Purpose of work is to analyze classical, quantum and quantum-inspired optimization methods in relation to the problem of ensuring the stability of blockchain systems, to develop a QUBO model of cumulative risk, taking into account the probabilities of attacks and resource constraints, to adapt the discrete algorithm of simulated dSB bifurcation and its modification HdSB to the problem of ensuring the stability of systems by minimizing risk. Research methods: comparative analysis of the performance of optimization algorithms on problems of various structures and dimensions, construction of a QUBO risk model with the incorporation of resource constraints through a quadratic penalty function, adaptation of dSB and HdSB algorithms by converting the QUBO formulation into an Ising model and adjusting the evolution parameters. Results of the study: a strictly defined QUBO formulation of the problem of ensuring the resilience of blockchain systems to a variety of classical and quantum attacks has been formed. In the model, the combined probabilities of various attack scenarios are reduced to a system of linear coefficients reflecting individual risks and quadratic coefficients describing the interactions between vulnerabilities. Resource constraints on the number of simultaneously implemented protective measures are incorporated by means of a quadratic penalty function, which allows us to consider the choice of the optimal configuration of protective measures as a single task of discrete global optimization. The dSB and HdSB algorithms were adapted to the task of minimizing the QUBO function of cumulative risk. The adaptation includes the transformation of binary variables to a spin representation and the determination of the parameters of the evolution of a system of oscillators with nonlinear interactions. A series of computational experiments on synthetic problems modeling the structural properties of vulnerability graphs of real blockchain platforms is presented, confirming the effectiveness of adapted algorithms. Based on the analysis of the structure of the QUBO risk model, the prospects for further improvement of optimization quality are substantiated by integrating game theory methods for local configuration adjustment after the evolution stage according to the dynamics of simulated bifurcation. It is shown that the QUBO problem can be interpreted as a potential game using Nash equilibrium search procedures using the best response method to systematically improve solutions. Scientific novelty: for the first time, a specialized QUBO model of cumulative risk has been proposed, adapted to the challenges of ensuring the stability of blockchain systems while taking into account complex interactions between vulnerabilities and limited resources, and a discrete simulated bifurcation algorithm and its modifications have been adapted to solve this problem.
Purpose of work is to analyze classical, quantum and quantum-inspired optimization methods in relation to the problem of ensuring the stability of blockchain systems, to develop a QUBO model of cumulative risk, taking into account the probabilities of attacks and resource constraints, to adapt the discrete algorithm of simulated dSB bifurcation and its modification HdSB to the problem of ensuring the stability of systems by minimizing risk. Research methods: comparative analysis of the performance of optimization algorithms on problems of various structures and dimensions, construction of a QUBO risk model with the incorporation of resource constraints through a quadratic penalty function, adaptation of dSB and HdSB algorithms by converting the QUBO formulation into an Ising model and adjusting the evolution parameters. Results of the study: a strictly defined QUBO formulation of the problem of ensuring the resilience of blockchain systems to a variety of classical and quantum attacks has been formed. In the model, the combined probabilities of various attack scenarios are reduced to a system of linear coefficients reflecting individual risks and quadratic coefficients describing the interactions between vulnerabilities. Resource constraints on the number of simultaneously implemented protective measures are incorporated by means of a quadratic penalty function, which allows us to consider the choice of the optimal configuration of protective measures as a single task of discrete global optimization. The dSB and HdSB algorithms were adapted to the task of minimizing the QUBO function of cumulative risk. The adaptation includes the transformation of binary variables to a spin representation and the determination of the parameters of the evolution of a system of oscillators with nonlinear interactions. A series of computational experiments on synthetic problems modeling the structural properties of vulnerability graphs of real blockchain platforms is presented, confirming the effectiveness of adapted algorithms. Based on the analysis of the structure of the QUBO risk model, the prospects for further improvement of optimization quality are substantiated by integrating game theory methods for local configuration adjustment after the evolution stage according to the dynamics of simulated bifurcation. It is shown that the QUBO problem can be interpreted as a potential game using Nash equilibrium search procedures using the best response method to systematically improve solutions. Scientific novelty: for the first time, a specialized QUBO model of cumulative risk has been proposed, adapted to the challenges of ensuring the stability of blockchain systems while taking into account complex interactions between vulnerabilities and limited resources, and a discrete simulated bifurcation algorithm and its modifications have been adapted to solve this problem.
This study explores quantum-inspired optimization algorithms (QIOAs) as practical tools for solving constrained combinatorial problems on classical machines. We analyze tasks that can be formulated in Ising or QUBO forms and benchmark three representative approaches: Simulated Bifurcation (SB), Quantum-Inspired Particle Swarm Optimization (QPSO), and a tensor-network (TN) method. A unified evaluation protocol is introduced that captures solution quality, feasibility, runtime, energy consumption, parameter sensitivity, and scalability. To ensure reliable performance, we develop automated penalty-adjustment and schedule-calibration strategies. Experimental results across diverse benchmarks show that SB and TN together yield the best trade-offs between accuracy and runtime: SB is efficient on dense instances with moderate penalties and low energy use, while TN is advantageous for sparse or modular networks, especially on GPUs. QPSO is competitive in smoother landscapes but more sensitive to hyperparameters. By linking performance to structural properties such as spectral gaps and constraint activity, we provide guidance for selecting suitable algorithms. Overall, QIOAs emerge as effective intermediaries between existing classical heuristics and emerging quantum devices, supported by a reproducible, energy-aware evaluation framework.
Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.
Managing inventory in large-scale supply chains necessitates quick, cost-effective decisions that adhere to constraints such as storage limits and variable demand. This paper describes a novel hybrid approach that uses both quantum and classical computers to tackle inventory problems structured as Quadratic Unconstrained Binary Optimization (QUBO). Each choice variable, such as restocking a product, is represented in binary form, with related costs and penalties built into the objective function. Business constraints are communicated indirectly using adjustable weights, allowing the model to remain unconstrained while discouraging unrealistic conclusions. Optimization is carried out using both classical methods like simulated annealing and quantum solvers such as D-Wave and QAOA, where a hybrid strategy selects the most viable solution. The results indicate that the hybrid system consistently produces lower total costs and better constraint compliance compared to individual solvers, especially for complex, high-dimensional datasets. To ensure secure, automated execution of these optimized decisions, a blockchain layer is introduced. Inventory actions—such as placing orders or updating stock—are carried out through smart contracts that provide tamper-proof, verifiable enforcement. By employing a lightweight Proof of Authority (PoA) mechanism, transaction validation remains fast while maintaining transparency across all nodes in the network. This integration of quantum optimization with blockchain automation enables a responsive and trustworthy framework for modern inventory management.
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary Optimization (QUBO) formulation provides a unifying modeling framework for a broad class of NP-hard problems and is naturally suited to quantum computing and quantum-inspired algorithms. Location science, network design, and logistics represent core application domains of discrete optimization, combining high practical impact with substantial computational challenges. In this work, we develop QUBO formulations for several fundamental problems in these domains, including a nonlinear integer formulation of the Discrete Ordered Median Problem (DOMP). Beyond their modeling relevance, these QUBO formulations serve as representative benchmark problems for assessing quantum algorithms and quantum hardware. We further derive a tight bound for the penalty parameter ensuring equivalence between the QUBO formulation and its underlying integer program. Finally, we conduct a comprehensive computational study using QAOA, WS-QAOA, and classical heuristics for QUBO instances of the p-Median Problem and the Fixed-Charge Facility Location Problem (FCFLP), and introduce two effective warm-start strategies for WS-QAOA based on its linear programming relaxation.
The article investigates the problem of ensuring cryptographic stability of information and communication systems in the conditions of increasing intensity of cyber threats and development of quantum computing, which reduces the efficiency of classical cryptographic algorithms. An analysis of modern approaches to the application of post-quantum cryptographic algorithms was conducted, which showed their predominantly static nature of use without taking into account the dynamics of changes in the operating environment, risk level and attack parameters. The need to develop adaptive mechanisms for selecting cryptographic algorithms capable of providing an appropriate level of protection in conditions of changing threats was substantiated. A model for dynamic selection of post-quantum cryptographic algorithms based on an integral assessment of efficiency and risk is proposed, which allows taking into account both the technical characteristics of the algorithms (speed, cryptographic stability, resource intensity) and the current state of system security. An integral efficiency indicator and a risk function are introduced within the model, which are formed taking into account the level of vulnerabilities, threat intensity and criticality of information resources. An adaptation mechanism is implemented, which provides automatic review and selection of the optimal algorithm depending on the change in risk in real time. The results of the study indicate that the use of the proposed model creates the prerequisites for increasing the level of cryptographic protection, provides a formalized basis for adaptive management of the system's functioning, and allows for reasonable optimization of the use of computing resources. The results obtained confirm the scientific novelty and practical feasibility of implementing adaptive approaches to cryptographic protection of information and communication systems. Keywords: post-quantum cryptography, information and communication systems, cryptographic protection, integral risk assessment, adaptive model, dynamic algorithm selection, cybersecurity
Abstract Modern national blockchain ecosystems and platforms must account for emerging quantum threats. Currently, however, there are no formalized methods for the quantitative assessment of blockchain stability under adversarial quantum attacks. The development of such a methodology enables a quantitative evaluation of quantum impacts on various ecosystem components, the establishment of resilience metrics, and the prediction of potential compromise timelines for cryptographic primitives, given the capabilities of contemporary quantum hardware. This article proposes and substantiates an original method for analyzing the quantum resilience of national blockchain ecosystems – including those based on Enterprise Ethereum Alliance, Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Masterchain, and Microsoft Azure Blockchain. The proposed framework includes: (i) a mathematical model of blockchain stability accounting for diverse attack vectors; (ii) a resilience assessment methodology based on threat, vulnerability, and risk analysis; (iii) algorithms for evaluating cryptographic strength using modified Shor’s and Grover’s quantum algorithms; and (iv) an optimized Approximate Quantum Fourier Transform (AQFT) scheme to assess the feasibility of compromising blockchain cryptographic primitives.