Description
Encodes a \(K\)-dimensional logical Hilbert space into \(n_1\) modular qudits of dimension \(q\) and \(n_2 \neq 0\) oscillators, i.e., the Hilbert space of \(\ell^2\)-normalizable functions on \(\mathbb{Z}_q^{n_1} \times \mathbb{R}^{n_2}\). In photonic systems, photonic states of multiple degrees of freedom of a photon (e.g., frequency, amplitude, and polarization) are called hyper-entangled states [1].
Notes
Parent
- Bosonic code — The physical Hilbert space of a hybrid qubit-oscillator code contains at least one oscillator.
Cousins
- Qudit-into-oscillator code — A hybrid qudit-oscillator code with \(n_1=0\) is a qudit-into-oscillator code.
- Very small logical qubit (VSLQ) code — VSLQ decoder utilizes two ancillary oscillators.
- EA qubit stabilizer code — A minimal EA qubit stabilizer code has been realized in using hyper-entangled states [5].
References
- [1]
- P. G. Kwiat, “Hyper-entangled states”, Journal of Modern Optics 44, 2173 (1997) DOI
- [2]
- U. L. Andersen et al., “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 DOI
- [3]
- A. Furusawa and P. van Loock, Quantum Teleportation and Entanglement (Wiley, 2011) DOI
- [4]
- Y. Liu et al., “Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications”, (2024) arXiv:2407.10381
- [5]
- M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement-assisted quantum error-correcting code”, Physical Review A 79, (2009) arXiv:0807.4906 DOI
Page edit log
- Victor V. Albert (2021-11-03) — most recent
Cite as:
“Hybrid qudit-oscillator code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/hybrid_qudit_oscillator