The principle of quantum superposition has long been a foundational theoretical and computational tool for elucidating chemical bonds and molecular structures. Chemical bonds form when particles are shared and become delocalized across atoms or molecules. We explore particle delocalization within biomolecules and the quantum superpositions that emerge from these delocalizations, particularly from the quantum information perspective. Our research includes the examination of electron delocalization in covalent bonds [J.6, U.4], proton delocalization in hydrogen bonds [J.1, J.2, J.3], and excitation delocalization in van der Waals interactions [J.10, U.5]. The resulting superpositions reduce system energy [1] and enhance molecular stability. Additionally, based on matter-wave interferometer experiments [2], it has been suggested that these superpositions can extend to macroscopic scales within biomolecules. Moreover, the structures of molecules stabilized by chemical bonds dictate their physicochemical properties and biological functions. These observations, together with our preliminary results, lead to an intriguing question: Could nature have discovered how to generate robust and large-scale quantum superpositions long before we did and control them for the functions of biomolecules? Our research is founded on this inquiry but does not assume that the answer should necessarily be yes. Regardless of the ultimate answer, this line of inquiry could deepen our understanding of biochemical phenomena and inspire a new direction in quantum technologies.
[1] F. Weinhold, J. Chem. Edu. 76, 1141 (1999); F. Weinhold and R.A. Klein, Chem. Educ. Res. Pract.15, 276 (2014).
[2] Y.Y. Fein et al., Nat. Phys. 15, 1242 (2019); A. Shayegh et al., Nat. Commun. 11, 144 (2020); F. Brand et al., Phys. Rev. Lett. 125, 033604 (2020).
The delocalization of electrons through covalent bonds generates fermionic mode entanglement and discord between molecular orbitals while stabilizing bonded atoms and molecules by a certain amount of energy. In our research, we aim to investigate the dynamical behavior of multipartite orbital correlations and interrogate their relation to the physicochemical properties and biological functions of various molecules. To accurately quantify bipartite orbital correlations using fermionic information theory for the first time in the literature, we have developed a methodology that is compatible with all conventional quantum chemistry algorithms and software. This methodology has been successfully tested on several prototypical molecules [J.6]. However, the scope of this work has so far been limited to small molecules, as accurately characterizing strongly correlated molecular electronic states presents significant computational challenges, often necessitating a trade-off between accuracy and computational cost.
To overcome this limitation, we achieve advances beyond the current state of the art in collaboration with esteemed colleagues. We reduce computational complexity by employing cutting-edge numerical methods derived from quantum computation, condensed matter theory, and computer engineering. Our approach enables more efficient representations of the electronic states of strongly correlated molecules and complexes. These methods include, but are not limited to, quantum computational chemistry mappings, tensor network methods such as the quantum chemistry version of the density matrix renormalization group, and neural network methods like the restricted and deep Boltzmann machine algorithm. Furthermore, we utilize the same quantum state representations to extend the resource theory of entanglement and discord to multipartite systems.
Similar to how covalent bonds gain stability through electron delocalization, hydrogen bonds can also be stabilized through proton delocalization. Exploring this possibility was one of the primary objectives of Onur Pusuluk’s Ph.D. research [J.1, J.2, J.3]. Investigating the quantum coherence and correlations arising within hydrogen bond networks and their contributions to the physical, chemical, and biological properties and functions of molecules is another part of our research agenda.
The identification of biomolecular correlations in terms of the discord and entanglement shared between molecular orbitals presents a unique issue from a quantum information perspective. Hartree-Fock orbitals, for instance, are often delocalized across different atoms. However, in quantum information theory, the local agents or laboratories that share correlations are typically localized in space. Constructing molecular orbitals that are specifically localized around individual atoms is feasible only in a few specialized cases. In contrast, atomic orbitals, which describe individual atoms, tend to overlap in space.
To address this challenge, we have recently proposed a novel approach [U.2] within the resource theory of superposition to quantify multipartite superpositions in molecular systems. Specifically, we utilized the notion of biorthogonality and represented the superposition of nonorthogonal states by a non-Hermitian but trace-one state whose eigenvalues are real. Through this new framework, our subsequent research focused on electron delocalization in aromatic molecules [U.4]. Our preliminary findings indicate that an increase in (anti)aromatic character is associated with a significant enhancement in multipartite superposition within the molecule. Furthermore, the degree of superposition in an aromatic system appears to grow exponentially as the number of electrons and the atoms around which they are delocalized rises. We aim to advance this biorthogonal / non-Hermitian framework further to gain a deeper understanding of the multipartite correlations generated in chemical bond formation and dissociation.
Additionally, we extend this study to investigate the role of quantum superposition in the broader hierarchy of nonclassicality. We believe this biorthogonal / non-Hermitian framework holds the potential to guide us toward a complete theory of nonclassicality, unifying concepts such as contextuality, superposition, coherence, and discord.
Our proposed research in quantum-molecular biology also aims to investigate the role of molecular correlations in nonequilibrium biochemical processes within the framework of single-shot quantum thermodynamics and its associated resource theories [J.7]. This approach facilitates the application of quantum information theory to study small, strongly correlated thermodynamic systems that fall outside the purview of traditional statistical methods. The analysis of such systems, in terms of their disorder and stability, should be conducted using majorization and thermomajorization pre-orders, rather than relying solely on entropy and free energy criteria. Through the application of this methodology, we have recently demonstrated that biomolecular correlations can enhance the efficiency of photoisomerization in the retinal chromophore of rhodopsin [J.10]. In the near future, we plan to more systematically investigate the contribution of molecular correlations in nonequilibrium biochemical processes, starting from the chemical bond formation and dissociation.
