Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry

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(VQE) 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 the 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 C2H4(28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C2H4, which enables the largest molecule ever numerically simulated by VQE-UCC to the best of our knowledge. This also shed light into the further work of this direction to construct even shallower ansatz with enough expressive power and simulate even larger scale system.