The XYZ(2) hexagonal stabilizer code
Journal article, 2022

We consider a topological stabilizer code on a honeycomb grid, the "XYZ(2) " code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [1], with a specific implementation of the boundary. It utilizes weight-six (XYZXYZ) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d(2) qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y, or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50 %. In contrast to the rotated surface code and the XZZX code, which have code distance d(2) only for pure Y noise, here the code distance is 2d(2) for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.

Author

Basudha Srivastava

University of Gothenburg

Anton Frisk Kockum

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Mats Granath

University of Gothenburg

Quantum

2521327X (eISSN)

Vol. 6 698-

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing

DOI

10.22331/Q-2022-04-27-698

More information

Latest update

4/21/2023