Spin cat code

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 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].

Gates

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

Decoding

Measurement-free error correction protocol [2].

Parent

Single-spin code

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”, 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

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

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