Quantum Gambling: Best-Arm Strategies for Generator Selection in Adaptive Variational Algorithms

Adaptive variational algorithms require additional measurements during the generator-selection step compared to static ansatze, since energy gradients must be estimated for a large operator pool. This scaling bottleneck limits their applicability to larger molecular systems on near-term quantum devices. We address this challenge by reformulating generator selection as a Best Arm Identification (BAI) problem, where the goal is to identify the generator with the largest energy gradient using as few measurements as possible. To solve this, we employ the Successive Elimination (SE) algorithm, which adaptively allocates measurements and discards unpromising candidates early. Numerical experiments on molecular systems demonstrate that this approach substantially reduces the number of measurements required while preserving ground-state energy accuracy. By cutting measurement overhead without sacrificing performance, our method makes adaptive variational algorithms more practical for near-term quantum simulations.