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 \(\mathbb{Z}_q^{n_1} \times \mathbb{R}^{n_2}\).
Codewords of a simple hybrid code [1] are \(|\alpha\rangle|+\rangle\) and \(|-\alpha\rangle|V\rangle\), i.e., hyper-entangled states of the polarization \(|\pm\rangle\) and occupation-number degrees of freedom of a photon, with the latter being in a coherent state \(|\pm\alpha\rangle\).
Notes
See review [2] for an introduction to hybrid qudit-oscillator codes.
Parent
- Bosonic code — The physical Hilbert space of a hybrid qubit-oscillator code contains at least one oscillator.
Cousins
- Qudit-into-oscillator code — Hybrid code with \(n_1=0\).
- Very small logical qubit (VSLQ) code — VSLQ decoder utilizes two ancillary oscillators.
References
- [1]
- S.-W. Lee and H. Jeong, “Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits”, Physical Review A 87, (2013) arXiv:1112.0825 DOI
- [2]
- U. L. Andersen et al., “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 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