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.
The exact evaluation of the molecular ground state in quantum chemistry requires an exponential increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum algorithms. A quantum-classical hybrid optimization scheme known as the variational quantum eigensolver (VQE) is preferred for this task for noisy intermediate-scale quantum devices. However, the circuit depth becomes one of the bottlenecks of its application to large molecules of more than 20 qubits. In this work, we propose a new strategy by employing the point group symmetry to reduce the number of operators in constructing ansatz to achieve a more compact quantum circuit. We illustrate this methodology with a series of molecules ranging from LiH (12 qubits) to C2H4 (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C2H4, which enables the largest molecule ever simulated by VQE to the best of our knowledge.
Quantum computation represents a revolutionary means for solving problems in quantum chemistry. However, due to the limited coherence time and relatively low gate fidelity in the current noisy intermediate-scale quantum (NISQ) devices, realization of quantum algorithms for large chemical systems remains a major challenge. In this work, we demonstrate how the circuit depth of the unitary coupled cluster ansatz in the algorithm of variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are pre-screened from the unitary coupled-cluster singles and doubles (UCCSD) operator pool according to its contribution to the total energy. The procedure is then iteratively repeated until the convergence of the final energy to within the chemical accuracy. For demonstration, this method has been sucessfully applied to systems of molecules and periodic hydrogen chain. Particularly, a reduction up to 14 times in the number of operators is observed while retaining the accuracy of the origin UCCSD operator pools. This method can be widely extended to other variational ansatz other than UCC.
