  Quantum computing has recently exhibited great potentials in predicting
chemical properties for various applications in drug discovery, material
design, and catalyst optimization. Progress has been made in simulating small
molecules, such as LiH and hydrogen chains of up to 12 qubits, by using quantum
algorithms such as variational quantum eigensolver (VQE). Yet, originating from
limitations of the size and the fidelity of near-term quantum hardware, how to
accurately simulate large realistic molecules remains a challenge. Here,
integrating an adaptive energy sorting strategy and a classical computational
method, the density matrix embedding theory, which effectively finds a
shallower quantum circuit and reduces the problem size, respectively, we show a
means to circumvent the limitations and demonstrate the potential toward
solving real chemical problems. We numerically test the method for the
hydrogenation reaction of C6H8 and the equilibrium geometry of the C18
molecule, with basis sets up to cc-pVDZ (at most 144 qubits). The simulation
results show accuracies comparable to those of advanced quantum chemistry
methods such as coupled-cluster or even full configuration interaction, while
the number of qubits required is reduced by an order of magnitude (from 144
qubits to 16 qubits for the C18 molecule) compared to conventional VQE. Our
work implies the possibility of solving industrial chemical problems on
near-term quantum devices.
