Topological Dynamical Decoupling

TL;DR

This paper introduces a topological approach to dynamical decoupling in 2D lattice-based qubit systems, utilizing topological classes of circles to protect quantum information from local Hamiltonians, compatible with existing decoupling methods.

Contribution

It presents a novel topological method for designing dynamical decoupling procedures using lattice circle classes, enhancing error suppression in quantum systems.

Findings

Effective decoupling of local Hamiltonians in 2D lattice qubits.

Compatibility with Eulerian and concatenated decoupling techniques.

Application to error suppression in surface codes.

Abstract

We show that topological equivalence classes of circles in a two-dimensional square lattice can be used to design dynamical decoupling procedures to protect qubits attached on the edges of the lattice. Based on the circles of the topologically trivial class in the original and the dual lattices, we devise a procedure which removes all kinds of local Hamiltonians from the dynamics of the qubits while keeping information stored in the homological degrees of freedom unchanged. If only the linearly independent interaction and nearest-neighbor two-qubit interactions are concerned, a much simpler procedure which involves the four equivalence classes of circles can be designed. This procedure is compatible with Eulerian and concatenated dynamical decouplings, which make it possible to implement the procedure with bounded-strength controls and for a long time period. As an application, it is shown that our method can be directly generalized to finite square lattices to suppress uncorrectable errors in surface codes.