Exploring the use of quantum computers for resilience analysis in critical infrastructure networks

Guest Editorial – Special Issue on Quantum Circuits

Quantum Computing represents a paradigm shift in computation, leveraging the principles of quantum mechanics to solve problems intractable for classical computers. This book provides a comprehensive exploration of quantum computing, encompassing its foundational concepts, architecture, algorithms, programming techniques, and real-world applications. Beginning with an overview and historical evolution, it delves into the fundamental differences between classical and quantum computing, highlighting key quantum mechanical phenomena such as superposition, entanglement, and interference. The book further examines quantum states, qubits, and gates, elucidating their roles in quantum computation. The architecture of quantum systems, including superconducting qubits, trapped ions, and photonic qubits, is analyzed alongside quantum circuits, hardware challenges, and error correction mechanisms. Core quantum algorithms, including Shor’s algorithm for factorization and Grover’s algorithm for search, are discussed with practical examples. The book also emphasizes quantum programming, featuring tools like Qiskit, Cirq, and PyQuil, and explores challenges in quantum simulation and circuit development. Applications in cryptography, artificial intelligence, drug discovery, and optimization are detailed, underscoring quantum computing’s transformative potential. The book concludes with an examination of challenges such as scalability, noise, and ethical concerns, while providing insights into future directions, including hardware advancements, emerging algorithms, and integration with classical systems. It serves as an essential resource for students, researchers, and professionals aiming to understand and contribute to the quantum revolution. Keywords: Quantum computing, classical computing, quantum mechanics, qubits, quantum gates, superposition, entanglement, quantum algorithms, Shor’s algorithm, Grover’s algorithm, quantum programming, Qiskit, Cirq, quantum circuits, quantum hardware, error correction, cryptography, artificial intelligence, drug discovery, optimization, scalability, quantum noise, ethical implications, future directions

Researchers are today exploring models for cloud-based usage of quantum computers where multi-tenancy can be used to share quantum computer hard-ware among multiple users. Multi-tenancy has a promise of allowing better utilization of the quantum computer hardware, but also opens up the quantum computer to new types of security attacks. As this and other recent research shows, it is possible to perform a fault injection attack using crosstalk on quantum computers when a victim and attacker circuits are instantiated as co-tenants on the same quantum computer. To ensure such attacks do not happen, this paper proposes that new techniques should be developed to help catch malicious circuits before they are loaded onto quantum computer hardware. Following ideas from classical computers, a compile-time technique can be designed to scan quantum computer programs for mali-cious or suspicious code patterns before they are compiled into quantum circuits that run on a quantum computer. This paper presents ongoing work which demonstrates how crosstalk can affect Grover's algorithm, and then presents suggestions of how quantum programs could be analyzed to catch circuits that generate large amounts of crosstalk with malicious intent.

Abstract: Quantum Computing: The Next Information Age explores the theoretical, algorithmic, technological, and societal dimensions of quantum computing, offering a comprehensive framework that integrates foundational physics with cutting-edge computational innovation. Rooted in the principles of quantum mechanics—superposition, entanglement, and measurement—the book systematically builds a conceptual and mathematical foundation for quantum computation. It addresses the limitations of classical paradigms and articulates the shift toward quantum models such as the quantum circuit model and quantum Turing machines. Through a detailed analysis of quantum algorithms, including Shor’s and Grover’s, and complexity classes such as BQP and QMA, the book outlines the computational advantages offered by quantum systems. It investigates real-world implementations across leading hardware platforms, evaluates error correction and coherence challenges, and examines the feasibility of scalable, fault-tolerant architectures. The role of quantum information in cryptography and secure communication is explored through key protocols (BB84, E91), with attention to the implications for post-quantum security infrastructures. Methodologically, the book combines theoretical modeling, algorithmic construction, comparative complexity analysis, and system-level design review. Results from recent industrial breakthroughs, such as quantum supremacy demonstrations, are synthesized to highlight both promise and limitations. The work concludes with a critical reflection on the philosophical, ethical, and geopolitical implications of the quantum age. This volume provides a rigorous, interdisciplinary foundation for researchers, technologists, and policymakers navigating the emerging quantum frontier. Keywords Quantum computing, quantum algorithms, quantum information, Shor’s algorithm, Grover’s algorithm, quantum cryptography, BB84 protocol, BQP, quantum supremacy, quantum hardware, quantum error correction, NISQ devices, quantum communication, post-quantum security, quantum Turing machine, quantum circuits, entanglement, Hilbert space, quantum internet, computational complexity

