Magnon code[1]
Description
An \(n\)-spin approximate code whose codespace of \(k=\Omega(\log n)\) qubits is efficiently described in terms of particular matrix product states or Bethe ansatz tensor networks. Magnon codewords are low-energy excited states of the frustration-free Heisenberg-XXX model Hamiltonian [1].
Protection
Distance \(d=\Omega(n^{1-\nu})\) for any \(\nu\in(0,1)\).
Parents
- Spin code — Magnon codewords are low-energy excited states of the frustration-free Heisenberg-XXX model Hamiltonian [1].
- Frustration-free Hamiltonian code — Magnon codewords are low-energy excited states of the frustration-free Heisenberg-XXX model Hamiltonian [1].
- Approximate quantum error-correcting code (AQECC) — Magnon codes approximately protect against erasures in the thermodynamic limit.
Cousins
- Eigenstate thermalization hypothesis (ETH) code — Magnon codes have been shown to protect against non-geometrically local noise, while ETH codes protect only against erasures on geometrically local patches.
- Symmetry-protected topological (SPT) code — Magnon codewords [1] are associated with 1D SPT orders [2–5].
References
- [1]
- M. Gschwendtner et al., “Quantum error-detection at low energies”, Journal of High Energy Physics 2019, (2019) arXiv:1902.02115 DOI
- [2]
- X. Chen, Z.-C. Gu, and X.-G. Wen, “Classification of gapped symmetric phases in one-dimensional spin systems”, Physical Review B 83, (2011) arXiv:1008.3745 DOI
- [3]
- N. Schuch, D. Pérez-García, and I. Cirac, “Classifying quantum phases using matrix product states and projected entangled pair states”, Physical Review B 84, (2011) arXiv:1010.3732 DOI
- [4]
- X. Chen, Z.-C. Gu, and X.-G. Wen, “Complete classification of one-dimensional gapped quantum phases in interacting spin systems”, Physical Review B 84, (2011) arXiv:1103.3323 DOI
- [5]
- X. Chen et al., “Symmetry protected topological orders and the group cohomology of their symmetry group”, Physical Review B 87, (2013) arXiv:1106.4772 DOI
Page edit log
- Victor V. Albert (2022-12-28) — most recent
Cite as:
“Magnon code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/mps
Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/many_spin/mps.yml.