  One of the most significant challenges for molecular simulation on quantum
computers is the encoding of the particle statistics of electrons which are
fermions into quantum bits or qubits in a process known as fermionic encoding.
Such encoding increases the complexity of the calculations, which can be
especially challenging on current and intermediate-term noisy quantum
computers. Here we show that exact molecular simulation on quantum computers
can be performed without fermionic encoding of the many-electron wave function.
We prove that the two-electron reduced density matrix (2-RDM) is expressible as
a functional of an unencoded qubit-particle wave function without
approximation, and hence, only the 2-RDM needs to be encoded for the exact
calculation of total energy and other properties. The present theoretical
result provides a rigorous explanation for the surprising accuracy of recent
simulations without encoding. Quantum simulation with qubit-particle wave
functions promises new levels of accuracy and efficiency for molecular
calculations on quantum computers.
