Quantum Self-Correcting Stabilizer Codes

TL;DR

This paper constructs anyonic excitations in 2D stabilizer Hamiltonians, demonstrating their inability for self-correcting quantum memory under thermal noise, and extends the argument to 3D systems.

Contribution

It provides a explicit construction of anyonic excitations in local 2D stabilizer codes and argues against their self-correcting quantum memory capability.

Findings

2D stabilizer codes cannot serve as self-correcting quantum memories under thermal noise.

The construction extends to 3D, suggesting self-correction is impossible in higher dimensions.

The results challenge the feasibility of quantum hard drives based on stabilizer codes.

Abstract

In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conclusion that, in the presence of local thermal noise, such systems cannot be used for the fault-tolerant storage of quantum information by self-correction i.e. they are ruled out as candidates for a `quantum hard drive'. We suggest that in 3D, the same construction leads to an argument that self-correction is impossible.