# 2D Compass Codes

@article{Li20182DCC,
title={2D Compass Codes},
author={Muyuan Li and Daniel Miller and M. Newman and Yukai Wu and K. Brown},
journal={Physical Review X},
year={2018},
volume={9}
}
The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity… Expand

#### Figures and Tables from this paper

Fault-tolerant compass codes
• Physics
• 2020
We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achievedExpand
Topological and Subsystem Codes on Low-Degree Graphs with Flag Qubits
• Computer Science, Physics
• 2020
This work modify minimum weight perfect matching decoding to efficiently and scalably incorporate information from measurements of the flag qubits and correct up to the full code distance while respecting the limited connectivity. Expand
Logical performance of 9 qubit compass codes in ion traps with crosstalk errors
• Physics
• 2019
We simulate four quantum error correcting codes under error models inspired by realistic noise sources in near-term ion trap quantum computers: $T_2$ dephasing, gate overrotation, and crosstalk. WeExpand
Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
• Physics, Mathematics
• 2020
We introduce a framework for constructing a quantum error correcting code from any classical error correcting code. This includes CSS codes and goes beyond the stabilizer formalism to allow quantumExpand
The XZZX Surface Code
• Physics, Computer Science
• 2020
We show that a variant of the surface code---the XZZX code---offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved withExpand
Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Physics, Mathematics
• 2019
One of the leading quantum computing architectures is based on the two-dimensional (2D) surface code. This code has many advantageous properties such as a high error threshold and a planar layout ofExpand
Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Physics, Mathematics
• 2020
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured,Expand
High-Threshold Code for Modular Hardware With Asymmetric Noise
• Computer Science, Physics
• 2019
A customised decoder is developed to process the information about the likely location of errors, obtained from the error detect stage, with an advanced variant of the minimum weight perfect matching algorithm. Expand
Tailoring surface codes for highly biased noise
• Physics
• 2018
The surface code, with a simple modification, exhibits ultra-high error correction thresholds when the noise is biased towards dephasing. Here, we identify features of the surface code responsibleExpand
Generating Fault-Tolerant Cluster States ewline from Crystal Structures
Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work hasExpand

#### References

SHOWING 1-10 OF 80 REFERENCES
Direct measurement of Bacon-Shor code stabilizers
• Physics
• 2018
A Bacon-Shor code is a subsystem quantum error-correcting code on an $L \times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $(L-1)^2$ weight-2Expand
Topological quantum memory
• Physics
• 2002
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, andExpand
Optimal Bacon-Shor codes
• Computer Science, Physics
• Quantum Inf. Comput.
• 2013
It is shown that a single Bacon-Shor code block, used by itself without concatenation, can provide very effective protection against logical errors if the noise is highly biased and the physical error rate pZ is a few percent or below. Expand
Tailored codes for small quantum memories
• Physics, Computer Science
• 2017
We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant errorExpand
Strong resilience of topological codes to depolarization
• Physics
• 2012
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stabilityExpand
Incoherent dynamics in the toric code subject to disorder
• Physics
• 2012
We numerically study the effects of two forms of quenched disorder on the anyons of the toric code. First, a class of codes based on random lattices of stabilizer operators is presented and shown toExpand
Low-distance Surface Codes under Realistic Quantum Noise
• Physics, Computer Science
• ArXiv
• 2014
It is found that architectures with gate times in the 5-40 ns range and T1 times of at least 1-2 us range will exhibit improved logical error rates with a 17-qubit surface code encoding. Expand
Subsystem fault tolerance with the Bacon-Shor code.
• Medicine, Physics
• Physical review letters
• 2007
A lower bound on the quantum accuracy threshold, 1.94 x 10(-4) for adversarial stochastic noise, is proved, that improves previous lower bounds by nearly an order of magnitude. Expand
Topological subsystem codes
A general mapping connecting suitable classical statistical mechanical models to optimal error correction in subsystem stabilizer codes that suffer from depolarizing noise is given. Expand
Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not theExpand