Simulation of the nuclear shell-model with quantum circuits

Abstract

This thesis focuses on the study of the nuclear shell-model through the implementation of quantum circuits. Each single-particle state in a shell is associated with a qubit in state |1⟩ if occupied and |0⟩ if empty. By employing the system’s Hamiltonian and utilizing the Jordan-Wigner mapping, creation and annihilation fermion operators are transformed into Pauli matrix terms, enabling their implementation in a quantum circuit through quantum gates. To simulate this system, an Adaptive Variational Quantum Eigensolver (ADAPT-VQE) is employed, which iteratively constructs a wavefunction that minimizes the energy at each step. Through repeated iterations, an upper bound for the ground state energy is obtained