Consensus-based qubit configuration optimization for variational algorithms on neutral atom quantum systems

In this work, we report an algorithm that is able to tailor qubit interactions for individual variational quantum algorithm problems. Here, the algorithm leverages the unique ability of a neutral atom tweezer platform to realize arbitrary qubit position configurations. These configurations determine the degree of entanglement available to a variational quantum algorithm via the interatomic interactions. Good configurations will accelerate pulse optimization convergence and help mitigate barren plateaus. As gradient-based approaches are ineffective for position optimization due to the divergent $R^{-6}$ nature of neutral atom interactions, we opt to use a consensus-based algorithm to optimize the qubit positions. By sampling the configuration space instead of using gradient information, the consensus-based algorithm is able to successfully optimize the positions, yielding adapted variational quantum algorithm ansatzes that lead to both faster convergence and lower errors. In this work, we show that these optimized configurations generally result in large improvements in the system's ability to solve ground state minimization problems for both random Hamiltonians and small molecules.