Circuit Design Informed Adaptive Variational Quantum Algorithms

Resource-efficient computation is of central importance in the noisy intermediate-scale quantum (NISQ) era, where decoherence, gate errors, and restricted qubit connectivity severely limit the reliable execution of quantum algorithms. In this work, we demonstrate that incorporating circuit design considerations is crucial for developing resource-efficient variational quantum algorithms. By focusing on the Hadamard test circuit architecture, hardware-aware qubit connectivity, and problem-specific adaptive framework, we analyze how circuit design constraints can systematically reduce the measurement overhead associated with repeated evaluations of the candidate gate pool in adaptive algorithms. Specifically, we demonstrate reductions in the required measurement resources ranging from at least 25% to as high as 50% - 55%. To assess the effectiveness of our approach, we investigate the ground state problem of the nonlinear Schr\"{o}dinger equation. Overall, our work contributes to resource-friendly strategies for quantum computation and underscores that algorithmic frameworks should systematically integrate circuit design constraints with hardware-aware and problem-specific structures to enhance the practical feasibility of quantum devices in the NISQ era.