"Quantum information and contemporary smart network domains are so large and complex as to be beyond the reach of current research approaches. Hence, new theories are needed for their understanding and control. Physics is implicated as smart networks are physical systems comprised of particle-many items interacting and reaching criticality and emergence across volumes of macroscopic and microscopic states. Methods are integrated from statistical physics, information theory, and computer science. Statistical neural field theory and the AdS/CFT correspondence are employed to derive a smart network field theory (SNFT) and a smart network quantum field theory (SNQFT) for the orchestration of smart network systems. Specifically, a smart network field theory (conventional or quantum) is a field theory for the organization of particle-many systems from a characterization, control, criticality, and novelty emergence perspective"--
"Quantum information and contemporary smart network domains are so large and complex as to be beyond the reach of current research approaches. Hence, new theories are needed for their understanding and control. Physics is implicated as smart networks are physical systems comprised of particle-many items interacting and reaching criticality and emergence across volumes of macroscopic and microscopic states. Methods are integrated from statistical physics, information theory, and computer science. Statistical neural field theory and the AdS/CFT correspondence are employed to derive a smart network field theory (SNFT) and a smart network quantum field theory (SNQFT) for the orchestration of smart network systems. Specifically, a smart network field theory (conventional or quantum) is a field theory for the organization of particle-many systems from a characterization, control, criticality, and novelty emergence perspective"--
This paper provides a comprehensive review and synthesis of phase transitions and criticality in random linear systems. Such systems, characterized by matrices with stochastic entries, are ubiquitous across statistical physics, machine learning, signal processing, and control theory. We examine how their macroscopic properties undergo abrupt qualitative changes as underlying parameters vary, analogous to physical phase transitions. Criticality, the state at these phase boundaries, exhibits unique statistical properties like scaling laws and universal behavior, often defying characterization by conventional perturbation theories. The paper reviews foundational concepts from Random Matrix Theory and statistical mechanics of disordered systems, connecting them to modern high-dimensional data analysis and artificial intelligence. We discuss theoretical frameworks, including the replica and cavity methods, and numerical approaches employed to uncover these transitions. Furthermore, we highlight the practical implications of understanding criticality for designing robust algorithms, predicting system performance limits, and comprehending emergent complexity. Our aim is to offer an interdisciplinary synthesis, bridging classical insights with cutting-edge developments, to provide a unified perspective on these profound phenomena across diverse research fields.
Quantum computing (QC) has established itself as a disruptive technology that has the potential to enhance computational capabilities across next-generation energy systems. Its integration into smart grids can enable intelligent decision-making, secure control mechanisms, and advanced optimization strategies. However, existing research remains methodologically fragmented and lacks a unified discussion for practical adoption. This highlights the need for a systematic assessment of the current research landscape to establish structured pathways for effective integration. To address this gap, we have presented a scientometric review that examines the intersection of QC and smart grids based on 133 articles published between 2020 and 2025. The study investigates publication trends, keyword co-occurrence networks, and centrality–density interactions to trace the intellectual evolution of Quantum-enabled Smart Grids (QmSGs). The findings identify post-quantum cryptography and quantum key distribution as dominant motor themes within the field. In parallel, emerging research frontiers include hybrid quantum–classical optimization, federated quantum learning, and AI-driven quantum energy management. The thematic analysis reveals several critical challenges, including scalability constraints, interoperability gaps, and the lack of standardized benchmarking frameworks. Based on these insights, we have proposed a forward-looking research pathway that highlights actionable opportunities for future development. In particular, stronger integration efforts are needed in areas such as explainable quantum learning, adaptive resource orchestration, and sustainable grid governance. These insights can help to enhance the practical relevance and understanding of the field.
Abstract These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
Abstract: Quantum computing and quantum information science constitute a rapidly evolving discipline at the intersection of physics, computer science, and information theory. This paper presents a systematic analysis of the conceptual foundations, theoretical frameworks, and technological challenges shaping the field. The discussion begins with the quantum-mechanical principles underpinning computation and information, followed by a rigorous framework analysis of key models such as qubits, entanglement, and quantum channels. The central problem addressed is the fragility of quantum states under noise and the corresponding need for reliable methods of computation, communication, and security. Methodologically, the paper integrates formal analysis of entropy and channel capacities with the study of error-correcting codes, fault-tolerant architectures, and emerging hardware platforms. The results synthesize advances in quantum algorithms, quantum error correction, quantum cryptography, and hybrid quantum–classical systems, highlighting both their theoretical limits and engineering realizations. The impact is evaluated through implications for secure communication, computational complexity, and future architectures, alongside ethical and societal reflections. By bridging foundational theory with practical challenges, the book offers a comprehensive resource that informs both academic inquiry and technological development. Its neutral, integrative perspective emphasizes not only the purpose of advancing reliable quantum technologies but also their broader implications for science, security, and society. Keywords Quantum computing, quantum information theory, quantum algorithms, quantum error correction, fault-tolerant quantum computation, quantum cryptography, quantum key distribution, post-quantum cryptography, entanglement, quantum channels, von Neumann entropy, quantum capacity, hybrid quantum–classical systems, quantum machine learning, quantum networks, emerging quantum architectures
The AdS/CFT correspondence, a remarkable duality between certain gravitational theories in anti-de Sitter (AdS) spacetime and quantum field theories with conformal symmetry (CFT), has had a profound effect on the development of theoretical physics in the past two decades. Recently, many connections of AdS/CFT to quantum information theory have been found, in particular by providing gravitationally dual descriptions of various entanglement measures. Understanding these manifestions of AdS/CFT --- or more generally, the conjectured holographic principle encompassing it --- requires the combination of tools from both high-energy theory and quantum information physics. In this cumulative thesis, the convergence between these two fields is approached from two fronts: First, by calculations within the dual gravitational theory, and second, using a tensor network ansatz to describe the quantum states suspected to possess such a gravitational description. In the first approach, using the gravitational side of AdS/CFT, entanglement entropies of complicated 2+1-dimensional excited CFTs are computed, thus showing how the holographic approach provides access to systems previously out of reach of practical methods, while introducing new numerical methods that this approach necessitates. The second approach is given by tensor networks, a highly successful ansatz for computing properties of one- and two-dimensional quantum systems. Efficiently computable classes of tensor networks are tested in their ability to represent simple holographic systems, successfully reproducing both hyperbolic geometrical features as well as critical boundary states. In addition, the general properties of tensor networks on regular hyperbolic tesselations are considered, leading to new connections to models not previously considered in the context of holography. This interplay of different approaches to quantum information holography showcases the richness of this new field and suggests that a wide range of physical phenomena is accessible via the new tools now at our disposal.