Progress toward larger molecular simulation on a quantum computer: Simulating a system with up to 28 qubits accelerated by point-group symmetry

Abstract

The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially 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 is preferred 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 employ point-group symmetry to reduce the number of operators in constructing ansatz so as to achieve a more compact quantum circuit. We illustrate this methodology with a series of molecules ranging from LiH (12 qubits) to ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$. This also sheds light onto further work in this direction to construct even shallower ansatz with enough expressive power and simulate even larger scale systems.