Lifetime of topological quantum memories in thermal environment

TL;DR

This paper studies how lattice geometry affects the lifetime of two-dimensional topological quantum memories in thermal environments, providing formulas and optimal designs for implementation.

Contribution

It introduces lattice-dependent error tolerance and a simple formula for memory lifetime, guiding optimal geometries for quantum memory hardware.

Findings

Error tolerance varies with lattice structure.

Lifetime depends on average lattice degree.

Optimal geometries for Josephson junctions are proposed.

Abstract

Here we investigate the effect lattice geometry has on the lifetime of two-dimensional topological quantum memories. Initially, we introduce various lattice patterns and show how the error-tolerance against bit-flips and phase-flips depends on the structure of the underlying lattice. Subsequently, we investigate the dependence of the lifetime of the quantum memory on the structure of the underlying lattice when it is subject to a finite temperature. Importantly, we provide a simple effective formula for the lifetime of the memory in terms of the average degree of the lattice. Finally, we propose optimal geometries for the Josephson junction implementation of topological quantum memories.