Quantum simulation of molecules without fermionic encoding of the wave function

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