Description
A variant of the Kitaev surface code on a 3D lattice. The closely related solid code [3] consists of several 3D surface codes stitched together in a way that the distance scales faster than the linear size of the system.
Decoding
Flip decoder and its modification p-flip [4].
Threshold
Phenomenological noise model for the 3D toric code: \(2.90(2)\%\) under BP-OSD decoder [5], \(7.1\%\) under improved BP-OSD [6], and \(2.6\%\) under flip decoder [4]. For 3D surface code: \(3.08(4)\%\) under flip decoder [5].
Parents
Cousins
- Single-shot code — Some 3D surface codes are single-shot codes [7].
- Self-correcting quantum code — The 3D welded solid code is partially self-correcting with a power-law energy barrier [3]. The 3D toric code is a classical self-correcting memory, whose protected bit admits a membrane-like logical operator [8], but it is not a quantum self-correcting memory [9].
- 3D subsystem surface code
References
- [1]
- E. Dennis et al., “Topological quantum memory”, Journal of Mathematical Physics 43, 4452 (2002) arXiv:quant-ph/0110143 DOI
- [2]
- A. Hamma, P. Zanardi, and X.-G. Wen, “String and membrane condensation on three-dimensional lattices”, Physical Review B 72, (2005) arXiv:cond-mat/0411752 DOI
- [3]
- K. P. Michnicki, “3D Topological Quantum Memory with a Power-Law Energy Barrier”, Physical Review Letters 113, (2014) arXiv:1406.4227 DOI
- [4]
- T. R. Scruby and K. Nemoto, “Local Probabilistic Decoding of a Quantum Code”, (2023) arXiv:2212.06985
- [5]
- A. O. Quintavalle et al., “Single-Shot Error Correction of Three-Dimensional Homological Product Codes”, PRX Quantum 2, (2021) arXiv:2009.11790 DOI
- [6]
- O. Higgott and N. P. Breuckmann, “Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes”, PRX Quantum 4, (2023) arXiv:2206.03122 DOI
- [7]
- C. Stahl, “Single-Shot Quantum Error Correction in Intertwined Toric Codes”, (2023) arXiv:2307.08118
- [8]
- O. Landon-Cardinal et al., “Perturbative instability of quantum memory based on effective long-range interactions”, Physical Review A 91, (2015) arXiv:1501.04112 DOI
- [9]
- Y. Li et al., “Phase diagram of the three-dimensional subsystem toric code”, (2023) arXiv:2305.06389
Page edit log
- Aleksander Kubica (2022-05-16) — most recent
- Victor V. Albert (2022-05-16)
Cite as:
“3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/3d_surface