An Optimized Construction of Lie Algebra Generator Pools for Variational Quantum Eigensolvers in Chemistry

Lie algebras are essential mathematical structures used in physics to describe sets of quantum operators. Identifying a minimal set of generators to construct these algebras is a central challenge. The traditional search for such generators relies on greedy construction steps applied to an exponentially growing number of candidate operators, making it computationally intractable. Here we show a general, polynomial-scaling strategy, based on fundamental Lie-algebraic properties, to overcome this bottleneck. We apply this framework to quantum chemistry, specifically to adaptive variational algorithms that simulate molecular ground states. By integrating our mathematically verified generator pools into a batched algorithmic framework, we reduce the required quantum resources and improve convergence for strongly correlated systems. Furthermore, this approach eliminates computational bottlenecks that previously restricted fixed-ansatz non-iterative coupled-cluster methods to small molecules, enabling simulations of complex systems well beyond previous limits. This foundational framework also presents broad applications across quantum computing, including quantum error correction, machine learning, and hardware control.