Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines

Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the NISQ era. Since the inception of the first such algorithm, ADAPT-VQE, many improvements have appeared in the literature. We combine the key improvements with a Hessian recycling protocol and a novel operator pool, which we term Coupled Exchange Operator (CEO) pool, to create the most cost- and hardware-efficient version of ADAPT-VQE to date. We use the resulting algorithm on a range of molecular systems, and assess the cost of executing it on hardware. We show a dramatic reduction of these quantum resources compared to prior versions of the algorithm and find that our state-of-the-art CEO-ADAPT-VQE outperforms UCCSD, the most widely regarded static VQE ansatz, in all relevant metrics.