Isolated quantum-state networks in ultracold molecules

TL;DR

This paper introduces a graph theory-based method to efficiently navigate complex hyperfine state networks in ultracold molecules, enabling rapid state preparation and robust quantum computation pathways.

Contribution

It presents a heuristic and graph-theoretic approach to identify optimal state pathways in ultracold molecules, including loops and decoherence-resistant sets for quantum applications.

Findings

Identified a closed loop of four states in RbCs with minimal leakage.

Optimized three-state sets for quantum computation considering magnetic noise.

Demonstrated rapid and high-fidelity state preparation methods.

Abstract

Precise control over rotational angular momentum is at the heart of recent advances in quantum chemistry, quantum simulation, and quantum computation with ultracold bialkali molecules. Each rotational state comprises a rich manifold of hyperfine states arising from combinations of rotation and nuclear spins; this often yields hundreds of transitions available between a given pair of rotational states, and the efficient navigation of this complex space is a current challenge for experiments. Here, we describe a general approach based on a simple heuristic and graph theory to quickly identify optimal sets of states in ultracold bialkali molecules. We explain how to find pathways through the many available transitions to prepare the molecule in a specific state with maximum speed for any desired fidelity. We then examine networks of states where multiple couplings are present at the same time. As example applications, we first identify a closed loop of four states in the RbCs molecule where there is minimal population leakage out of the loop during simultaneous microwave coupling; we then extend the optimisation procedure to account for decoherence induced by magnetic-field noise and obtain an optimal set of 3 states for quantum computation applications.