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.
Cousins
- Low-density parity-check (LDPC) code — The LHZ code is an LDPC c-q code designed to convert the long-range interactions of a quantum annealer into local constraints.
- Concatenated cat code — LHZ parity-codes have been concatenated with cat codes [6].
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, R. ter Hoeven, B. E. Niehoff, M. Drieb-Schön, and W. Lechner, “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, A. Messinger, K. Ender, and W. Lechner, “Universal Parity Quantum Computing”, Physical Review Letters 129, (2022) arXiv:2205.09505 DOI
- [6]
- A. Messinger, V. Torggler, B. Klaver, M. Fellner, and W. Lechner, “Fault-tolerant quantum computing with the parity code and noise-biased qubits”, (2024) arXiv:2404.11332
Page edit log
- Victor V. Albert (2024-04-21) — most recent
Cite as:
“Lechner-Hauke-Zoller (LHZ) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/lhz