Analytical energy gradient for state-averaged orbital-optimized variational quantum eigensolvers and its application to a photochemical reaction

Abstract

Elucidating photochemical reactions is vital to understand various biochemical phenomena and develop functional materials such as artificial photosynthesis and organic solar cells, albeit its notorious difficulty by both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multi-configurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for large systems we are interested in. Utilizing quantum computers was recently proposed as a promising approach to overcome such computational cost, dubbed as state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE). Here we extend a theory of SA-OO-VQE so that analytical gradients of energy can be evaluated by standard techniques that are feasible with near-term quantum computers. The analytical gradients, known only for the state-specific OO-VQE in previous studies, allow us to determine various characteristics of photochemical reactions such as the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical cis-trans isomerization of 1,3,3,3-tetrafluoropropene. Numerical simulations of quantum circuits and measurements can correctly capture the photochemical reaction pathway of this model system, including the CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.

arXiv comment21 pages, 6 figures

References in corpus (16)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Quantum computational advantage using photons
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Variational Quantum Computation of Excited States
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• Subspace-search variational quantum eigensolver for excited states
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Orbital optimized unitary coupled cluster theory for quantum computer
• A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states

Cited by in corpus (11)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Efficient quantum computation of molecular forces and other energy gradients
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Variational quantum algorithm for ergotropy estimation in quantum many-body batteries
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization
• Quantum Chemistry Calculations using Energy Derivatives on Quantum Computers
• Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
• Noise-Robust Detection of Quantum Phase Transitions
• Ab initio extended Hubbard model of short polyenes for efficient quantum computing
• State-Averaged Orbital-Optimized VQE: A quantum algorithm for the democratic description of ground and excited electronic states
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures