# Quantum storage in quantum ferromagnets

## TL;DR

This paper explores the potential of Heisenberg ferromagnets for robust quantum storage by using permutation-invariant codes and energy error bounds, aiming to improve quantum memory lifetime.

## Contribution

It introduces a novel approach to quantum storage in Heisenberg ferromagnets using permutation-invariant codes and energy bounds, with theoretical and numerical analysis of storage lifetime.

## Key findings

- Increasing effective dimension improves storage lifetime.
- Maximal effective dimension yields an upper bound on storage error.
- Numerical bounds enhance understanding of quantum memory lifetimes.

## Abstract

We must protect inherently fragile quantum data to unlock the potential of quantum technologies. A pertinent concern in schemes for quantum storage is their potential for near-term implementation. Since Heisenberg ferromagnets are readily available, we investigate their potential for robust quantum storage. We propose to use permutation-invariant quantum codes to store quantum data in Heisenberg ferromagnets, because the ground space of any Heisenberg ferromagnet must be symmetric under any permutation of the underlying qubits. By exploiting an area law on the expected energy of Pauli errors, we show that increasing the effective dimension of Heisenberg ferromagnets can improve the storage lifetime. When the effective dimension of Heisenberg ferromagnets is maximal, we also obtain an upper bound for the storage error. This result relies on perturbation theory, where we use Davis' divided difference representation for Fr{\'e}chet derivatives along with the recursive structure of these divided differences. Our numerical bounds allow us to better understand how quantum memory lifetimes can be enhanced in Heisenberg ferromagnets.