Dynamical Phase Error in Interacting Topological Quantum Memories

TL;DR

This paper investigates how topological quantum order (TQO) protects quantum memories from phase errors caused by dynamical processes, using spectral density correlations and numerical models of superconducting wires.

Contribution

It introduces a method to quantify spectral density correlations in topological sectors and demonstrates this with numerical simulations of an interacting p-wave superconducting wire.

Findings

TQO suppresses phase errors in quantum memories.

Spectral densities in different topological sectors are correlated to a quantifiable degree.

Numerical models confirm theoretical predictions about phase error suppression.

Abstract

A local Hamiltonian with Topological Quantum Order (TQO) has a robust ground state degeneracy that makes it an excellent quantum memory candidate. This memory can be corrupted however if part of the state leaves the protected ground state manifold and returns later with a dynamically accrued phase error. Here we analyse how TQO suppresses this process and use this to quantify the degree to which spectral densities in different topological sectors are correlated. We provide numerical verification of our results by modelling an interacting p-wave superconducting wire.