Master thesis defense by August Luplau Gliese

Quantum FEAST: A projective subspace method for eigenvalue problems

Extracting useful information from chemical models has been a central goal of computational chemistry for decades, with much effort focused on ground state and low energy excited state calculations. However, computing states within a specified energy interval remains computationally challenging. FEAST uses contour integration to target eigenvalues in selected intervals. Quantum computing has also emerged as a computational platform with promising applications in quantum chemistry. Most quantum algorithms in this area have focused on the ground state and low energy excited states. In this thesis, quantum FEAST implementations are developed and assessed across three regimes of quantum hardware: noisy intermediate-scale quantum (NISQ) devices, early fault-tolerant quantum computers, and fully fault-tolerant quantum computers. The NISQ implementation is based on the variational quantum linear solver (VQLS). The results show that the approach can reproduce the target eigenvalues, but the classical optimization landscape limits its scalability. In the early fault-tolerant regime, a formulation based on the quantum Szegö quadrature rule is shown to be a promising alternative with better scalability prospects. In the fully fault-tolerant regime, the HHL algorithm is identified as a possible implementation, although the resource requirements are too large to classically simulate.