Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H₁₀) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H₂, LiH, H₂O, OH^-, and NH₃, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation.