Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control

TL;DR

This paper presents an optimal control approach to implement fault-tolerant quantum logic gates on encoded qubits, overcoming limitations of geometric control methods in realistic, imperfect quantum systems.

Contribution

It introduces an optimal control framework that efficiently designs quantum gates, including difficult ones like the T-gate, within fixed time and limited resources.

Findings

Optimal control successfully implements all elementary gates in fixed time.

The method handles system imperfections like qubit inhomogeneity.

Difficult gates such as the T-gate are feasible with optimal control.

Abstract

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control.