Dynamical decoupling of interacting spins through group factorization

TL;DR

This paper introduces a method to optimize dynamical decoupling sequences in quantum spin systems by exploiting existing symmetries in the Hamiltonian, leading to more efficient error suppression.

Contribution

It presents a novel framework that uses group factorization to design shorter, more robust decoupling sequences by leveraging symmetries in the interaction Hamiltonian.

Findings

Recover classical NMR pulse sequences like Lee-Goldburg.

Create new sequences that suppress disorder and many-body interactions.

Show improved decoupling efficiency in various spin models.

Abstract

Dynamical decoupling (DD) is a well-known open-loop protocol for suppressing unwanted interactions in a quantum system, thereby drastically extending the coherence time of useful quantum states. In the original framework of evolution symmetrization, a DD sequence was shown to enforce a symmetry on the unwanted Hamiltonian, thereby suppressing it if the symmetry was inaccessible. In this work, we show how symmetries already present in the undesired Hamiltonian can be harnessed to reduce the complexity of decoupling sequences and to construct nested protocols that correct dominant errors at shorter timescales, using the factorization of DD symmetry groups into a product of its subgroups. We provide many relevant examples in various spin systems, using the Majorana constellation and point-group factorization to identify and exploit symmetries in the interaction Hamiltonian. Our framework recovers tailored pulse sequences developed in the context of NMR, including the classical Lee-Goldburg protocol, and further produces novel short and robust sequences capable of suppressing on-site disorder, dipole-dipole interactions, and more exotic many-body interactions in spin ensembles.