Algoritmi di calcolo quantistico per sistemi chimici: approcci variazionali con bassa profondità di circuito

In the evolving landscape of quantum computing, variational algorithms have emerged as powerful tools for studying molecular systems. Accurately representing these systems' wavefunctions is challenging due to the limitations of current noisy quantum computers, which can only handle short-depth circuits. This thesis addresses this challenge by providing improved descriptions of wavefunctions using heuristic Ansätze with shallow circuit depth. Two primary approaches are explored: one focused on enhancing wave functions via gate-based circuits, and the other involving pulse-level control of hardware. The non-unitary VQE (nu-VQE) algorithm is introduced to improve trial wave functions using a non-unitary quantum operator, aiming to work with compact circuit Ansätze. Another approach, the Wavefunction-Adapted Hamiltonian Through Orbital Rotation (WAHTOR), exploits the invariance of the molecular Hamiltonian through orbital rotations to adapt it to the empirical circuit Ansatz. Both adiabatic and non-adiabatic optimization strategies are explored for the WAHTOR algorithm, demonstrating its resilience to Ansatz topology variations and noise effect mitigation capability. Furthermore, the convergence of the WAHTOR algorithm, with a computational cost not significantly higher than the VQE, leads to optimized orbitals coinciding with the natural ones. The Pulse-VQE strategy directly encodes variational parameters as pulse amplitudes and durations, significantly reducing the pulse schedule and circuit duration. Both gate-based and pulse-based strategies improve energy results while enhancing circuit compactness, thereby reducing the impact of quantum noise. Finally, ongoing research includes studying wave functions that preserve spin-inversion symmetry and developing entanglement pulses for devices with fixed-frequency transmons coupled by tunable buses.