  Exploring the potential application of quantum computers in material design
and drug discovery has attracted a lot of interest in the age of quantum
computing. However, the quantum resource requirement for solving practical
electronic structure problems are far beyond the capacity of near-term quantum
devices. In this work, we integrate the divide-and-conquer (DC) approaches into
the variational quantum eigensolver (VQE) for large-scale quantum computational
chemistry simulations. Two popular divide-and-conquer schemes, including
many-body expansion~(MBE) fragmentation theory and density matrix embedding
theory~(DMET), are employed to divide complicated problems into many small
parts that are easy to implement on near-term quantum computers. Pilot
applications of these methods to systems consisting of tens of atoms are
performed with adaptive VQE algorithms. This work should encourage further
studies of using the philosophy of DC to solve electronic structure problems on
quantum computers.
