PMR_nullity

In this project, an output file of a Hamiltonian is generated from an input file of an unrotated Hamiltonian and that of a Unitary transformation. The format of the input file is as follows

$$\displaylines{c_{1} \quad n_{11} \, p_{11} \, n_{12} \, p_{12} \ldots n_{1k} \, p_{1k} \\\ c_{2} \quad n_{21} \, p_{21} \, n_{22} \, p_{22} \ldots n_{2k} \, p_{2k} \\\ \vdots \\\ c_m \quad n_{m1} \, p_{m1} \, n_{m2} \, p_{m2} \ldots n_{mk} \, p_{mk} }$$

Here, $c_m$ represents a coefficient (float), $n_{mi}$ indicates the spin number (which spin), and $p_{mi}$ represents the pauli matrix acting on the spin $n_{mi}$. $p_{mi}$ could only take on integer values of ${0,1,2,3}$, where $0$ is the identity matrix, $1$ is the pauli X matrix, $2$ is the pauli Y matrix, and $3$ is the pauli Z matrix. So, using this format of input and output for an input Hamiltonian and a Unitary transformation, we create another file of the same format.