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

Abstract

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 C 2 H 4 (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C 2 H 4 , which enables the largest molecule ever simulated by VQE to the best of our knowledge.

Exploring Accurate Potential Energy Surfaces via Integrating Variational Quantum Eigensolver with Machine Learning

“…We first assess the DNN-VQE method with the H 4 molecule, each hydrogen atom equispaced along a line. The input parameter of the DNN model for the H 4 molecule is the H–H bond length, and outputs are 30 nonzero parameters in the VQE (utilizing the symmetry of Hartree–Fock orbitals reduces the number of parameters of H 4 from 66 to 30) . All nonzero parameter curves as a function of the H–H bond length are listed in the Supporting Information.…”

Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity

“…VQE is a hybrid quantum-classical algorithm in which the quantum device is used to prepare a circuit ansatz and the classical computer performs optimization to find the parameters for the quantum ansatz such that the parameterized state is close to the unknown ground state. There is dramatic progress in experimental and theoretical study of VQE recently [8,29,51,[54][55][56][57][58][59][60][61][62][63][64][65][66][67]. However, several problems exist which may limit the power of VQE.…”

Symmetry enhanced variational quantum spin eigensolver

“…Therefore, all variational quantumclassical algorithms demand two types of resources: (i) quantum resources which is quantified through either the circuit depth or equivalently the number of gates; and (ii) classical resources which is quantified through the convergence speed. So far, these variational algorithms have been developed for addressing problems in quantum machine learning [25][26][27][28][29][30], combinatorial optimization [31,32], dynamical simulations in closed [23,[33][34][35][36] * abolfazl.bayat@uestc.edu.cn and open [23,[37][38][39][40] systems, quantum sensing [41][42][43][44][45][46][47], computational chemistry [16,20,[48][49][50] and condensed matter physics [51][52][53][54].…”

“…For fulfilling this task, the Variational Quantum Eigensolver (VQE) algorithm has been designed to target the ground state of a many-body system through minimizing the average energy [20,22]. The VQE has been extensively applied to quantum chemistry problems [16,[48][49][50] and experimentally realized on superconducting [16,49,55,56] and ion trap [1,10,57] quantum simulators. Several attempts have been made to enhance the VQE performance, including: minimizing the number of required measurements [58][59][60][61][62][63], improving the initialization [52,64,65], speeding up the classical optimization [66][67][68] and designing better circuits [69][70][71][72][73][74].…”