous results in two ways: (i) we treat frequency modulated pulses and (ii) we pass from time-independent baths to analytically time-dependent baths. First and second order solutions for \pi- and \pi/2-pulses are presented. They are useful in experiments where amplitude modulation is difficult to realize.