Lechner-Hauke-Zoller (LHZ) code[1,2] 

Also known as Lechner-Hauke-Zoller (LHZ) parity code.

Description

LDPC c-q code designed to convert the long-range interactions of a quantum annealer into local constraints. The code maps the bits of a classical Ising model with all-to-all \(D\)-body interactions into one on a \(D\)-dimensional lattice. An extension maps more general models onto the same lattice [3].

Encoding

Arbitrary quantum states [4].

Gates

Universal gate set [5].

Decoding

BP decoder [2].

Parent

  • Qubit c-q code — The LHZ code is an LDPC c-q code designed to convert the long-range interactions of a quantum annealer into local constraints.

Cousin

References

[1]
W. Lechner, P. Hauke, and P. Zoller, “A quantum annealing architecture with all-to-all connectivity from local interactions”, Science Advances 1, (2015) DOI
[2]
F. Pastawski and J. Preskill, “Error correction for encoded quantum annealing”, Physical Review A 93, (2016) arXiv:1511.00004 DOI
[3]
K. Ender et al., “Parity Quantum Optimization: Compiler”, Quantum 7, 950 (2023) arXiv:2105.06233 DOI
[4]
A. Messinger, M. Fellner, and W. Lechner, “Constant Depth Code Deformations in the Parity Architecture”, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) (2023) arXiv:2303.08602 DOI
[5]
M. Fellner et al., “Universal Parity Quantum Computing”, Physical Review Letters 129, (2022) arXiv:2205.09505 DOI
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Zoo Code ID: lhz

Cite as:
“Lechner-Hauke-Zoller (LHZ) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/lhz
BibTeX:
@incollection{eczoo_lhz, title={Lechner-Hauke-Zoller (LHZ) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/lhz} }
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Permanent link:
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Cite as:

“Lechner-Hauke-Zoller (LHZ) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/lhz

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical_into_quantum/qubits/lhz.yml.