# Diatomic molecular code[1; Sec. VI]

## Description

Approximate quantum code that encodes a qudit in the finite-dimensional Hilbert space of a rigid body with \(SO(2)\) symmetry (e.g., a heteronuclear diatomic molecule). This state space is the space of normalized functions on the two-sphere, consisting of a direct sum of all non-negative integer angular momenta. Ideal codewords may not be normalizable because the space is infinite-dimensional, so approximate versions have to be constructed in practice.

Construction is based on nested subgroups \(H\subset K \subset SO_3\), where \(H,K\) are finite. Codewords consist of orbits of particular position states under \(H\), while some elements of \(K\) can cycle between codewords.

## Protection

## Parent

## Cousins

- Molecular code — Molecular (diatomic molecular) codes are constructed using two nested subgroups of \(SO(3)\) on the state space of a particle on \(SO(3)\) (the two-sphere).
- Æ code — Diatomic molecular codes are supported on states with various total angular momenta, while the more practical Æ codes are supported on only one subspace of fixed total momentum. The latter codes are thus more practical and more applicable to other spin spaces.

## References

- [1]
- V. V. Albert, J. P. Covey, and J. Preskill, “Robust Encoding of a Qubit in a Molecule”, Physical Review X 10, (2020) arXiv:1911.00099 DOI

## Page edit log

- Victor V. Albert (2023-11-22) — most recent

## Cite as:

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