Optimal control of quantum gates in an exactly solvable non-Markovian open quantum bit system

TL;DR

This paper uses quantum optimal control theory to design high-fidelity quantum gates in a non-Markovian open qubit system, accounting for environmental effects and proposing a measure for gate error correction.

Contribution

It introduces an exact solvable model for non-Markovian open quantum systems and develops a control method to improve quantum gate fidelity considering environmental interactions.

Findings

Quantum control can significantly reduce gate errors in non-Markovian environments.

The improvement measure $\\mathcal{I}$ quantifies error correction effectiveness.

Conditions for optimal error correction are identified.

Abstract

We apply quantum optimal control theory (QOCT) to an exactly solvable non-Markovian open quantum bit (qubit) system to achieve state-independent quantum control and construct high-fidelity quantum gates for moderate qubit decaying parameters. An important quantity, improvement $\mathcal{I}$, is proposed and defined to quantify the correction of gate errors due to the QOCT iteration when the environment effects are taken into account. With the help of the exact dynamics, we explore how the gate error is corrected in the open qubit system and determine the conditions for significant improvement. The model adopted in this paper can be implemented experimentally in realistic systems such as the circuit QED system.