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 [3–5] 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 [6].
Gates
CNOT gate preserving the rank of spherical-tensor noise operators [2].Decoding
Measurement-free error correction protocol [2].Realizations
Trapped ions: autonomous error-correction scheme reduces errors by a factor up to 2.2, as demonstrated by the Chiaverini group [7].Silicon spin qubits: cat-state initialization [8].Cousins
- Two-component cat code— The spin-cat code construction utilizes the Holstein-Primakoff mapping [3–5] 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 [6].
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. Klein and E. R. Marshalek, “Boson realizations of Lie algebras with applications to nuclear physics”, Reviews of Modern Physics 63, 375 (1991) DOI
- [6]
- A. Kruckenhauser et al., “Dark Spin-Cat States as Biased Qubits”, Physical Review Letters 135, (2025) arXiv:2408.04421 DOI
- [7]
- K. DeBry, N. Meister, A. V. Martinez, C. D. Bruzewicz, X. Shi, D. Reens, R. McConnell, I. L. Chuang, and J. Chiaverini, “Error correction of a logical qubit encoded in a single atomic ion”, (2025) arXiv:2503.13908
- [8]
- X. Yu et al., “Schrödinger cat states of a nuclear spin qudit in silicon”, Nature Physics 21, 362 (2025) arXiv:2405.15494 DOI
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