Combining dynamical decoupling with fault-tolerant quantum computation

TL;DR

This paper demonstrates how dynamical decoupling (DD) pulse sequences can enhance the fault tolerance of quantum computers by providing bounds on gate accuracy and conditions for outperforming unprotected gates, especially under Hamiltonian noise.

Contribution

It provides theoretical bounds and conditions under which DD-protected gates improve fault-tolerance and reduce overhead in quantum circuits, considering bath dynamics and noise models.

Findings

DD can improve quantum gate accuracy under certain conditions.

Fault-tolerant circuits with DD gates tolerate stronger noise.

Performance depends on bath Hamiltonian and correlation spectrum.

Abstract

We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise, and have a lower overhead cost, than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer, and can be expressed either in terms of the operator norm of the bath's Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.