Abstract: Quantum computing is on the brink of transforming computation, cryptography, artificial intelligence, and materials science, with quantum computing chips at the core of this revolution. "Quantum Computing Chips: Advances in Superconducting and Topological Qubits" provides an in-depth exploration of the latest advancements in quantum hardware, focusing on superconducting and topological qubits, two of the most promising approaches for scalable, fault-tolerant quantum computing. The book examines the fundamental principles of quantum computing, qubit architectures, and fabrication techniques, highlighting how Josephson junctions, transmon qubits, and Majorana fermions contribute to quantum logic operations. It delves into quantum chip integration, error correction strategies, hybrid quantum-classical computing, and emerging quantum networking technologies, offering insights into how industry leaders such as Google, IBM, and Microsoft are advancing quantum processor development. The book also explores the commercialization, industrial impact, and policy challenges of quantum computing chips, discussing applications in cryptography, AI acceleration, quantum simulation, and financial modeling. Through technical analysis, case studies, and expert insights, this book serves as a comprehensive resource for scientists, engineers, researchers, and technology leaders navigating the rapidly evolving quantum computing landscape. Keywords: Quantum computing, superconducting qubits, topological qubits, Josephson junctions, transmon qubits, Majorana fermions, non-Abelian anyons, quantum error correction, quantum chip fabrication, cryogenic quantum systems, hybrid quantum-classical computing, quantum networking, quantum supremacy, quantum cryptography, quantum AI acceleration, quantum materials science, fault-tolerant quantum computing, scalable quantum processors, quantum circuit design, quantum gate fidelity, quantum simulation, IBM quantum computing, Google quantum computing, Microsoft quantum computing, quantum industry, quantum economy, quantum policy, quantum innovation.

Recent developments in quantum computers have been pushing up the number of qubits. However, the state-of-the-art Noisy Intermediate Scale Quantum (NISQ) computers still do not have enough qubits to accommodate the error correction circuit. Noise in quantum gates limits the reliability of quantum circuits. To characterize the noise effects, prior methods such as process tomography, gateset tomography and randomized benchmarking have been proposed. However, the challenge is that these methods do not scale well with the number of qubits. Noise models based on the understanding of underneath physics have also been proposed to study different kinds of noise in quantum computers. The difficulty is that there is no widely accepted noise model that incorporates all different kinds of errors. The realworld errors can be very complicated and it remains an active area of research to produce accurate noise models. In this paper, instead of using noise models to estimate the reliability, which is measured with success rates or inference strength, we treat the NISQ quantum computer as a black box. We use several quantum circuit characteristics such as the number of qubits, circuit depth, the number of CNOT gates, and the connection topology of the quantum computer as inputs to the black box and derive a reliability estimation model using (1) polynomial fitting and (2) a shallow neural network. We propose randomized benchmarks with random numbers of qubits and basic gates to generate a large data set for neural network training. We show that the estimated reliability from our black-box model outperforms the noise models from Qiskit. We also showcase that our black-box model can be used to guide quantum circuit optimization at compile time.

<p><span>In flood risk analysis it is a key principle to predetermine consequences of flooding to assets, people and infrastructures. Damages to critical infrastructures are not restricted to the flooded area. The effects of directly affected objects cascades to other infrastructures, which are not directly affected by a flood. Modelling critical infrastructure networks is one possible answer to the question ‘how to include indirect and direct impacts to critical infrastructures?’.</span></p><p>Critical infrastructures are connected in very complex networks. The modelling of those networks has been a basis for different purposes (Ouyang, 2014). Thus, it is a challenge to determine the right method to model a critical infrastructure network. For this example, a network-based and topology-based method will be applied (Pant et al., 2018). The basic model elements are points, connectors and polygons which are utilized to resemble the critical infrastructure network characteristics.</p><p>The objective of this model is to complement the state-of-the-art flood risk analysis with a quantitative analysis of critical infrastructure damages and disruptions for people and infrastructures. These results deliver an extended basis to differentiate the flood risk assessment and to derive measures for flood risk mitigation strategies. From a technical point of view, a critical infrastructure damage analysis will be integrated into the tool ProMaIDes (Bachmann, 2020), a free software for a risk-based evaluation of flood risk mitigation measures.</p><p>The data on critical infrastructure cascades and their potential linkages is scars but necessary for an actionable modelling. The CIrcle method from Deltares delivers a method for a workshop that has proven to deliver applicable datasets for identifying and connecting infrastructures on basis of cascading effects (de Bruijn et al., 2019). The data gained from CIrcle workshops will be one compound for the critical infrastructure network model.</p><p>Acknowledgment: This work is part of the BMBF-IKARIM funded project PARADes (Participatory assessment of flood related disaster prevention and development of an adapted coping system in Ghana).</p><p>Bachmann, D. (2020). ProMaIDeS - Knowledge Base. https://promaides.myjetbrains.com</p><p>de Bruijn, K. M., Maran, C., Zygnerski, M., Jurado, J., Burzel, A., Jeuken, C., & Obeysekera, J. (2019). Flood resilience of critical infrastructure: Approach and method applied to Fort Lauderdale, Florida. Water (Switzerland), 11(3). https://doi.org/10.3390/w11030517</p><p>Ouyang, M. (2014). Review on modeling and simulation of interdependent critical infrastructure systems. Reliability Engineering and System Safety, 121, 43–60. https://doi.org/10.1016/j.ress.2013.06.040</p><p>Pant, R., Thacker, S., Hall, J. W., Alderson, D., & Barr, S. (2018). Critical infrastructure impact assessment due to flood exposure. Journal of Flood Risk Management, 11(1), 22–33. https://doi.org/10.1111/jfr3.12288</p>

