Magnon code

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 \(\nu\in(0,1)\).

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].

Member of code lists

Primary Hierarchy

Quantum Domain

Spin Kingdom

Spin codeQECC Quantum

Parents

Spin code

Magnon codewords are low-energy excited states of the frustration-free Heisenberg-XXX model Hamiltonian [1].

Frustration-free Hamiltonian codeHamiltonian-based QECC Quantum

Magnon codewords are low-energy excited states of the frustration-free Heisenberg-XXX model Hamiltonian [1].

Approximate quantum error-correcting code (AQECC)Quantum

Magnon codes approximately protect against erasures in the thermodynamic limit.

Magnon code

References

[1]: M. Gschwendtner, R. König, B. Şahinoğlu, and E. Tang, “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, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, “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 (2026-06-08) — most recent
Victor V. Albert (2022-12-28)

Cite as:

“Magnon code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/mps, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/many_spin/mps.yml.