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.

Parents

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 TFIM code. However, the TFIM code can be encoded in constant depth.

Zoo code information

Internal code ID: tfim

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: tfim

Cite as:
“Transverse-field Ising model (TFIM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tfim
BibTeX:
@incollection{eczoo_tfim, title={Transverse-field Ising model (TFIM) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/tfim} }
Permanent link:
https://errorcorrectionzoo.org/c/tfim

References

[1]
Yifan Hong et al., “Quantum error correction in a time-dependent transverse field Ising model”. 2205.12998

Cite as:

“Transverse-field Ising model (TFIM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tfim

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