While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available quantum hardware. Due to these limitations, the depth and dimension of the possible quantum circuits are restricted. This motivates the study of circuits with parameterized operations that can be classically optimized in hybrid methods as variational quantum algorithms, enabling the reduction of circuit depth and size. The characteristics of these Parameterized Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application, motivating the study of their intrinsic properties. In this work, we analyse the generation of random states in PQCs under restrictions on the qubits connectivities, justified by different quantum computer architectures. We apply the expressibility quantifier and the average entanglement as diagnostics for the characteristics of the generated states and classify the circuits depending on the topology of the quantum computer where they can be implemented. As a function of the number of layers and qubits, circuits following a Ring topology will have the highest entanglement and expressibility values, followed by Linear/All-to-all almost together and the Star topology. In addition to the characterization of the differences between the entanglement and expressibility of these circuits, we also place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement. Circuits generating average and standard deviation for entanglement closer to values obtained with the truly uniformly random ensemble of unitaries present a steeper evolution when compared to others.

While current quantum computers, referred to as Noisy Intermediate-Scale Quantum (NISQ) computers, are expected to be beneficial for different applications, they are prone to different types of errors. In order to enhance the reliability of quantum systems, noise-aware quantum compilers are used to generate physical quantum circuits to be executed on NISQ computers. The quantum hardware is calibrated very frequently and its error rates are computed accordingly. Based on the hardware error rates, a quantum compiler allocates physical qubits and schedules quantum operations. However, error rates may change post-calibration. To incorporate dynamic error rates into quantum circuit compilation with minimum cost, we propose a Machine Learning (ML)-based scheme to detect the incorrect output of the quantum circuit and predict the Probability of Successful Trials (PST) with high accuracy. Our approach can verify the error rates of the quantum hardware and validate the correctness of the extracted quantum circuit output. We provide a case study of our ML-based reliability models using IBM Q16 Melbourne quantum computer. Our results show that the proposed scheme achieves a very high prediction accuracy.

Today’s society is becoming highly dependent on the services provided by various critical infrastructure networks. The increasing complexities and interdependencies among infrastructure networks have exacerbated their susceptibility to various disruption or failure events. It is therefore crucial to understand how the failure of the components in a critical infrastructure network affects the performance and integrity of the whole network. Different types of component failures may result in different levels of failure consequence and it is interesting to investigate which type of failure results in the largest failure consequence in an infrastructure network. A review on critical infrastructure protection shows that there is a need to incorporate geographic proximities in the failure cascading process in infrastructure networks. Hence this research initially investigates the failure consequence in a critical infrastructure network resulting from different types of component removals using a proximity-based cascading model for failure propagation. The feasibility of the proposed study is tested on a real-world transportation network. A review on critical infrastructure simulation and analysis also suggests that all the analyses and subsequent policy decisions on critical infrastructure networks have been made based on the assumption that the infrastructure interdependencies model has been constructed to a fair degree of completeness. Although such analyses that aim at the identification of weaknesses and vulnerabilities in infrastructure networks may go some way in preventing or alleviating disastrous outcomes, the failure to consider unforeseen interdependencies among critical infrastructures can result in extreme disruptions not being anticipated. The review also indicates that although approaches for vulnerability/consequence analysis have been widely studied, a complete risk assessment of infrastructure network disruptions incorporating the probabilities as well as consequences of disruption events has not been given serious attention. Therefore this research also proposes using an optimization algorithm to iteratively search for the possible unforeseen interdependencies as well as the failure points that can result in extreme risk in critical infrastructures, thereby anticipating extreme risk events. In order to illustrate the feasibility of the proposed approach, an agent based model of an infrastructure network along with its known interdependencies has been presented, with a genetic algorithm applied to search for potential unforeseen interdependencies as well as failure modes/points that can result in extreme disruptions. The results from this study show the feasibility of anticipating extreme risk events in infrastructure networks, thereby providing valuable insights for proactive risk management of critical infrastructures.

