Comparative Analysis of Excited-State Quantum Algorithms with ADAPT Resource Reduction

The usage of noisy intermediate-scale quantum (NISQ) devices offers great promise in finding ground and excited states of quantum chemistry systems. With recent developments of variational and hybrid quantum-classical algorithms for this goal, we perform a comparative analysis for ground- and excited-state simulations. We do a systematic study of Quantum self-consistent Equation of Motion (q-sc-EOM), Variational Quantum Deflation (VQD), Subspace-Search Variational Quantum Eigensolver (SSVQE), and Truncated Eigenvalue Parametrized Initial Density (TEPID)-ADAPT. We explore the accuracy and quantum resource efficiency of these algorithms over different molecular configurations and correlation regimes. Leveraging ADAPT (Adaptive Derivative-Assembled Pseudo-Trotter) ansatz construction, allows reduction of circuit depth and gate operations while maintaining fidelity. This illuminates the trade-offs between ansatz flexibility, resource requirements, and chemical accuracy. Our study provides quantitative guidance for prominent excited-state algorithm performance under NISQ constraints and shows how resource reduction through integrating the ADAPT method can scale the hybrid quantum algorithms for quantum chemistry.