Spin cat code[1,2] 

Description

An analogue of the two-component cat code designed for a large spin, which is often realized in the permutation-invariant 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].

Gates

CNOT gate preserving the rank of spherical-tensor noise operators [2].

Decoding

Measurement-free error correction protocol [2].

Parent

Cousin

  • 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.

References

[1]
W. Qin et al., “Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles”, Physical Review Letters 127, (2021) arXiv:2101.03662 DOI
[2]
S. Omanakuttan et al., “Fault-tolerant quantum computation using large spin cat-codes”, (2024) arXiv:2401.04271
[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
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Zoo Code ID: spin_cat

Cite as:
“Spin cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/spin_cat
BibTeX:
@incollection{eczoo_spin_cat, title={Spin cat code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/spin_cat} }
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Cite as:

“Spin cat code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/spin_cat

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/single_spin/spin_cat.yml.