Nowadays society is more and more dependent on critical infrastructures. Critical network infrastructures (CNI) are communication networks whose disruption can create a severe impact on other systems including critical infrastructures. In this work, we propose TOWER, a framework for the provision of adequate strategies to optimize service provision and system resilience in CNIs. The goal of TOWER is being able to compute new network topologies for CNIs under the event of malicious attacks. For doing this, TOWER takes into account a risk analysis of the CNI, the results from a cyber-physical IDS and a multilayer model of the network, for taking into account all the existing dependences. TOWER analyses the network structure in order to determine the best strategy for obtaining a network topology, taking into account the existing dependences and the potential conflicting interests when not all requirements can be met. Finally, we present some lines for further development of TOWER.

The execution of a quantum algorithm typically requires various classical pre- and post-processing tasks. Hence, workflows are a promising means to orchestrate these tasks, benefiting from their reliability, robustness, and features, such as transactional processing. However, the implementations of the tasks may be very heterogeneous and they depend on the quantum hardware used to execute the quantum circuits of the algorithm. Additionally, today’s quantum computers are still restricted, which limits the size of the quantum circuits that can be executed. As the circuit size often depends on the input data of the algorithm, the selection of quantum hardware to execute a quantum circuit must be done at workflow runtime. However, modeling all possible alternative tasks would clutter the workflow model and require its adaptation whenever a new quantum computer or software tool is released. To overcome this problem, we introduce an approach to automatically select suitable quantum hardware for the execution of quantum circuits in workflows. Furthermore, it enables the dynamic adaptation of the workflows, depending on the selection at runtime based on reusable workflow fragments. We validate our approach with a prototypical implementation and a case study demonstrating the hardware selection for Simon’s algorithm.

Over the past few years, several quantum software stacks (QSS) have been developed in response to rapid hardware advances in quantum computing. A QSS includes a quantum programming language, an optimizing compiler that translates a quantum algorithm written in a high-level language into quantum gate instructions, a quantum simulator that emulates these instructions on a classical device, and a software controller that sends analog signals to a very expensive quantum hardware based on quantum circuits. In comparison to traditional compilers and architecture simulators, QSSes are difficult to tests due to the probabilistic nature of results, the lack of clear hardware specifications, and quantum programming complexity.This work devises a novel differential testing approach for QSSes, named QDiff with three major innovations: (1) We generate input programs to be tested via semantics-preserving, source to source transformation to explore program variants. (2) We speed up differential testing by filtering out quantum circuits that are not worthwhile to execute on quantum hardware by analyzing static characteristics such as a circuit depth, 2-gate operations, gate error rates, and T1 relaxation time. (3) We design an extensible equivalence checking mechanism via distribution comparison functions such as Kolmogorov–Smirnov test and cross entropy.We evaluate QDiff with three widely-used open source QSSes: Qiskit from IBM, Cirq from Google, and Pyquil from Rigetti. By running QDiff on both real hardware and quantum simulators, we found several critical bugs revealing potential instabilities in these platforms. QDiff’s source transformation is effective in producing semantically equivalent yet not-identical circuits (i.e., 34% of trials), and its filtering mechanism can speed up differential testing by 66%.

Social vulnerability and equity perspectives on interdependent infrastructure network component importance

Quantum circuits are an abstract framework to represent quantum dynamics. They are used to formally describe and reason about processes within quantum information technology. They are primarily used in quantum computation, quantum communication, and quantum cryptography—for which they provide a machine code–level description of quantum algorithms and protocols. The quantum circuit model is an abstract representation of these technologies based on the use of quantum circuits, with which algorithms and protocols can be concretely developed and studied. Quantum circuits are typically based on the concept of qubits: two-level quantum systems that serve as a fundamental unit of quantum hardware. In their simplest form, circuits take a set of qubits initialized in a simple known state, apply a set of discrete single- and two-qubit evolutions known as “gates,” and then finally measure all qubits. Any quantum computation can be expressed in this form through a suitable choice of gates, in a quantum analogy of the Boolean circuit model of conventional digital computation. More complex versions of quantum circuits can include features such as qudits, which are higher level quantum systems, as well as the ability to reset and measure qubits or qudits throughout the circuit. However, even the simplest form of the model can be used to emulate such behavior, making it fully sufficient to describe quantum information technology. It is possible to use the quantum circuit model to emulate other models of quantum computing, such as the adiabatic and measurement-based models, which formalize quantum algorithms in a very different way. As well as being a theoretical model to reason about quantum information technology, quantum circuits can also provide a blueprint for quantum hardware development. Corresponding hardware is based on the concept of building physical systems that can be controlled in the way required for qubits or qudits, including applying gates on them in sequence and performing measurements.