Project 1: Quantum state preparation: https://github.com/myoussef660/Quantum-state-preparation
The project begins with the simplest case of a single qubit and then moves to two-qubit systems and the general (n)-qubit case. We first focus on states with real and non-negative amplitudes, where the preparation can be understood using rotation gates. We then extend the discussion to states with complex amplitudes by including the appropriate phase information.

Project2: Quantum simulation of SYK: https://github.com/myoussef660/Block-Encoding-SYK-Ground-State
The goal of this project is to estimate the ground state energy for SYK with N=8 Majorana fermions through SOSSA protocol. In doing so, we implement 4 steps including block encoding the hamiltonian, rewriting the Hamiltonian in terms of sum of squares, amplifying the spectrum of the Hamiltonian and finally using quantum phase estimation to estimate the ground state.