PHYSICAL REVIEW A 105, 062452 (2022) Progress toward larger molecular simulation on a quantum computer: Simulating a system with up to 28 qubits accelerated by point-group symmetry Changsu Cao, 1, 2 Jiaqi Hu , 3 Wengang Zhang, 1, 3, 4 Xusheng Xu , 1 Dechin Chen , 1 Fan Yu, 1 Jun Li, 2, 5 Han-Shi Hu, 2 , * Dingshun Lv , 1, † and Man-Hong Yung 1, 3, 4 , ‡ 1 Central Research Institute, 2012 Labs, Huawei Technologies, Shenzhen, 518129, China 2 Department of Chemistry, Tsinghua University, Beijing 100084, China 3 Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China 4 Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China 5 Department of Chemistry, Southern University of Science and Technology, Shenzhen 518055, China (Received 27 October 2021; revised 16 March 2022; accepted 7 June 2022; published 27 June 2022) 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 C 2 H 4 (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C 2 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. DOI: 10.1103/PhysRevA.105.062452 I. INTRODUCTION Quantum computing is proposed to be a promising way to overcome the exponential issue in simulating the energies and properties of the many-electron molecular system by classi- cal computers, as speculated by Feynman in 1982 [1]. Since then, various quantum algorithms have been developed [2–8], among which, the variational quantum eigensolver (VQE) [8–12] is believed to be friendly to near-term quantum devices for its noise-resilient property and its small need for quantum gates, which is a benefit of its hybrid quantum-classical frame- work [13]. The VQE has been applied to simulate chemical systems both experimentally and numerically. The first demonstration of H 2 (2 qubits) on quantum devices was presented in Ref. [8]. After that, a variety of quantum simulations were performed for BeH 2 (6 qubits) [11], H 2 O (8 qubits) [14], and H 12 (12 qubits) [15]. To benchmark the performance or optimize the algorithm, the numerical results are also presented using virtual quantum simulators on different molecules [16–18]. To date, the largest is 20 qubits for H 2 O[17] with 6-31G basis set. The scale of the simulation is limited by two correlated fac- tors, the number of controllable qubits and the circuit depth. Although the top record of the controllable qubit number * hshu@mail.tsinghua.edu.cn † ywlds@163.com ‡ yung.manhong@huawei.com reached 66 [19], the depth of the quantum circuit is still a problematic limitation on large-scale quantum chemical sim- ulation. Therefore, to extend the scale of quantum chemical simulation, a better ansatz initialization requires not only smaller demand for qubit number but also using less parame- ters for a more compact quantum circuit. The unitary coupled-cluster (UCC) ansatz was used when VQE was initially proposed, and has been one of the most popular choices since then. In order to represent the molecule with less parameters for a more compact quantum circuit, one feasible method is to screen out the less important parameters based on UCC ansatz by precalculations or using adap- tive methods [20–23]. Different improved coupled-cluster (CC) ansatzes are also proposed and reached hopeful results [24–27]. Besides these methods, for the chemical system, using the intrinsic information of it might be of more benefit to obtain. the compact ansatz and introduce less approximations. For example, the particle number conservation (U(1) sym- metry) and the fermionic parity conservation (Z 2 symmetry) are used as restrictions in VQE [28–30]. The geometric prop- erty of molecules described by the point-group symmetry will also provide great convenience for quantum chemical simu- lation, for which the power has already been demonstrated in conventional ab initio chemical calculations in classical computers [31–33]. However, the power of point-group sym- metry is rarely explored in the quantum computing regime. Currently, point-group symmetry has been used for two pur- poses: removing qubits in simulation [34,35] and reducing the depth of quantum circuits in quantum computing [36,37]. 2469-9926/2022/105(6)/062452(12) 062452-1 ©2022 American Physical Society