2024/04/01 by Tyler Kharazi, Kharazi, Tyler, Torin F. Stetina +7 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2404.01454
openalex publication_date 2024/04/01 · openalex created_date 2024/04/05 · openalex updated_date 2026/07/28
We develop and analyze a fault-tolerant quantum algorithm for computing n-th order response properties necessary for analysis of non-linear spectroscopies of molecular and condensed phase systems. We use a semi-classical description in which the electronic degrees of freedom are treated quantum mechanically and the light is treated as a classical field. The algorithm we present can be viewed as an implementation of standard perturbation theory techniques, focused on \it ab initio calculation of n-th order response functions. We provide cost estimates in terms of the number of queries to the block encoding of the unperturbed Hamiltonian, as well as the block encodings of the perturbing dipole operators. Using the technique of eigenstate filtering, we provide an algorithm to extract excitation energies to resolution γ, and the corresponding linear response amplitude to accuracy ε using O(N6η2γ-1ε-1log(1/ε)) queries to the block encoding of the unperturbed Hamiltonian H0, in double factorized representation. Thus, our approach saturates the Heisenberg O(γ-1) limit for energy estimation and allows for the approximation of relevant transition dipole moments. These quantities, combined with sum-over-states formulation of polarizabilities, can be used to compute the n-th order susceptibilities and response functions for non-linear spectroscopies under limited assumptions using \widetildeO(N5n+1ηn+1/γnε) queries to the block encoding of H0.