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
- Qubit code
- Hamiltonian-based code — MPS codewords are low-energy excited states of a local Hamiltonian.
- Approximate quantum error-correcting code (AQECC) — MPS codes approximately protect against erasures in the thermodynamic limit.
Cousin
- Eigenstate thermalization hypothesis (ETH) code — MPS codes have been shown to protect against non-geometrically local noise, while ETH codes protect only against erasures on geometrically local patches.
References
- [1]
- M. Gschwendtner et al., “Quantum error-detection at low energies”, Journal of High Energy Physics 2019, (2019) arXiv:1902.02115 DOI
Page edit log
- Victor V. Albert (2022-12-28) — most recent
Cite as:
“Matrix-product state (MPS) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/mps