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DOE OSTI2020

Model-Agnostic Algorithm for Real-Time Attack Identification in Power Grid using Koopman Modes

Malicious activities on measurements from sensors like Phasor Measurement Units (PMUs) can mislead the control center operator into taking wrong control actions resulting in disruption of operation, financial losses, and equipment damage. In particular, false data attacks initiated during power systems transients caused due to abrupt changes in load and generation can fool the conventional model-based detection methods relying on thresholds comparison to trigger an anomaly. In this paper, we propose a Koopman mode decomposition (KMD) based algorithm to detect and identify false data attacks in real-time. The Koopman modes (KMs) are capable of capturing the nonlinear modes of oscillation in the transient dynamics of the power networks and reveal the spatial embedding of both natural and anomalous modes of oscillations in the sensor measurements. The Koopman-based spatio-temporal nonlinear modal analysis is used to filter out the false data injected by an attacker. The performance of the algorithm is illustrated on the IEEE 68-bus test system using synthetic attack scenarios generated on GridSTAGE, a recently developed multivariate spatio-temporal data generation framework for simulation of adversarial scenarios in cyber-physical power systems.

Nandanoori, Sai Pushpak↗

DOE OSTI2022

Simulating Energy and Security Interactions in Semiconductor Manufacturing: Insights from the Intel Minifab Model

Semiconductor manufacturing is a highly complex. Fabrication plants must deal with re-entrant flows to support multiple types of wafers being produced simultaneously, each with their own deadlines and specifications. The manufacturing process itself depends upon the ability to control and programmatically adjust a variety of environmental conditions including temperature, humidity, and air quality. In addition, wafer fabrication consumes large amounts of electricity. Emerging technologies may help reduce the energy footprint of such facilities but can introduce cybersecurity risks. Therefore, this paper presents a modeling and simulation framework to quantify tradeoffs between operational measures of performance, energy consumption, and cybersecurity controls. We augment the Intel Minifab model, with the Purdue Enterprise Reference Architecture (PERA) for cybersecurity as well as tool-level energy consumption data from a real-world semiconductor manufacturing testbed. In this manner, we intend to provide stakeholders with a systematic, data-driven approach to evaluate emerging risks within the manufacturing process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

Modeling and Detection of Future Cyber-Enabled DSM Data Attacks

Demand-Side Management (DSM) is an essential tool to ensure power system reliability and stability. In future smart grids, certain portions of a customer’s load usage could be under the automatic control of a cyber-enabled DSM program, which selectively schedules loads as a function of electricity prices to improve power balance and grid stability. In this scenario, the security of DSM cyberinfrastructure will be critical as advanced metering infrastructure and communication systems are susceptible to cyber-attacks. Such attacks, in the form of false data injections, can manipulate customer load profiles and cause metering chaos and energy losses in the grid. The feedback mechanism between load management on the consumer side and dynamic price schemes employed by independent system operators can further exacerbate attacks. To study how this feedback mechanism may worsen attacks in future cyber-enabled DSM programs, we propose a novel mathematical framework for (i) modeling the nonlinear relationship between load management and real-time pricing, (ii) simulating residential load data and prices, (iii) creating cyber-attacks, and (iv) detecting said attacks. In this framework, we first develop time-series forecasts to model load demand and use them as inputs to an elasticity model for the price-demand relationship in the DSM loop. This work then investigates the behavior of such a feedback loop under intentional cyber-attacks. We simulate and examine load-price data under different DSM-participation levels with three types of random additive attacks: ramp, sudden, and point attacks. We conduct two investigations for the detection of DSM attacks. The first studies a supervised learning approach, with various classification models, and the second studies the performance of parametric and nonparametric change point detectors. Results conclude that higher amounts of DSM participation can exacerbate ramp and sudden attacks leading to better detection of such attacks, especially with supervised learning classifiers. We also find that nonparametric detection outperforms parametric for smaller user pools, and random point attacks are the hardest to detect with any method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Modeling Cyber Supply Chain Incidents with Multilayered Graph Motifs

As noted within the literature, supply chain includes people and organizations---manufacturers, integrators, and third-party vendors---that are involved in one or more stages of a product lifecycle. Since supply chains, by definition, include organizations and people, supply chain risk management activities must consider dependencies between an organization's business processes and third-party resources. Just as adversarial tactics can be implemented via techniques implemented via networked computer systems, so can such tactics be expressed via legal business relationships. A cyber incident may have an exponential impact downstream, for example, by leveraging a product's distribution channel (e.g. malicious updates in SolarWinds, buggy updates in CrowdStrike). Similarly, legitimate and legal business relationships also affect the attack surface exposure of systems, enabling long-term persistence and/or unknown impacts to product quality that are hard to detect. This paper catalogs several recent digital supply chain incidents and applies a multilayered network formalism to develop structural indicators (graph motifs) that reflect potentially-adversarial behavior. Finally, we compare and contrast the characteristics of adversarial tactics (e.g. Loss of Availability, Data Collection) that leverage cyber-physical dependencies to those that leverage legal organizational relationships.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2022

