  Calculating the ground state properties of a Hamiltonian can be mapped to the
problem of finding the ground state of a smaller Hamiltonian through the use of
embedding methods. These embedding techniques have the ability to drastically
reduce the problem size, and hence the number of qubits required when running
on a quantum computer. However, the embedding process can produce a relatively
complicated Hamiltonian, leading to a more complex quantum algorithm. In this
paper we carry out a detailed study into how density matrix embedding theory
(DMET) could be implemented on a quantum computer to solve the Hubbard model.
We consider the variational quantum eigensolver (VQE) as the solver for the
embedded Hamiltonian within the DMET algorithm. We derive the exact form of the
embedded Hamiltonian and use it to construct efficient ansatz circuits and
measurement schemes. We conduct detailed numerical simulations up to 16 qubits,
the largest to date, for a range of Hubbard model parameters and find that the
combination of DMET and VQE is effective for reproducing ground state
properties of the model.
