Expanding variational quantum eigensolvers to larger systems by dividing the calculations between classical and quantum hardware

We present a hybrid classical/quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources by splitting the workload between classical and quantum processors. This algorithm reduces the needed number of qubits at the expense of an increased number of quantum evaluations. We demonstrate the method for the Hubbard model and show how the conservation of the z-component of the total spin allows the spin-up and spin-down configurations to be computed on classical and quantum hardware, respectively. Other symmetries can be exploited in a similar manner.