Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation

The Adaptive Variational Quantum Eigensolver (ADAPT-VQE) is a promising approach for quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era, offering advantages over traditional VQE methods by reducing circuit depth and mitigating challenges in classical optimization. However, a major challenge in ADAPT-VQE is the high quantum measurement (shot) overhead required for circuit parameter optimization and operator selection. In this work, we propose two integrated strategies to reduce the shot requirements in ADAPT-VQE. First, we reuse Pauli measurement outcomes obtained during VQE parameter optimization in the subsequent operator selection step of the next ADAPT-VQE iteration, which involves operator gradient measurements. Second, we apply variance-based shot allocation to both Hamiltonian and operator gradient measurements. Our numerical results demonstrate that each method, individually and in combination, significantly reduces the number of shots needed to achieve chemical accuracy while maintaining result fidelity across the studied molecular systems.