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Transverse-field Ising model (TFIM) code[1]

Description

A 1D translationally invariant stabilizer code whose encoding is a constant-depth circuit of nearest-neighbor gates on alternating even and odd bonds that consist of transverse-field Ising Hamiltonian interactions. The code allows for perfect state transfer of arbitrary distance using local operations and classical communications (LOCC).

Protection

Code distance is 1 for open boundary conditions similar to a repetition code, and 3 for periodic boundary conditions with an encoding circuit depth of 4.

Encoding

1D geometrically local constant-depth brickwork circuit of nearest-neighbor gates on alternating even and odd bonds. Gates are generated by interaction terms of the transverse-field Ising Hamiltonian.

Cousins

  • Majorana stabilizer code— The TFIM code stabilizers can be expressed in terms of Majorana operators.
  • Quantum repetition code— When written in the computational basis, the phase-flip and TFIM codewords are superpositions of qubit states of fixed total parity. The superposition is equal for the phase-flip code, whereas some states appear with a \(-1\) coefficient for the TFIM code. However, the TFIM code can be encoded in constant depth.

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Small-distance qubit stabilizer codeSmall-distance block quantum QECC Quantum
Parents
Small-distance qubit stabilizer code
Qubit QLDPC codeStabilizer Hamiltonian-based Qubit QECC Quantum
1D lattice stabilizer codeLattice stabilizer Stabilizer Hamiltonian-based QECC Quantum
Transverse-field Ising model (TFIM) code

References

[1]
Y. Hong, J. T. Young, A. M. Kaufman, and A. Lucas, “Quantum error correction in a time-dependent transverse-field Ising model”, Physical Review A 106, (2022) arXiv:2205.12998 DOI
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Zoo Code ID: tfim

Cite as:
“Transverse-field Ising model (TFIM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/tfim, arXiv:2606.11484
BibTeX:
@incollection{eczoo_tfim,
title={Transverse-field Ising model (TFIM) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/tfim}
}
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Permanent link:
https://errorcorrectionzoo.org/c/tfim

Cite as:

“Transverse-field Ising model (TFIM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/tfim, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/tfim.yml.