Description
A hybrid qubit-oscillator code admitting codewords that are tensor products of a single-qubit (e.g., photon polarization) state with either a cat state or a coherent state.
Codewords of the coherent-state version [1] are \(|\alpha\rangle|+\rangle\) and \(|-\alpha\rangle|-\rangle\), i.e., hyper-entangled states of the occupation-number and polarization degrees of freedom of a photon. Codewords of the cat-state version [2,3] are proportional to \((\left|\alpha\right\rangle +\left|-\alpha\right\rangle )|+\rangle\) and \((\left|i\alpha\right\rangle -\left|-i\alpha\right\rangle )|-\rangle\)
Fault Tolerance
Photonic architecture based on concatenation with RBH codes [2].
Notes
Parent
- Bosonic code — The physical Hilbert space of a hybrid qubit-oscillator code contains at least one oscillator.
Cousins
- Cat code — Hybrid cat codewords consist of a bosonic mode in either coherent or cat states.
- Raussendorf-Bravyi-Harrington (RBH) cluster-state code — Hybrid cat codes can be concatenated with RBH codes [2].
- Concatenated bosonic code — Hybrid cat codes can be concatenated with RBH codes [2].
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]
- J. Lee, N. Kang, S.-H. Lee, H. Jeong, L. Jiang, and S.-W. Lee, “Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons”, (2023) arXiv:2401.00450
- [3]
- D. V. Sychev, A. E. Ulanov, E. S. Tiunov, A. A. Pushkina, A. Kuzhamuratov, V. Novikov, and A. I. Lvovsky, “Entanglement and teleportation between polarization and wave-like encodings of an optical qubit”, Nature Communications 9, (2018) arXiv:1712.10206 DOI
- [4]
- U. L. Andersen, J. S. Neergaard-Nielsen, P. van Loock, and A. Furusawa, “Hybrid discrete- and continuous-variable quantum information”, Nature Physics 11, 713 (2015) arXiv:1409.3719 DOI
- [5]
- Y. Liu et al., “Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications”, (2024) arXiv:2407.10381
Page edit log
- Victor V. Albert (2021-11-03) — most recent
Cite as:
“Hybrid cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/hybrid_cat