One-hot quantum code[1]
Also known as 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].
Parents
- Chuang-Leung-Yamamoto (CLY) code
- Group-representation code — One-hot quantum codes are group-representation codes with the \(G = SU(q)\) subgroup of Gaussian rotations [8].
Child
Cousin
- One-hot code — The one-hot quantum code is the quantum version of the one-hot 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 et al., “Universal quantum simulation with prethreshold superconducting qubits: Single-excitation subspace method”, (2015) arXiv:1505.04990
- [4]
- S. McArdle et al., “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 et al., “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, “Multimode bosonic cat codes with an easily implementable universal gate set”, (2023) arXiv:2306.11621
Page edit log
- Victor V. Albert (2023-03-06) — most recent
Cite as:
“One-hot quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/one_hot_quantum