Bachelor defense by August Luplau Gliese

Fermionic Hamiltonian to Qubit Hamiltonian

In quantum chemistry the accurate calculations of correlation remains a significant challenge. A typical measure of correlation in molecules is the difference between the Hartree-Fock energy and the exact energy. The electronic Hamiltonian contains terms that fit the criteria for this type of correlation, which arises when a single Slater determinant fails to describe the interaction. Recently, quantum computing have shown promise in resolving this problem, however they cannot directly implement the fermionic operators. This thesis explicitly demonstrates the transformation of fermionic operators into qubit operators for H2 in the STO-3G basis set using both the Jordan-Wigner and parity transformations. Both methods create Pauli strings containing only correlation coefficients. For this basis, the correlation terms only describe interactions where both electrons switch orbital. In larger bases or molecules, correlation will also include hopping terms and terms where one electron remains in its orbital while the other switches. This thesis handles correlation gathered from the Hamiltonian and relates them to other methods of calculating correlation. The aim of this thesis, is not to implement quantum computing in correlation calculations, but to build intuition for understanding correlation.