Subspace methods for the simulation of molecular response properties on a quantum computer

Abstract

We explore Davidson methods for obtaining excitation energies and other linear response properties within quantum self-consistent linear response (q-sc-LR) theory. 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 H${}_{10}$) 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 H${}_2$, LiH, H${}_2$O, OH${}^{-}$, and NH${}_3$, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the $C_6$ coefficients of H${}_2$, LiH, H${}_2$O, OH${}^{-}$, and NH${}_3$.

35 pages, 5 figures

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• Reduced density matrix formulation of quantum linear response
• Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers
• Divergences in classical and quantum linear response and equation of motion formulations
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements
• Self-consistent Quantum Linear Response with a Polarizable Embedding environment
• Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
• Equation-of-motion internally contracted multireference unitary coupled-cluster theory