The Non-Equilibrium Reliability of Quantum Memories

TL;DR

This paper investigates the limitations of the 2D Toric code for quantum memory, showing it cannot reliably store quantum information for times proportional to system size, unlike classical models like the 2D Ising model.

Contribution

It provides a detailed analysis of the non-equilibrium reliability of the 2D Toric code under realistic noise and perturbations, highlighting fundamental limitations for quantum memory.

Findings

Toric code cannot store quantum information for time O(N) on N^2 qubits.

2D Ising model can protect classical information for exponentially long times.

Implications for robustness of topological quantum computation operations.

Abstract

The ability to store quantum information without recourse to constant feedback processes would yield a significant advantage for future implementations of quantum information processing. In this paper, limitations of the prototypical model, the Toric code in two dimensions, are elucidated along with a sufficient condition for overcoming these limitations. Specifically, the interplay between Hamiltonian perturbations and dynamically occurring noise is considered as a system in its ground state is brought into contact with a thermal reservoir. This proves that when utilizing the Toric code on N^2 qubits in a 2D lattice as a quantum memory, the information cannot be stored for a time O(N). In contrast, the 2D Ising model protects classical information against the described noise model for exponentially long times. The results also have implications for the robustness of braiding operations in topological quantum computation.