CANShield: Signal-based Intrusion Detection for Controller Area Networks

Modern vehicles rely on complex cyber-physical systems made up of hundreds of electronic control units (ECUs) connected through controller area network (CAN) buses. However, the CAN bus attack surface is increasing due to advanced features in automobiles, making it prone to injection attacks. The ordinary injection attacks disrupt the typical timing properties of the CAN data stream, and the rule-based intrusion detection systems (IDS) can easily detect them. However, advanced attackers can inject false data to the signal level, maintaining the regular pattern/frequency of the CAN messages. Such attacks can bypass the rule-based IDS or any anomaly-based IDS built on binary payload data. To make the vehicles robust against such intelligent attacks, we propose CANShield, a signal-based intrusion detection framework for the CAN bus that consists of three modules. A data preprocessing module handles the high-dimensional CAN data stream at the signal level and make them suitable for any machine learning model. A data analyzer module consists of multiple deep autoencoder networks, each analyzing the time series data from a different perspective. Finally, an attack detection module uses an ensemble method to make the final decision. Evaluation results on a standard signal-based dataset show the effectiveness of the CANShield in detecting five advanced attacks.

Shahriar, Md Hasan↗

DOE OSTI2022

Game-Theoretic Strategies for Cyber-Physical Infrastructures Under Component Disruptions

In this work, networked infrastructures of recursively defined systems composed of discrete cyber and physical components are considered. The components of basic systems at the finest levels can be disrupted by cyber or physical means, and can be reinforced to survive at certain costs. A problem of ensuring the infrastructure performance is formulated as a game between a provider and an attacker, who probabilistically choose components to reinforce and attack, respectively. The disruptions of this infrastructure are characterized using the aggregate failure correlation function that specifies the conditional failure probability of the infrastructure given the failure of an individual system at that level. The survival probabilities of basic systems satisfy simple product-form, first-order differential equations expressed in terms of the multiplier functions. The utility functions of the provider and attacker are composed of the reward and cost terms, both expressed in terms of the component reinforcement and attack probabilities. The Nash equilibrium of this game is characterized, along with the sensitivity functions of the survival probabilities of basic systems that highlight their dependence individually on the cost-benefit terms, the correlation functions, and the multiplier functions. These results are illustrated using simplified models of a distributed cloud servers infrastructure, a 5G data network infrastructure, a high performance computing federation, and a smart energy grid infrastructure.

42 ENGINEERING↗

DOE OSTI2022

Cyber Attack Sequences Generation for Electric Power Grid

Security assessment of cyber-physical energy systems (CPESs) such as the electric power grid is a critical operation to maintain availability, reliability, and quality of service in the presence of persistent threats from malicious cyber actors. Existing security assessment approaches such as penetration testing and red teaming rely on subject matter expert experience and forensic cyber analysis of historical events to perform realistic, threat-informed assessments of CPES defense. CPESs have a large attack surface because of the heterogeneity and complexity of underlying topology, devices, measurements, and vulnerabilities. The aforementioned approaches lead to partial coverage of the attack surface with a large set of unknown but possible exploits. There is a need to automate the CPES attack surface discovery and contextualize it for relevant, highly probable, real-world attack scenarios. We propose a methodology and framework to facilitate the discovery of the CPES attack surface. We present a multilayer attack graph with ranked attack sequences to describe CPES failure scenarios. We present a work-in-progress framework that lists key components to automate the attack modeling and sequence generation. We demonstrate the published National Electric Sector Cybersecurity Organization Resource CPES failure scenario to highlight the trustworthiness of generated attack sequences.

