Manyfermion simulation from the contracted quantum eigensolver without fermionic encoding of the wave function
Abstract
Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of manyfermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding—a mapping by which the qubits are encoded with fermion statistics. Here we generalize the contracted quantum eigensolver (CQE) to avoid fermionic encoding of the wave function. In contrast to the variational quantum eigensolver, the CQE solves for a manyfermion stationary state by minimizing the contraction (projection) of the Schrödinger equation onto two fermions. We avoid fermionic encoding of the wave function by contracting the Schrödinger equation onto an unencoded pair of particles. Solution of the resulting contracted equation by a series of unencoded twobody exponential transformations generates an unencoded wave function from which the energy and twofermion reduced density matrix (2RDM) can be computed. We apply the unencoded and the encoded CQE algorithms to the hydrogen fluoride molecule, the dissociation of oxygen O_{2}, and a series of hydrogen chains. Both algorithms show comparable convergence towards the exact groundstate energies and 2RDMs, but the unencoded algorithm has computational advantages in terms of state preparation and tomography.
 Publication:

Physical Review A
 Pub Date:
 June 2022
 DOI:
 10.1103/PhysRevA.105.062424
 arXiv:
 arXiv:2205.01725
 Bibcode:
 2022PhRvA.105f2424S
 Keywords:

 Quantum Physics;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 doi:10.1103/PhysRevA.105.062424