  Molecular simulations generally require fermionic encoding in which fermion
statistics are encoded into the qubit representation of the wave function.
Recent calculations suggest that fermionic encoding of the wave function can be
bypassed, leading to more efficient quantum computations. Here we show that the
energy can be expressed as a functional of the two-electron reduced density
matrix (2-RDM) where the 2-RDM is a unique functional of the unencoded
$N$-qubit-particle wave function. Contrasts are made with current
hardware-efficient methods. An application to computing the ground-state energy
and 2-RDM of H$_{4}$ is presented.
