Although NP-complete problems have solutions that can be verified in polynomial time, their exponential computational complexity presents significant challenges for classical computing methods. This study focuses on transferring various NP-complete problems into the quantum computing framework. The application of specific quantum computing algorithms is proposed for solving these problems. Within the scope of this study, a reusable quantum component with problem-specific constraints is designed, and a quantum circuit model is introduced to adapt the Quantum Feasibility Labeling algorithm for solving the Maximum Clique problem. Additionally, the Quick Quantum Search algorithm, which performs a search with a single oracle call, is integrated into the solution of the Maximum Independent Set problem. The proposed quantum circuits provide illustrative examples of how the components of an NP-complete problem can be represented in a quantum computing environment and how problem-specific constraints can be implemented within a quantum circuit. The utilization of modular circuit designs effectively demonstrates the applicability of larger and more complex problems in quantum environments. These approaches not only enable more efficient use of computational resources compared to traditional methods but also lead to significant reductions in solution times. This study provides a comprehensive framework that not only demonstrates the practicality of quantum circuits for small-scale NP-complete problems but also lays the groundwork for addressing larger and more complex challenges in future quantum computing applications.
Although NP-complete problems have solutions that can be verified in polynomial time, their exponential computational complexity presents significant challenges for classical computing methods. This study focuses on transferring various NP-complete problems into the quantum computing framework. The application of specific quantum computing algorithms is proposed for solving these problems. Within the scope of this study, a reusable quantum component with problem-specific constraints is designed, and a quantum circuit model is introduced to adapt the Quantum Feasibility Labeling algorithm for solving the Maximum Clique problem. Additionally, the Quick Quantum Search algorithm, which performs a search with a single oracle call, is integrated into the solution of the Maximum Independent Set problem. The proposed quantum circuits provide illustrative examples of how the components of an NP-complete problem can be represented in a quantum computing environment and how problem-specific constraints can be implemented within a quantum circuit. The utilization of modular circuit designs effectively demonstrates the applicability of larger and more complex problems in quantum environments. These approaches not only enable more efficient use of computational resources compared to traditional methods but also lead to significant reductions in solution times. This study provides a comprehensive framework that not only demonstrates the practicality of quantum circuits for small-scale NP-complete problems but also lays the groundwork for addressing larger and more complex challenges in future quantum computing applications.
Determining the cardinality of the maximum clique on a simple graph is a NP-hard problem with several applications of interest. The best know classical algorithm for this problem has 𝒪(3𝑛/3) time complexity. Classical computing uses phenomena from classical physics to model, store and process information. Consequently, the entire model of classical computing is bounded superiorly by the limits of classical physics. As an alternative, Quantum Computing has been developed to take advantage of quantum phenomena and provide the constructions of circuits capable of performing certain computations more efficiently. In this paper, two quantum solutions to the maximum clique problem will be proposed and analyzed, based on the Grover Quantum Search algorithms and the Quantum Minimal Search Algorithm, comparing their respective time complexities with the best known classical solution.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
Cloud computing platforms increasingly rely on large-scale microservice architectures, in which hundreds of independent services interact through complex communication structures. Analyzing these interaction patterns and identifying highly connected service groups are critical for service placement strategies aimed at optimizing communication efficiency and resource utilization. Structural analysis problems of this type can often be formulated as NP-complete problems when considered on a large scale. Quantum computing is a promising paradigm that extends the capabilities of conventional computational approaches by exploiting its advantages of quantum mechanics. This study proposes a quantum-classical hybrid algorithm based on an adapted Quantum Feasibility Labeling (QFL) algorithm to identify highly interacting microservice clusters in cloud environments and support their optimal placement. Simulation results demonstrate that the proposed modular circuit architecture can represent graph feasibility relationships and support the systematic identification of clique structures in small-scale proof-of-concept cases. In addition, the SXNORR-based modular design improves circuit reusability and structural scalability compared with the monolithic circuit structures commonly used in existing quantum graph algorithms. These findings indicate that modular quantum circuit architectures can provide a promising foundation for the application of quantum computing in the analysis of complex systems, such as cloud-based microservice interaction networks.
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on classical techniques, we offer both a quantum-inspired matrix method and a quantum matrix method that neutralizes common contradictions and inconsistencies that appear in these types of problems. We then use our new method to show how a potential polynomial solution for NP-Complete problems could be found using quantum computation. We state this as a potential solution, rather than an actual solution, as the outcome of any quantum computation may not be the same as the expected outcome. We start by formally defining a Set Constraint Problem. We then explain current, classical methods that are used to solve these problems and the drawbacks of such methods. After this, we explain a new quantum-inspired matrix method that allows us to solve these problems, with classical limitations. Then, we explain a new quantum matrix method that solves these problems using quantum information science. Finally, we describe how we can extend this method to potentially solve NP-Complete problems in polynomial time using quantum computation.
The growing complexity of Very Large Scale Integration (VLSI) circuit designs has significantly increased the demand for innovative approaches to enhance design efficiency and fabrication accuracy. Traditional computational methods face limitations in terms of scalability and optimization for complex VLSI systems. The advent of quantum computing presents a promising paradigm shift, offering exponential speedup in solving computationally intensive problems such as optimization, simulation, and data analysis in VLSI design and fabrication. This research investigates the potential of quantum computing algorithms to optimize VLSI circuit design and fabrication processes, addressing key challenges such as layout optimization, routing, and process variation. The problem lies in the increasing complexity and size of VLSI circuits, which often lead to inefficient designs, longer manufacturing times, and increased cost. Current methods such as classical algorithms and heuristic techniques struggle to achieve optimal solutions within reasonable time frames. Quantum algorithms, particularly those based on quantum annealing and variational quantum eigensolvers (VQE), have shown promise in solving combinatorial optimization problems with much higher efficiency. By leveraging quantum computing, the goal is to improve the optimization of circuit layouts, minimize power consumption, and reduce production costs in VLSI systems. The proposed method utilizes quantum computing techniques to model and solve optimization problems related to VLSI circuit design and fabrication. Simulations and comparisons with classical methods show significant improvements in design efficiency, reduced error rates, and faster optimization cycles. The outcomes of this study could transform the future of VLSI design and fabrication, leading to more efficient, cost-effective, and scalable solutions for semiconductor manufacturing.
Quantum computing offers an accelerated mechanism for solving combinatorial optimization problems that could be hardly solvable with classical tools, in this context, this paper highlights the utility of quantum computing in solving NP-complete problems efficiently and shows up the importance of employing quantum algorithms achieving parallel calculation in the purpose of reducing the algorithmic complexity and simplifying the development of optimization applications. Within this publication, an optimized version of quantum circuit conception for developing the oracle of the Grover's search algorithm is introduced for solving the vertex cover problem, and it was also tested using the Qiskit library and applied to a set of instances to evaluate its performance.