Description
Member of the family of \([[2n,(0,2),(2,n)]]_{\mathbb{Z}}\) homological rotor codes storing a logical qubit on a thin Möbius strip. The ideal code can be obtained from a Josephson-junction [4] system [3].
Logical codewords can be expressed in the basis of angular momentum states as \begin{align} \begin{split} |\overline{0}\rangle&=\sum_{\overset{\ell_{1},\dots,\ell_{n}\in\mathbb{Z}}{\sum_{k=1}^{n}\ell_{k}=\mathrm{even}}}\left|\ell_{1},\dots,\ell_{n},-\ell_{1},\dots,-\ell_{n}\right\rangle \\|\overline{1}\rangle&=\sum_{\overset{\ell_{1},\dots,\ell_{n}\in\mathbb{Z}}{\sum_{k=1}^{n}\ell_{k}=\mathrm{odd}}}\left|\ell_{1},\dots,\ell_{n},-\ell_{1},\dots,-\ell_{n}\right\rangle~. \end{split} \tag*{(1)}\end{align}
Protection
Gates
Parents
Cousin
- Square-lattice GKP code — Current-mirror code phase gates utilize ancillary osillators in square-lattice GKP states [1,6].
References
- [1]
- A. Kitaev, “Protected qubit based on a superconducting current mirror”, (2006) arXiv:cond-mat/0609441
- [2]
- Kitaev, Alexei Yu. "Protected qubit based on superconducting current mirror." United States Patent Number 7858966B2 (2006).
- [3]
- C. Vuillot, A. Ciani, and B. M. Terhal, “Homological Quantum Rotor Codes: Logical Qubits from Torsion”, Communications in Mathematical Physics 405, (2024) arXiv:2303.13723 DOI
- [4]
- S. M. Girvin, “Circuit QED: superconducting qubits coupled to microwave photons”, Quantum Machines: Measurement and Control of Engineered Quantum Systems 113 (2014) DOI
- [5]
- D. K. Weiss, A. C. Y. Li, D. G. Ferguson, and J. Koch, “Spectrum and coherence properties of the current-mirror qubit”, Physical Review B 100, (2019) arXiv:1908.04615 DOI
- [6]
- P. Brooks, A. Kitaev, and J. Preskill, “Protected gates for superconducting qubits”, Physical Review A 87, (2013) arXiv:1302.4122 DOI
Page edit log
- Victor V. Albert (2023-04-12) — most recent
Cite as:
“Kitaev current-mirror qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/current_mirror