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One-hot quantum code[1]

Alternative names: Single-excitation subspace code, Direct mapping, Multi-rail code.

Description

Encoding of a \(q\)-dimensional qudit into the single-excitation subspace of \(q\) modes. The \(j\)th logical state is the multi-mode Fock state with one photon in mode \(j\) and zero photons in the other modes. This code is useful for encoding and performing operations on qudits in multiple qubits [2–6].

Another name for this code [7], not used here, is a unary code. This term is reserved for a mapping between the natural numbers \(N\) and binary strings with the first \(N\) coordinates being 1 and the rest 0.

Protection

This is an error-detecting code against one photon loss event.

Gates

Non-deterministic gates using linear optics and photon-number resolving detectors [1].The group \(SU(q)\) can be realized via Gaussian rotations [8].

Cousin

  • One-hot code— The one-hot quantum code is the quantum version of the one-hot code.

Member of code lists

Primary Hierarchy

Quantum Domain
Bosonic Kingdom
Bosonic codeQECC Quantum
Qudit-into-oscillator code
Fock-state bosonic codeAmplitude-damping (AD) QECC AQECC Quantum
Chuang-Leung-Yamamoto (CLY) codeCE Amplitude-damping (AD) AQECC Hamiltonian-based QECC Quantum
Parents
Chuang-Leung-Yamamoto (CLY) code
Group-representation codeQECC Quantum
One-hot quantum codes are group-representation codes with the \(G = SU(q)\) subgroup of Gaussian rotations [8].
One-hot quantum code
Children
Dual-rail quantum code

References

[1]
M. Karácsony, L. Oroszlány, and Z. Zimborás, “Efficient qudit based scheme for photonic quantum computing”, (2023) arXiv:2302.07357
[2]
R. D. Somma, “Quantum Computation, Complexity, and Many-Body Physics”, (2005) arXiv:quant-ph/0512209
[3]
M. R. Geller, J. M. Martinis, A. T. Sornborger, P. C. Stancil, E. J. Pritchett, H. You, and A. Galiautdinov, “Universal quantum simulation with prethreshold superconducting qubits: Single-excitation subspace method”, (2015) arXiv:1505.04990
[4]
S. McArdle, A. Mayorov, X. Shan, S. Benjamin, and X. Yuan, “Digital quantum simulation of molecular vibrations”, Chemical Science 10, 5725 (2019) arXiv:1811.04069 DOI
[5]
N. P. D. Sawaya and J. Huh, “Quantum Algorithm for Calculating Molecular Vibronic Spectra”, The Journal of Physical Chemistry Letters 10, 3586 (2019) arXiv:1812.10495 DOI
[6]
N. P. D. Sawaya, T. Menke, T. H. Kyaw, S. Johri, A. Aspuru-Guzik, and G. G. Guerreschi, “Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians”, npj Quantum Information 6, (2020) arXiv:1909.12847 DOI
[7]
N. Chancellor, “Domain wall encoding of discrete variables for quantum annealing and QAOA”, Quantum Science and Technology 4, 045004 (2019) arXiv:1903.05068 DOI
[8]
A. Denys and A. Leverrier, “Quantum Error-Correcting Codes with a Covariant Encoding”, Physical Review Letters 133, (2024) arXiv:2306.11621 DOI
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Zoo Code ID: one_hot_quantum

Cite as:
“One-hot quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/one_hot_quantum
BibTeX:
@incollection{eczoo_one_hot_quantum, title={One-hot quantum code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/one_hot_quantum} }
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Permanent link:
https://errorcorrectionzoo.org/c/one_hot_quantum

Cite as:

“One-hot quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/one_hot_quantum

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/fock_state/constant_excitation/one_hot_quantum.yml.