Matrix-product state (MPS) code[1] 

Description

Also called a magnon code. An \(n\)-qubit approximate code whose codespace of \(k=\Omega(\log n)\) qubits is efficiently described in terms of matrix product states (MPS) or Bethe ansatz tensor networks. A no-go theorem states that open-boundary MPS that form a degenerate ground-state space of a gapped local Hamiltonian yield codes with distance that is only constant in the number of qubits \(n\), so MPS excitation ansatze have to be used to achieve a distance scaling nontrivially with \(n\).

Protection

Distance \(d=\Omega(n^{1-\nu})\) for any \(\nu\in(0,1)\).

Parents

Cousin

References

[1]
M. Gschwendtner et al., “Quantum error-detection at low energies”, Journal of High Energy Physics 2019, (2019) arXiv:1902.02115 DOI
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Zoo Code ID: mps

Cite as:
“Matrix-product state (MPS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/mps
BibTeX:
@incollection{eczoo_mps, title={Matrix-product state (MPS) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/mps} }
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Cite as:

“Matrix-product state (MPS) 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/qubits/nonstabilizer/mps.yml.