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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Davidson methods offer efficient computation of selected excitation energies by avoiding full Hessian construction.
• Quantum self-consistent linear response (q-sc-LR) is a novel method for electronic property calculations.

Purpose of the Study:

• To adapt and apply Davidson methods within the q-sc-LR framework.
• To compute excitation energies and linear response properties for various molecular systems.
• To assess the performance of different quantum computing approaches for these calculations.

Main Methods:

• Application of Davidson-type methods for Hessian-vector multiplications in q-sc-LR.
• Calculation of excitation energies for hydrogen chains (H2 to H10).
• Computation of static polarizabilities and C6 coefficients for small molecules.
• Formulation of Davidson method for damped (complex) linear response.

Main Results:

• Accurate excitation energies were obtained for hydrogen chains.
• Statistical noise in quantum simulations for excitation energies was analyzed.
• Unitary coupled cluster demonstrated superior performance over classical projected coupled cluster for strongly correlated systems.
• Nitrogen K-edge X-ray absorption spectra of ammonia and C6 coefficients were computed.

Conclusions:

• Davidson methods are effective for computing excitation energies and linear response properties using q-sc-LR.
• The study highlights the potential of quantum computing for accurate molecular property calculations.
• Unitary coupled cluster is advantageous for strongly correlated systems in linear response calculations.