GFlowNets for Hamiltonian decomposition in groups of compatible operators

Quantum computing presents a promising alternative for the direct simulation of quantum systems; however, these algorithms are often limited by the increased number of measurements required to achieve chemical accuracy. To address this challenge, techniques for grouping commuting and anti-commuting terms, driven by heuristics, have been developed to reduce the number of measurements needed in quantum algorithms on near-term quantum devices. In this work, we propose a probabilistic framework using GFlowNets to group fully or qubit-wise commuting terms within a given Hamiltonian. The significance of this approach is demonstrated by the reduced number of measurements, 55\% with respect to largest first and DSAT algorithms, highlighting the potential of GFlowNets for future applications in the measurement problem.