Jordan-Wigner Hamiltonian for H2

The first step of using quantum computers to perform quantum chemical simulations is to translate the fermionic Hamiltonian to a qubit Hamiltonian (represented by Pauli operators). The fermionic Hamiltonian in spin basis is: \[H = \sum_{pq}h_{pq}a^\dagger_p a_q + \frac{1}{2}\sum_{pqrs}g_{pqrs}a^\dagger_p a^\dagger_q a_s a_r\] Note here that for the second term the indicies \(s\) and \(r\) are flipped on the annihilation operators. Here the integral elements are defined as: \[h_{pq} = \int\phi...

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