Dutta, Ashutosh↗

DOE OSTI2022

Estimation of the time for steam generator trip due to cyber intrusions

The time required to trip a pressurized water reactor (PWR) by inserting malicious signals into its steam generator (SG) control system has been studied using the Generic PWR (GPWR) Simulator. A semi-analytical model is developed to approximately reproduce the simulator response and understand the dynamics of the control unit. A series of two proportional-integral controllers determines control action according to preset constants, the readings from the feedwater level sensor, and those from feedwater and steam flowrate transmitters. It is observed that the most important factor that determines whether a trip will occur is how much additional water is added to or withheld from the SG over time compared to normal operating conditions. In order to determine the effects of control action on the SG, changes in mass inventory are considered. This approach models the SG water level as a function of mass inventory and has a backward temporal memory. A Python interface is developed for the GPWR framework to automatically simulate different spoofing scenarios and post-process the related data. We observe that the trip times predominantly depend on flow mismatch and/or level errors. Controller parameters, including the integral time and gain constants, either speed up or slow down the rate of progression to a trip setpoint but do not cause a trip by themselves. The reactor can trip on a high-level signal when the reading crosses above 78%, increased from its reference level of 57%, or a low-level reading when it is below 25%. The present results show roughly how long the operators would have to respond to an attack, given a specific set of spoofing signals within the issue space analyzed. Furthermore, we have generated a simple surface by fitting a combination of exponential functions to the data obtained from the GPWR Simulator. In general, trips on a low level have been observed to occur faster than those on a high level.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Distributed Energy Resource Visual Emulator: Phase 1

To help federal energy managers assess, monitor, and manage cybersecurity while achieving decarbonization, the National Renewable Energy Laboratory's Distributed Energy Resource Cybersecurity Framework (DER-CF) offers a comprehensive, web-based assessment tool focusing on cyber governance or policies, technical management, and physical security. The DER-CF currently presents users with a series of pertinent cybersecurity questions, which are used to generate a site-specific report and recommendations. This paper outlines a technical approach to integrate the DER-CF with another key asset—NREL's Advanced Research on Integrated Energy Systems (ARIES) Cyber Range—to visualize cybersecurity resilience and compliance and to enhance the usability and accessibility of the DER-CF. The result is a new tool called the Distributed Energy Resource Visual Emulator (DER-VE). Its development will include regular conversations with stakeholders to assess the effectiveness of these efforts, refine the visualization capability, and ensure its value to our partners. Phase 0 of the integration project was concluded in 2021. Phase 1, completed in 2022, has two components: The first is developing a working visualization of system compliance using the DER-CF, and the second is planning the design of a server application that takes input data from the DER-CF and creates a personal emulated environment of the user's system or a selected reference architect. Major components that were addressed in this phase are the DER-CF output, compliance visualization, data model, and compliance server design.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Enhancing Security and Resiliency in Operational Technology Environments Through Network Slicing and Federated Learning

The growing convergence of Information Technology (IT) and Operational Technology (OT) within Industry 4.0 environments has introduced new demands on industrial network infrastructure. As cyber-physical systems become increasingly interconnected, ensuring the secure, timely, and efficient exchange of critical data is essential. This thesis explores how network slicing, a method of creating isolated virtual network segments, can be applied within OT environments to address challenges such as latency, security, and resource allocation. The first research question addressed in this thesis is: How can OT networks take advantage of NFV and SDN technology to become cyber resilient? This study examines the operational, security, and architectural implications of introducing network slicing into traditionally static OT infrastructures such as Industrial Control Systems (ICS) and SCADA. Through simulated deployments and case studies, the research demonstrates how slicing enables better isolation between critical and non-critical services, thereby improving response time, throughput, and security in sensitive environments. The second question considers: How to dynamically implement network slicing and take advantage of network resources towards integrating decentralized machine learning? In response, this thesis proposes a framework that combines Software-Defined Networking (SDN), Network Function Virtualization (NFV), and Federated Learning (FL) to enable real-time analytics while maintaining data locality. The proposed approach reduces the burden on centralized infrastructure and minimizes privacy risks by supporting on-site training of models across distributed OT nodes, coordinated through dynamically allocated network slices. The third focus explores: How slicing helps to increase the resiliency of OT networks through the orchestration of a dynamic DMZ? To answer this, the thesis presents a method for creating and managing Dynamic Demilitarized Zones (DMZs) using network slicing. This enables flexible and automated isolation of sensitive subsystems during threat scenarios or high-risk operations. Coupled with intelligent orchestration and containerized security services, the dynamic DMZ significantly enhances the system's ability to respond to cyber incidents without halting production. Ultimately, this thesis contributes a comprehensive architecture that blends network slicing with machine learning, secure segmentation, and automation, paving the way for resilient, adaptive, and intelligent OT environments. Performance evaluations across multiple scenarios show improvements in system reliability, threat response time, model accuracy, and resource utilization, providing a strong foundation for future industrial automation systems.

