Absorption-Emission Codes for Atomic and Molecular Quantum Information Platforms

A molecule has a very large and highly structured set of states, enough to hold an error-correcting code inside a single particle and add a layer of protection before any multi-qubit code is involved. Earlier proposals, called molecular codes, treat the molecule as a rigid rotor and protect against small kicks to its orientation and angular momentum.

The noise that dominates in real atoms and molecules is different. It comes from spontaneous emission, stray electric and magnetic fields, and Raman scattering. Each of these events absorbs or emits a photon, and the photon’s energy and polarization can reveal to the environment which transition took place.

We showed that molecular codes fail against this photon-driven noise and derived simple necessary and sufficient conditions for a code to protect against it. The key observation is that the environment can tell apart states of different total angular momentum, but it cannot resolve the degenerate sublevels within a single angular-momentum manifold, so a code can hide information there.

We identified existing codes and built new ones that meet these conditions, which we call absorption–emission (Æ) codes. They are more practical than molecular codes: they need lower angular momentum and can protect against photon processes to arbitrary order. They are also compact enough for atoms and ions with sufficiently large total angular momentum, as well as molecules. That opens a way to correct spontaneous emission during laser-driven gates, which is the fundamental limit on gate fidelity in those systems.