Which Options Exist for NISQ-Friendly Linear Response Formulations?

Abstract

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136−9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resourceefficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing

“…There are however other operator transformations than the primitive { Ĝ I }∪{ Ĝ I † } and self-consistent { Ŝ I }∪{ Ŝ I † } manifold. We recently explored this in ref ., where we investigated eight different operator transformations for near and long-term quantum computing.…”

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

“…For example, absorption spectra can be obtained from excitation energies and oscillator strengths of a molecular system. Several approaches for obtaining excitation energies have emerged in recent years. − In this work, we will focus on the quantum linear response (qLR) method, which is similar to the quantum equation of motion (qEOM) of Ollitrault et al The qEOM method is an extension of the well-known classical EOM − approach that can potentially leverage near-term, noisy quantum hardware to obtain excitation energies of molecules. After preparing and optimizing a ground state using VQE, the method uses a quantum processor to measure individual matrix elements of an EOM secular equation.…”

“…The self-consistent operators have also been applied to obtain linear response properties within the self-consistent quantum linear response q-sc-LR approach . Recently, some of us have also explored the feasibility of other operator transformations for qLR formalisms …”

Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor

“…This motivates the development of hybrid quantum-classical (HQC) algorithms, such as the variational quantum eigensolver (VQE), which requires shallower circuits and less coherence time, although at the expense of additional classical computational resources. Variational HQC algorithms have been developed to compute the ground state of molecules, ,− excited states, − and molecular response properties − and perform ab initio molecular dynamics. , …”