Rodiles Delgado, Brian G↗

DOE OSTI2020

Artificial Intelligence for Digital Security and Protections

Proper functioning of nuclear power plants relies on a mix of well-regulated human and machine-driven workflows. This regulation supports nuclear safety through a series of processes and many of the tasks that support these processes have a repetitive nature that make artificial intelligence (AI) informed by machine learning (ML) a potential aid in a variety of tasks. AI is being evaluated for activities that include inspections, fuel processing, monitoring, and other activities. The introduction of any new technology presents a potential new attack vector. In the case of AI/ML, there are many attacks that have already been discovered and over time the attacks can be expected to follow the growth pattern observed in cyber security. While future planning is necessary, current efforts need to be established now to predict the threat emergence over the next year 10 years and mitigate potential threats. Based on these observations, AI/ML will need to become trustworthy, which corresponds to techniques and procedures that emphasize AI explainability along with resilience techniques to data, algorithms, models, and systems. This kind of system robustness is the foundation for defenses against AI/ML-specific attacks. Attempting to look forward and take a broad view of capabilities provides input to research roadmaps and the ability to distill vulnerabilities into specific use cases may provide greater assistance in understanding the technology benefits while introducing new risks. The impact of current and future AI in three areas—capabilities, challenges, and recovery strategies—represents an initial attempt at balancing both.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2024

Trust-Based Detection and Mitigation of Cyber Attacks in Distributed Cooperative Control of Islanded AC Microgrids

In this study, we address the challenge of detecting and mitigating cyber attacks in the distributed cooperative control of islanded AC microgrids, with a particular focus on detecting False Data Injection Attacks (FDIAs), a significant threat to the Smart Grid (SG). The SG integrates traditional power systems with communication networks, creating a complex system with numerous vulnerable links, making it a prime target for cyber attacks. These attacks can lead to the disclosure of private data, control network failures, and even blackouts. Unlike machine learning-based approaches that require extensive datasets and mathematical models dependent on accurate system modeling, our method is free from such dependencies. To enhance the microgrid’s resilience against these threats, we propose a resilient control algorithm by introducing a novel trustworthiness parameter into the traditional cooperative control algorithm. Our method evaluates the trustworthiness of distributed energy resources (DERs) based on their voltage measurements and exchanged information, using Kullback-Leibler (KL) divergence to dynamically adjust control actions. We validated our approach through simulations on both the IEEE-34 bus feeder system with eight DERs and a larger microgrid with twenty-two DERs. The results demonstrated a detection accuracy of around 100%, with millisecond range mitigation time, ensuring rapid system recovery. Additionally, our method improved system stability by up to almost 100% under attack scenarios, showcasing its effectiveness in promptly detecting attacks and maintaining system resilience. These findings highlight the potential of our approach to enhance the security and stability of microgrid systems in the face of cyber threats.

Computer Science↗

DOE OSTI2025

Cyber‐Resilient Distributed Energy Resource Control Algorithms for Smart Distribution Grids

ABSTRACT This paper focuses on the development of cyber‐resilient gradient‐based optimisation algorithms and theoretical proof for grid‐interactive distributed energy resource (DER) control to enable two grid services of virtual power plants (VPPs) dispatch and grid voltage regulation, considering the communication and security impacts. Firstly, the combined DER dispatch and voltage regulation as a real‐time gradient‐based optimisation problem is recapped. Thereafter, we consider a probabilistic traffic model to characterise packet delays and loss in a communication network, and study how the delays enter the process of information exchange among the grid measurement units, local DER controllers and the grid control centre that execute this control algorithm in a coordinated manner. Then, a strategy combining delay thresholds and message update rules is proposed to immunity the asynchrony resulting from the communications traffic and it avoids possible numerical instabilities and sensitivities of the power tracking and voltage regulation capabilities, resulting as cyber‐resilient DER control algorithms. Additionally, their convergence is theoretically proved. Effectiveness of proposed cyber‐resilient algorithms has been validated on the IEEE 37‐bus system in terms of convergence, VPP tracking and voltage regulation performance for smart distribution systems with high penetration of DERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Distributed Intrusion Detection System using Semantic-based Rules for SCADA in Smart Grid

