Description
An analogue of the two-component cat code designed for a large spin, which is often realized in the PI subspace of atomic ensembles.
The encoding was designed by using the Holstein-Primakoff mapping [3] (see also [4]) to pull back the phase-space structure of a bosonic system to the compact phase space of a quantum spin.
The codewords can be approximated by two spin-coherent states. The version where the two spin-coherent states are antipodal has been considered in Ref. [2].
An extended version of the spin cat code, the dark spin-cat code, encodes in two spins, both thought of as hyperfine manifolds [5].
Gates
CNOT gate preserving the rank of spherical-tensor noise operators [2].Decoding
Measurement-free error correction protocol [2].Cousins
- Two-component cat code— The spin-cat code construction utilizes the Holstein-Primakoff mapping [3] (see also [4]) to convert cat codes into codes for spin systems.
- Spin code— An extended version of the spin cat code, the dark spin-cat code, encodes in two spins, both thought of as hyperfine manifolds [5].
Member of code lists
Primary Hierarchy
References
- [1]
- W. Qin, A. Miranowicz, H. Jing, and F. Nori, “Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles”, Physical Review Letters 127, (2021) arXiv:2101.03662 DOI
- [2]
- S. Omanakuttan, V. Buchemmavari, J. A. Gross, I. H. Deutsch, and M. Marvian, “Fault-Tolerant Quantum Computation Using Large Spin-Cat Codes”, PRX Quantum 5, (2024) arXiv:2401.04271 DOI
- [3]
- T. Holstein and H. Primakoff, “Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet”, Physical Review 58, 1098 (1940) DOI
- [4]
- C. D. Cushen and R. L. Hudson, “A quantum-mechanical central limit theorem”, Journal of Applied Probability 8, 454 (1971) DOI
- [5]
- A. Kruckenhauser et al., “Dark spin-cats as biased qubits”, (2024) arXiv:2408.04421
Page edit log
- Victor V. Albert (2023-01-19) — most recent
Cite as:
“Spin cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/spin_cat