I would like to prepare an initial state for variational quantum algorithms.

The initial state should include the following states: $|000\rangle, |010\rangle, |100\rangle$, and $|001\rangle$.

How can I prepare this initial state?

FYI, I referred to this paper. In this paper, the circuit creates $|100\rangle$, $|101\rangle$, and $|001\rangle$.

In addition, the Hamiltonian I want to solve is $$ H = - \frac{1}{2} \varepsilon \sum_{i=1}^{N} Z_i + \frac{1}{4} V \sum_{i,j=1}^N(X_iXj - Y_iY_j) \;,$$ where $\varepsilon$ and $V$ is the coefficients and $N$ is the number of quits.