Continuously decoupling a Hadamard quantum gate from independent classes of errors

TL;DR

This paper demonstrates how continuous dynamical decoupling can protect a Hadamard quantum gate from multiple independent error sources, including dephasing, bit flipping, and dissipation, by optimizing control fields based on environmental spectral densities.

Contribution

It introduces a method for simultaneous protection of a Hadamard gate against multiple error types using tailored continuous control fields, considering different spectral densities.

Findings

Protection is achievable with higher frequency control fields for super-ohmic environments.

Partial protection against dephasing enhances robustness to bit flipping and dissipation.

An efficient control field arrangement can simultaneously mitigate three classes of errors.

Abstract

We consider protecting a Hadamard operation from independent dephasing, bit flipping, and dissipation. These environment-induced errors are represented by three uncorrelated reservoirs of thermalized bosons and we show that the protection is achievable through continuous dynamical decoupling. We find that, to decouple the Hadamard evolution from the environmental influence, we need a control field of higher frequency if the boson spectral density is super-ohmic than if it is ohmic. We also study the relevance of bit flipping and dissipation to the gate fidelity when it is protected from dephasing, showing how robust this partial protection is against these other perturbations. Finally, we calculate an efficient field arrangement capable of protecting simultaneously the gate operation from these three error classes.