# Variational quantum eigensolver unitary coupled cluster ansatz

In a previous post the Jordan-Wigner representation of the molecular Hamiltonian for the hydrogen molecule was constructed. This Hamiltonian was solved explicit diagonalization. The method of explicit diagonalization quickly becomes computationally impossible when the dimension of the Hamiltonian grow, and...

# Second quantization in matrix formulation

Coming from a theoretical chemistry background, I have mostly learned second quantization from Molecular Electronic-Structure Theory. From here the algebra is taught with the ON vector, $$\left|10\right>$$ denoting the first orbital being occupied and the second orbital being unoccupied. In...

# Multipole fit with Lagrangian multipliers

Consider the electrostatic potential due to multipoles places at the position of atoms: $E_{i}=\sum_{j}^{atom}\sum_{n}^{multipole}\frac{\left(-1\right)^{n}}{n!}T_{ij}^{(n)}m_{j}^{(n)}$ If the quantum mechanical electrostatic potential is to be minimized, a cost function can written of the form: $z=\sum_{i}^{point}\left(V_{i,\mathrm{QM}}-E_{i}\right)^{2}+\sum_{l}^{constraints}\lambda_{l}g_{l}$ Expanding the square: $z=\sum_{i}^{point}\left(V_{i,\mathrm{QM}}^{2}+E_{i}^{2}-2E_{i}V_{i,\mathrm{QM}}\right)+\sum_{l}^{constraints}\lambda_{l}g_{l}$ It is known...