Cyber-physical system (CPS) security for the smart grid enables secure communication for the SCADA and wide-area measurement system data. Power utilities world-wide use various SCADA protocols, namely DNP3, Modbus, and IEC 61850, for the data exchanges across substation field devices, remote terminal units (RTUs), and control center applications. Adversaries may exploit compromised SCADA protocols for the reconnaissance, data exfiltration, vulnerability assessment, and injection of stealthy cyberattacks to affect power system operation. In this paper, we propose an efficient algorithm to generate robust rule sets. We integrate the rule sets into an intrusion detection system (IDS), which continuously monitors the DNP3 data traffic at a substation network and detects intrusions and anomalies in real-time. To enable CPS-aware wide-area situational awareness, we integrated the methodology into an open-source distributed-IDS (D-IDS) framework. The D-IDS facilitates central monitoring of the detected anomalies from the geographically distributed substations and to the control center. The proposed algorithm provides an optimal solution to detect network intrusions and abnormal behavior. Different types of IDS rules based on packet payload, packet flow, and time threshold are generated. Further, IDS testing and evaluation is performed with a set of rules in different sequences. The detection time is measured for different IDS rules, and the results are plotted. All the experiments are conducted at Power Cyber Lab, Iowa State University, for multiple power grid models. After successful testing and evaluation, knowledge and implementation are transferred to field deployment.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

A Trilevel Model for Segmentation of the Power Transmission Grid Cyber Network

Network segmentation of a power grid's communication system can make the grid more resilient to cyberattacks. Here we develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technology (IT) administrator, attacker, and grid operator. The IT administrator is allowed to segment existing networks, and the attacker is given a budget to inflict damage on the grid by attacking the segmented communication system. Finally, the grid operator can redispatch the grid after the attack to minimize damage. The resulting problem is a trilevel interdiction problem that we solve using a branch and bound algorithm for bilevel problems. We demonstrate the benefits of optimal network segmentation through case studies on the 9-bus Western System Coordinating Council (WSCC) system and the 30-bus IEEE system. These examples illustrate that network segmentation can significantly reduce the threat posed by a cyberattacker.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Nominal and adversarial synthetic PMU data for standard IEEE test systems

GridSTAGE (Spatio-Temporal Adversarial scenario GEneration) is a framework for the simulation of adversarial scenarios and the generation of multivariate spatio-temporal data in cyber-physical systems. GridSTAGE is developed based on Matlab and leverages Power System Toolbox (PST) where the evolution of the power network is governed by nonlinear differential equations. Using GridSTAGE, one can create several event scenarios that correspond to several operating states of the power network by enabling or disabling any of the following: faults, AGC control, PSS control, exciter control, load changes, generation changes, and different types of cyber-attacks. Standard IEEE bus system data is used to define the power system environment. GridSTAGE emulates the data from PMU and SCADA sensors. The rate of frequency and location of the sensors can be adjusted as well. Detailed instructions on generating data scenarios with different system topologies, attack characteristics, load characteristics, sensor configuration, control parameters are available in the Github repository - https://github.com/pnnl/GridSTAGE. There is no existing adversarial data-generation framework that can incorporate several attack characteristics and yield adversarial PMU data. The GridSTAGE framework currently supports simulation of False Data Injection attacks (such as a ramp, step, random, trapezoidal, multiplicative, replay, freezing) and Denial of Service attacks (such as time-delay, packet-loss) on PMU data. Furthermore, it supports generating spatio-temporal time-series data corresponding to several random load changes across the network or corresponding to several generation changes. A Koopman mode decomposition (KMD) based algorithm to detect and identify the false data attacks in real-time is proposed in https://ieeexplore.ieee.org/document/9303022. Machine learning-based predictive models are developed to capture the dynamics of the underlying power system with a high level of accuracy under various operating conditions for IEEE 68 bus system. The corresponding machine learning models are available at https://github.com/pnnl/grid_prediction.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Software Bill of Materials in the Nuclear Industry

Nuclear power plants (NPP) have thousands of digital assets throughout their facility. Typically, NPPs have asset and configuration management programs that capture the make, model, and version of a component. This information, however, usually only includes first- or second-tier components and does not capture the complete enumeration of software components and their dependencies within operational technology (OT) equipment. As seen with recent cyberattacks, this level of detail is insufficient for identifying if and where an exploitable vulnerability exists within a facility. A software bill of materials (SBOM) provides this detailed enumeration. Further, integrating SBOMs with vulnerability data sources and vulnerability attestation reports can provide improved awareness leading to better cyber risk management and incident response. Preferably, SBOMs are provided by the supplier; however, when an NPP already owns a device, it is less likely they will have a supplier provided-SBOM. Fortunately, SBOMs can be generated on installed digital assets. This paper provides an introduction to the U.S. Department of Energy Office of Nuclear Energy paper titled “Towards Software Bill of Materials in the Nuclear Industry,” which describes the SBOM ecosystem and provides a suggested approach to methodically and seamlessly integrate an SBOM program in an NPP.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2026

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