In the build-up of a shell-model or FCI code that is meant to tackle large dimensionalities is the action of the Hamiltonian \( \hat{H} \) on a Slater determinant represented in second quantization as $$ |\alpha_1\dots \alpha_n\rangle = a_{\alpha_1}^{\dagger} a_{\alpha_2}^{\dagger} \dots a_{\alpha_n}^{\dagger} |0\rangle. $$ The time consuming part stems from the action of the Hamiltonian on the above determinant, $$ \left(\sum_{\alpha\beta} \langle \alpha|t+u|\beta\rangle a_\alpha^{\dagger} a_\beta + \frac{1}{4} \sum_{\alpha\beta\gamma\delta} \langle \alpha \beta|\hat{v}|\gamma \delta\rangle a_\alpha^{\dagger} a_\beta^{\dagger} a_\delta a_\gamma\right)a_{\alpha_1}^{\dagger} a_{\alpha_2}^{\dagger} \dots a_{\alpha_n}^{\dagger} |0\rangle. $$ A practically useful way to implement this action is to encode a Slater determinant as a bit pattern.