A passive self-correcting quantum memory in three dimensions

TL;DR

This paper presents a 3D quantum memory model that can store a qubit for exponentially long times at non-zero temperature, using a recursive transformation of a local Hamiltonian.

Contribution

It introduces a novel 3D stabilizer Hamiltonian with enhanced thermal stability for quantum information storage, maintaining locality through recursive transformations.

Findings

Ground state encodes a qubit for exponential time at non-zero temperature

Constructs a 3D local Hamiltonian with improved memory lifetime

Uses recursive transformations to maintain geometric locality

Abstract

We construct a 3D Pauli stabilizer Hamiltonian whose ground state space can encode a qubit for exponential time when coupled to a bath at non-zero temperature. Our construction recursively applies a sequence of transformations to a seed Hamiltonian that increases the memory lifetime of the encoded qubit while maintaining geometric locality in $\mathbb{R}^3$.