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Quantum computing is a promising approach to harnessing strong correlation inmolecular systems; however, current devices only allow for hybridquantum-classical algorithms with a shallow circuit depth, such as thevariational quantum eigensolver (VQE). In this study, we report the importanceof the Hamiltonian symmetry in constructing VQE circuits adaptively. Thistreatment often violates symmetry, thereby deteriorating the convergence offidelity to the exact solution, and ultimately resulting in deeper circuits. Wedemonstrate that symmetry-projection can provide a simple yet effectivesolution to this problem, by keeping the quantum state in the correct symmetryspace, to reduce the overall gate operations. The scheme also reveals thesignificance of preserving symmetry in computing molecular properties, asdemonstrated in our illustrative calculations.

Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems