Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation

arXiv:2606.04786v3 Announce Type: replace Abstract: Energy-based variants of ADAPT-VQE select operators by minimizing a one-parameter cost function for each candidate generator. In fermionic implementations, the cost of reconstructing this function often becomes a bottleneck. We reduce this cost using exact fermionic Hamiltonian transformations to obtain a generator-dependent partition of the Hamiltonian that reconstruct the same one-parameter energy function from fragment measurements. This method reproduces the fermionic Rotoselect scoring function exactly with approximately half the Pauli-string measurements. We use this formulation to benchmark the gradient-based and energy-based selection approaches in combination with two ansatz-optimization strategies---$\textit{last}$, where only the appended operator is optimized, and $\textit{full}$, where the full ansatz is re-optimized---and with both fixed-orbital and orbital-optimized formulations. The benchmark comprises $\text{LiH}$, $\text{BeH}_2$, and $\text{H}_2\text{O}$ at both equilibrium and stretched geometries. In the most weakly correlated system, pairing energy-based selection with $\textit{last}$ optimization enables the resource-efficient construction of an accurate ansatz, which avoids any VQE optimization. As correlation increases, full ansatz re-optimization and orbital optimization become the main factors governing convergence and overall resource cost. This study shows how exact Hamiltonian transformations provide an effective route to reducing the measurement overhead of fermionic energy-based ADAPT-VQE. Moreover, the benchmark clarifies the relative role of operator selection approach, parameter reoptimization strategy, and orbital optimization in the performance of ADAPT-VQE.