  Computations with quantum harmonic oscillators or qumodes is a promising and
rapidly evolving approach towards quantum computing. In contrast to qubits,
which are two-level quantum systems, bosonic qumodes can in principle have
infinite discrete levels, and can also be represented with continuous variable
bases. One of the most promising applications of quantum computing is
simulating many-fermion problems such as molecular electronic structure.
Although there has been a lot of recent progress on simulating many-fermion
systems on qubit-based quantum hardware, they can not be easily extended to
bosonic quantum devices due to the fundamental difference in physics
represented by qubits and qumodes. In this work, we show how an electronic
structure Hamiltonian can be transformed into a system of qumodes with a
fermion to boson mapping scheme and apply it to simulate the electronic
structure of dihydrogen molecule as a system of two qumodes. Our work opens the
door for simulating many-fermion systems by harnessing the power of bosonic
quantum devices.
