Alternative names: Gauge color code.
Description
A subsystem version of the color code. One way to obtain it is by expanding the vertices of a two-colex embedded in a surface of genus \(g\). Vertex expansion consists of spl every vertex into a triangle and splitting every edge into a pair of edges.Cousins
- Color code
- Entanglement-assisted operator-algebra QECC (EAOAQECC)— A 15-qubit subsystem color code can be converted into a hybrid code (an EA code) by converting its components to classical bits (ebits) [6].
- \([2^r-1,2^r-r-1,3]\) Hamming code— The \([10,6,3]\) shortened Hamming code can be converted into an EAOAQECC [6].
- Honeycomb Floquet code— Both honeycomb and subsystem color codes are generated via periodic sequences of measurements. However, any measurement sequence can be performed on the color code without destroying the logical qubits, while honeycomb codes can be maintained only with specific sequences. Honeycomb codes require a shorter measurement cycle and use fewer qubits at the given code distance [7].
- Majorana subsystem stabilizer code— The 3D subsystem color code has a Majorana variant which supports a 2D Majorana color code on its surface [8].
- Quantum pin code— Quantum pin codes have a subsystem version that can be viewed as a generalization of subsystem color codes [9].
Primary Hierarchy
Parents
Modular-qudit subsystem color codes reduce to subsystem color codes for \(q=2\).
Subsystem color code
Children
References
- [1]
- H. Bombin, “Topological subsystem codes”, Physical Review A 81, (2010) arXiv:0908.4246 DOI
- [2]
- H. Bombin, “Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes”, (2015) arXiv:1311.0879
- [3]
- B. J. Brown, N. H. Nickerson, and D. E. Browne, “Fault-tolerant error correction with the gauge color code”, Nature Communications 7, (2016) arXiv:1503.08217 DOI
- [4]
- H. M. Solanki and P. Kiran Sarvepalli, “Correcting Erasures with Topological Subsystem Color Codes”, 2020 IEEE Information Theory Workshop (ITW) 1 (2021) DOI
- [5]
- H. M. Solanki and P. K. Sarvepalli, “Decoding Topological Subsystem Color Codes Over the Erasure Channel using Gauge Fixing”, (2022) arXiv:2111.14594
- [6]
- P. J. Nadkarni, S. Adonsou, G. Dauphinais, D. W. Kribs, and M. Vasmer, “Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction”, (2024) arXiv:2411.14389
- [7]
- M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
- [8]
- A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, (2018) arXiv:1805.01836
- [9]
- C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
Page edit log
- Victor V. Albert (2022-05-18) — most recent
- Yi-Ting (Rick) Tu (2022-04-23)
- Victor V. Albert (2022-01-01)
Cite as:
“Subsystem color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/subsystem_color