Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function

TL;DR

This paper demonstrates that quantum molecular simulations can bypass fermionic encoding by expressing energy as a functional of the two-electron reduced density matrix, enabling more efficient quantum computations.

Contribution

It introduces a method to compute molecular energies without fermionic encoding by using the 2-RDM as a functional of the unencoded wave function.

Findings

Successfully computed ground-state energy of H4 molecule.

Showed energy as a functional of unencoded wave function.

Compared with hardware-efficient quantum methods.

Abstract

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.