Based on quantum biology and biological gauge field theory, we propose the biological lattice gauge theory as modeling of quantum neural networks. This method applies completely the same lattice theory in quantum field, but, whose two anomaly problems may just describe the double helical structure of DNA and violated chiral symmetry in biology. Further, we discuss the model of Neural Networks (NN) and the quantum neutral networks, which are related with biological loop quantum theory. Finally, we research some possible developments on described methods of networks by the extensive graph theory and their new mathematical forms.
Based on quantum biology and biological gauge field theory, we propose the biological lattice gauge theory as modeling of quantum neural networks. This method applies completely the same lattice theory in quantum field, but, whose two anomaly problems may just describe the double helical structure of DNA and violated chiral symmetry in biology. Further, we discuss the model of Neural Networks (NN) and the quantum neutral networks, which are related with biological loop quantum theory. Finally, we research some possible developments on described methods of networks by the extensive graph theory and their new mathematical forms.
Based on the extensive quantum theory of biology and NeuroQuantology, the Schrodinger equation with the linear potential may become the Bessel equation. Its solutions are Bessel functions, and may form the double helical structure of DNA in three dimensional spaces. From this model we may predict the discrete bound energy spectrum of DNA. Moreover, we discuss some solutions of quantum mechanics and their meaning. Further, we research the entangled state of neurobiology by the extensive quantum method and the nonlinear theory. New experiments shown that the quantum entangled state should be a new fifth interaction, for its verification neuroscience will possibly take a very important role.
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach -applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.
Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract
Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract:
Quantum Neural Networks (QNNs) are emerging as promising tools for complex biological data analysis due to their ability to exploit quantum mechanics for enhanced computational power. In Sec. 2 , we provide readers with a comprehensive overview of proteins, DNA sequencing, and recent updates on classical approaches to PTM prediction, protein function analysis and DNA analysis. Furthermore, we present recent findings that underscore the limitations of traditional methods and justify the need for quantum approaches. This section also highlights the unique advantages and potential benefits that quantum-based methods offer over classical techniques, paving the way for more powerful and accurate solutions in biological data analysis. These tasks are critical for understanding protein regulation, cellular processes and genetic information. In Sec. 3 , we provide a comprehensive review of various QNN architectures that have been proposed to date, categorized based on current theoretical and practical developments. The models discussed include Quantum McCulloch–Pitts (M–P) Neural Networks, Quantum Competitive Neural Networks, Quantum-Inspired Neural Networks, Quantum Dot Neural Networks, Quantum Cellular Neural Networks and Quantum Associative Neural Networks. Each of these models offers unique computational mechanisms rooted in quantum principles such as superposition, entanglement and interference, enabling them to capture complex patterns in high-dimensional biological data. We further highlight their potential and emerging applications in bioinformatics, particularly in the prediction of protein Post-translational Modifications (PTMs). Given the critical role of PTMs in regulating protein activity and cellular functions, leveraging QNNs provides a promising avenue for improving prediction accuracy and interpretability in large-scale proteomic datasets. In Sec. 4 , we present the latest advancements in the application of quantum machine learning in genomics, quantum computing for protein structure and function prediction, as well as quantum machine learning in drug discovery and molecular modeling. Section 5 discusses the current limitations of quantum hardware and the challenges in training quantum models. In Sec. 6 , we propose potential improvements for quantum machine learning models in bioinformatics, including hybrid quantum–classical architectures and more efficient quantum circuit designs. Finally, Sec. 7 concludes the review by summarizing the key insights and outlining specific future research directions, particularly focusing on extending our recent findings into the broader field of quantum machine learning. Together with a system of illustrative figures presented in Secs. 2 – 4 , as well as concrete examples of algorithms discussed in Sec. 4 , this review provides a solid foundation for future applications of quantum machine learning in bioinformatics and highlights the transformative potential of quantum models in revolutionizing biological data analysis.
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Z_{d} gauge group and non-Abelian Kitaev D(G) models on different geometries. Focusing on the special case of Z_{2} gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wave function for the Z_{2} theory away from the exactly solvable limit, and to demonstrate the confining or deconfining phase transition of the Wilson loop order parameter.