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

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References

SHOWING 1-10 OF 80 REFERENCES
Direct measurement of Bacon-Shor code stabilizers
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
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
TLDR
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
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
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
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
TLDR
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.
TLDR
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
TLDR
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
...
1
2
3
4
5
...