Description
Qubit stabilizer code whose encoding circuit corresponds to a branching MERA [4] tensor network. These codes generalize quantum polar codes by reinstating the disentanglers omitted in the branching-tree tensor-network construction [2].Protection
Numerical evidence indicates that channel polarization rapidly suppresses channels that are bad in both quadratures, allowing good performance without entanglement assistance [2].Rate
Numerics on depolarizing and erasure channels indicate low block-error rates at rates approaching coherent information, with better finite-size behavior than quantum polar codes [2].Encoding
Encoding uses a reversed branching-MERA CNOT circuit, with non-data inputs frozen to either \(|0\rangle\) or \(|+\rangle\) according to channel selection [2].Decoding
Decoding can be formulated as tensor-network contraction and supports successive-cancellation-style decoding inherited from branching-MERA constructions [1,2].A symmetric decoder that jointly uses \(x\)- and \(z\)-error information remains efficiently contractible and improves finite-size performance over standard quantum polar decoding [2].Cousins
- Polar code— Classical versions of branching MERA codes can be thought of as extensions of polar codes [1,3].
- Tensor-network code— Encoders for branching MERA codes are related to branching MERA tensor networks [1,2].
Primary Hierarchy
Parents
Branching MERA code
Children
Branching MERA codes generalize quantum polar codes by restoring the branching-MERA disentanglers while retaining efficient tensor-network decoding [2].
References
- [1]
- A. J. Ferris and D. Poulin, “Branching MERA codes: a natural extension of polar codes”, (2013) arXiv:1312.4575
- [2]
- A. J. Ferris and D. Poulin, “Tensor Networks and Quantum Error Correction”, Physical Review Letters 113, (2014) arXiv:1312.4578 DOI
- [3]
- A. J. Ferris and D. Poulin, “Branching MERA codes: A natural extension of classical and quantum polar codes”, 2014 IEEE International Symposium on Information Theory 1081 (2014) DOI
- [4]
- G. Evenbly and G. Vidal, “Class of Highly Entangled Many-Body States that can be Efficiently Simulated”, Physical Review Letters 112, (2014) arXiv:1210.1895 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-07-10)
Cite as:
“Branching MERA code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/branching_mera, arXiv:2606.11484