Subsystem surface code[1] 

Description

Subsystem version of the surface code defined on a square lattice with qubits placed at every vertex and center of everry edge.

For example, a \([[3L^2,2,L]]\) family has weight-six \(X,Z\)-type stabilizers supported on two of the four triangles of each plaquette.

Fault Tolerance

Gauge fixing and changing the order in which check operators are measured yields a fault-tolerant decoder [2].

Code Capacity Threshold

Independent \(X,Z\) noise: the threshold under ML decoding corresponds to the value of critical point of the two-dimensional hexagonal-lattice random-bond Ising model on the Nishimori line [1,3], calculated to be around \(7\%\) in Ref. [4].

Threshold

\(0.81\%\) threshold for circuit-level depolarizing noise under a variant of MWPM and using gauge-fixing and specific measurement schedules [2], improving the \(0.67\%\) threshold for standard measurement schedules [1].\(2.22\%\) threshold for circuit-level infinitely biased noise under a variant of MWPM and using gauge-fixing and specific measurement schedules [2], improving the \(0.52\%\) threshold with standarn measurement schedules.

Notes

See [5; Sec. III.C3] for an exposition.

Parent

Cousins

References

[1]
S. Bravyi et al., “Subsystem surface codes with three-qubit check operators”, (2013) arXiv:1207.1443
[2]
O. Higgott and N. P. Breuckmann, “Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead”, Physical Review X 11, (2021) arXiv:2010.09626 DOI
[3]
H. Nishimori, “Geometry-Induced Phase Transition in the ±JIsing Model”, Journal of the Physical Society of Japan 55, 3305 (1986) DOI
[4]
S. L. A. de Queiroz, “Multicritical point of Ising spin glasses on triangular and honeycomb lattices”, Physical Review B 73, (2006) arXiv:cond-mat/0510816 DOI
[5]
B. M. Terhal, “Quantum error correction for quantum memories”, Reviews of Modern Physics 87, 307 (2015) arXiv:1302.3428 DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: subsystem_surface

Cite as:
“Subsystem surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/subsystem_surface
BibTeX:
@incollection{eczoo_subsystem_surface, title={Subsystem surface code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/subsystem_surface} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/subsystem_surface

Cite as:

“Subsystem surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/subsystem_surface

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/subsystem/topological/surface/subsystem_surface.yml.