I understand how to apply UCC to a problem formulated in a second-quantized (fermion) form: you start with some state and then create a unitary operator out of single-body (or double-, triple- and so on) excitations, and then variationally find the best coefficients:

$$ T = T^{(1)} + T^{(2)} + \dots \\ T^{(1)} = \sum c_i a_i^\dagger, T^{(2)} = \sum c_{ij} a_i^\dagger a_j^\dagger\\ \Psi = e^{T - T^\dagger} \Psi_0. $$

To implement a variational quantum eigensolver (VQE) using this ansatz, you need to apply the Jordan-Wigner or Bravyi-Kitaev transformation to the Hamiltonian and all of the excitation operators.

But what if you start with a Hamiltonian written in spin form already? Do you first transform the Hamiltonian into the second-quantized form and then back? Or do you do something simpler instead? I remember seeing an ansatz simply consisting of the single-qubit and double-qubit Pauli rotations:

$$ U = \exp(i(\theta_1 X_1 + \theta_2 X_2 + \dots + \theta_k X_i Z_j + \dots)). $$

However, I can't find any reference to that.

Any hints to the literature would be appreciated.


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