Symmetry-Protected Infinite-Temperature Quantum Memory from Subsystem Codes

TL;DR

This paper introduces a symmetry-based mechanism for protecting quantum information in many-body systems, enabling infinite-temperature quantum memory through subsystem codes and symmetry considerations, with robustness against certain perturbations.

Contribution

It demonstrates a generic symmetry and locality-based approach to achieve long-lived quantum memory, connecting it to noiseless subsystems and stabilizer codes, and explores robustness under perturbations.

Findings

Quantum information can be protected indefinitely by symmetry and locality.

The mechanism applies to models inspired by the surface code and Bacon-Shor code.

Encoded information retains long lifetime even with symmetry-violating perturbations.

Abstract

We study a mechanism whereby quantum information present in the initial state of a quantum many-body system can be protected for arbitrary times due to a combination of symmetry and spatial locality. Remarkably, the mechanism is sufficiently generic that the dynamics can be fully ergodic upon resolving the protecting symmetry and fixing the encoded quantum state, resulting in an infinite-temperature quantum memory. After exemplifying the mechanism in a strongly nonintegrable two-dimensional (2D) spin model inspired by the surface code, we find it has a natural interpretation in the language of noiseless subsystems and stabilizer subsystem codes. This interpretation yields a number of further examples, including a nonintegrable Hamiltonian with quantum memory based on the Bacon-Shor code. The lifetime of the encoded quantum information in these models is infinite provided the dynamics respect the stabilizer symmetry of the underlying subsystem code. In the presence of symmetry-violating perturbations, we make contact with previous work leveraging the concept of prethermalization to show that the encoded quantum information retains a parametrically long lifetime under dynamics with an enlarged continuous symmetry group. We identify conditions on the underlying subsystem code that enable such a prethermal enhancement of the memory lifetime.