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arXiv:2402.12708 · The Journal of Physical Chemistry Letters

Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor

Shoukuan Zhao, Diandong Tang, Xiaoxiao Xiao, Ruixia Wang, Qiming Sun, Zhe Chen, Xiaoxia Cai, Zhendong Li, Haifeng Yu, Wei‐Hai Fang

Published Jul 8, 2024• 8 citations
arXivHTMLPDF

Abstract

Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C 2 H 4 ) and triatomic hydrogen (H 3 ). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.

DOI
10.1021/acs.jpclett.4c01314

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•Jul 27, 2021•5 citations
Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C 2 H 4 ) and triatomic hydrogen (H 3 ). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.
In this paper, we investigate the electronic structure of methanimine (CH 2 NH) and water (H 2 O) molecules in an effort to locate conical intersections (CIs) using variational quantum algorithms. Our approach implements and compares a range of hybrid quantum-classical methods, including the variational quantum eigensolver (VQE), variational quantum deflation (VQD), VQE with automatically-adjusted constraints (VQE-AC) and we explore molecular configurations of interest using a state-average (SA) approach. Exact diagonalization is employed as the classical benchmark to evaluate the accuracy of the quantum algorithms. We perform simulations across a range of molecular geometries, basis sets and active spaces to compare each algorithm’s performance and accuracy, and to enhance the detectability of CIs. This work confirms the quantum variational algorithms’ capability of describing CIs in both molecules, as long as appropriate active spaces and geometries of the molecule are chosen. We also compare the accuracy and reliability of VQE-based methods for computing excited states with classical benchmark methods, and we demonstrate good agreement within desired regions.
We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+_{3}^{+}3+​ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schr{ö}dinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.
Hybrid quantum-classical computing algorithms offer significant potential for accelerating the calculation of the electronic structure of strongly correlated molecules. In this work, we present the first quantum simulation of conical intersections (CIs) in a biomolecule, cytosine, using a superconducting quantum computer. We apply the contracted quantum eigensolver (CQE)─with comparisons to conventional variational quantum deflation (VQD)─to compute the near-degenerate ground and excited states associated with the conical intersection, a key feature governing the photostability of DNA and RNA. The CQE is based on an exact ansatz for many-electron molecules in the absence of noise─a critically important property for resolving strongly correlated states at CIs. Both methods demonstrate promising accuracy when compared with exact diagonalization, even on noisy intermediate-scale quantum computers, highlighting their potential for advancing the understanding of photochemical and photobiological processes. The ability to simulate these intersections is critical for advancing our knowledge of biological processes like DNA repair and mutation, with potential implications for molecular biology and medical research.
Elucidating photochemical reactions is vital to understanding various biochemical phenomena and developing functional materials such as artificial photosynthesis and organic solar cells, albeit with notorious difficulty in 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 multiconfigurational 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.
Abstract In the noisy intermediate-scale quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the ‘killer application’ for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While physically motivated, this approximation can severely impact the description of these complicated features. A perfect example is that of conical intersections (i.e. a singular point of degeneracy between electronic states), which are of primary importance to understand many prominent reactions. Designing active spaces so that the improved accuracy from a quantum computer is not rendered useless is key to finding useful applications of these promising devices within the field of chemistry. To answer this issue, we introduce a NISQ-friendly method called ‘state-averaged orbital-optimized variational quantum eigensolver’ which combines two algorithms: (1) a state-averaged orbital-optimizer, and (2) a state-averaged VQE. To demonstrate the success of the method, we classically simulate it on a minimal Schiff base model (namely the formaldimine molecule CH 2 NH) relevant also for the photoisomerization in rhodopsin—a crucial step in the process of vision mediated by the presence of a conical intersection. We show that merging both algorithms fulfil the necessary condition to describe the molecule’s conical intersection, i.e. the ability to treat degenerate (or quasi-degenerate) states on the same footing.
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 SA 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 minimal energy (ME) points and the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical {\it 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 ME and CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.