Robust quantum control with disorder-dressed evolution

TL;DR

This paper introduces a novel approach to robust quantum control by using disorder-dressed evolution equations, enabling the identification of control pulses that remain effective despite pulse perturbations, demonstrated on single-qubit tasks.

Contribution

It presents a new method to find robust quantum control pulses using disorder-dressed evolution equations and adapts Krotov's method for this purpose.

Findings

Successfully identified robust control pulses for single-qubit tasks.

Disorder-dressed evolution captures pulse perturbations via quantum master equations.

Robust control pulses maintain high purity and target state fidelity.

Abstract

The theory of optimal quantum control serves to identify time-dependent control Hamiltonians that efficiently produce desired target states. As such, it plays an essential role in the successful design and development of quantum technologies. However, often the delivered control pulses are exceedingly sensitive to small perturbations, which can make it hard if not impossible to reliably deploy these in experiments. Robust quantum control aims at mitigating this issue by finding control pulses that uphold their capacity to reproduce the target states even in the presence of pulse perturbations. However, finding such robust control pulses is generically hard, since the assessment of control pulses requires the inclusion of all possible distorted versions in the evaluation. Here we show that robust control pulses can be identified based on disorder-dressed evolution equations. The latter capture the effect of disorder, which here stands for the pulse perturbations, in terms of quantum master equations describing the evolution of the disorder-averaged density matrix. In this approach to robust control, the purities of the final states indicate the robustness of the underlying control pulses, and robust control pulses are singled out if the final states are pure (and coincide with the target states). We show that this principle can be successfully employed to find robust control pulses. To this end, we adapt Krotov's method for disorder-dressed evolution and demonstrate its application with several single-qubit control tasks.