The paper presents a quantum computational approach to calculate the ground-state energies of molecules, specifically focusing on water (H₂O) and lithium hydride (LiH). The authors demonstrate that quantum algorithms can significantly reduce the computational complexity compared to classical methods, which scales exponentially with system size. Using a recursive phase estimation algorithm, they achieve precise energy calculations with a modest number of qubits. The study shows that the number of qubits required scales linearly with the number of basis functions, and the number of quantum gates required grows polynomially with the number of qubits. The authors also introduce an adiabatic method to improve the overlap between the initial wave function and the exact ground state, enhancing the accuracy of the quantum simulation. The results indicate that quantum computers with tens to hundreds of qubits can match or exceed the capabilities of classical full configuration interaction (FCI) calculations, making quantum computing a promising tool for exact methods in computational quantum chemistry.The paper presents a quantum computational approach to calculate the ground-state energies of molecules, specifically focusing on water (H₂O) and lithium hydride (LiH). The authors demonstrate that quantum algorithms can significantly reduce the computational complexity compared to classical methods, which scales exponentially with system size. Using a recursive phase estimation algorithm, they achieve precise energy calculations with a modest number of qubits. The study shows that the number of qubits required scales linearly with the number of basis functions, and the number of quantum gates required grows polynomially with the number of qubits. The authors also introduce an adiabatic method to improve the overlap between the initial wave function and the exact ground state, enhancing the accuracy of the quantum simulation. The results indicate that quantum computers with tens to hundreds of qubits can match or exceed the capabilities of classical full configuration interaction (FCI) calculations, making quantum computing a promising tool for exact methods in computational quantum chemistry.