Quantum Algorithms for many-body systems simulation

In this thesis, two novel quantum algorithms are developed and presented, both of which focus on practical feasibility for near-term quantum hardware and the physics of many-body systems. The first project exploits the Hubbard-Stratonovich transformation to obtain an estimate for many-body quantum observables, proposing a method that could lead to a simplification of quantum circuits by reducing the need for multi-qubit gates. This approach is particularly suited to devices with limited qubit coherence times and gate fidelity, though its applicability is mainly limited to observables that can be mapped onto quadratic forms. The second project implements a Givens rotation-based decomposition for the Quantum METTS (Minimally Entangled Typical Thermal States) algorithm, trying to extend its applicability beyond finite-range Hamiltonians. This method is applied to a small test system of 4 supernovae neutrinos and demonstrates potential for efficient thermal state sampling in systems with high entanglement growth. Although neither method outperforms existing techniques, both contribute new perspectives and emphasize the importance of mathematical decomposition in optimizing quantum algorithms for near-term devices.