Optimized pulses for the control of uncertain qubits

TL;DR

This paper develops optimized quantum control pulses that enhance robustness against uncertainties in qubit systems, combining environment-decoupling criteria with optimal control theory, demonstrated through simulations on quantum dot qubits.

Contribution

It introduces a systematic method to integrate environment-decoupling criteria with optimal control, improving robustness of quantum gates against multiple uncertainties.

Findings

Enhanced gate fidelity with combined control strategies

Robust controls outperform traditional pulses under uncertainties

Realistic noise impacts are comparable to system and environment fluctuations

Abstract

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for \pi/2- and \pi-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from \pi/2- and \pi-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.