The Capabilities of a Perturbed Toric Code as a Quantum Memory

TL;DR

This paper investigates how typical perturbations affect the 2D toric code's ability to store quantum information, showing that survival time generally grows logarithmically with system size, with some variations under different conditions.

Contribution

It introduces a novel analysis of perturbations on the toric code using a mapping to a 1D transverse Ising model and Lieb-Robinson bounds, providing new insights into quantum memory stability.

Findings

Survival time grows at least logarithmically with system size for many perturbations.

A uniform magnetic field causes saturation of the logarithmic scaling.

Randomizing stabilizer strengths can lead to polynomial survival times depending on perturbation strength.

Abstract

We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on read-out. By transforming the system into a 1D transverse Ising model undergoing an instantaneous quench, and making extensive use of Lieb-Robinson bounds, we prove that for a large class of perturbations, the survival time of stored information grows at least logarithmically with the system size. A uniform magnetic field saturates this scaling behavior. We show that randomizing the stabilizer strengths gives a polynomial survival time with a degree that depends on the strength of the perturbation.