Abstract
Quantum computing is a promising approach to harnessing strong correlation in molecular systems; however, current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as the variational quantum eigensolver (VQE). In this paper, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively (ADAPT-VQE). This treatment often violates symmetry, thereby deteriorating the convergence of fidelity to the exact solution and ultimately resulting in deeper circuits. We demonstrate that spin-symmetry projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations. To further investigate the role of spin-symmetry in computing molecular properties with ADAPT-VQE, we have derived the analytical derivative of symmetry-projected VQE energy. Our illustrative calculations reveal the significance of preserving symmetry in providing accurate dipole moments and geometries with variational approximations.
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