Quantum computing is commonly considered one highly efficient computing method with the potential to revolutionize computation technology and solve problems that are currently unsolvable. However, due to the limitation of hardware equipment and an immature experimental base, quantum technology is still in its early stages and is far from achieving the expected performance, especially in solving large-scale complex problems. To break through these barriers, we propose a parallelized quantum annealing algorithm based on Lagrangian relaxation. The proposed algorithm divides the large-scale problem into several small problems and then employs multiple quantum computers to solve them. Our proposed approach overcomes the limited number of qubits and allows quantum computing to solve largescale optimization problems. Additionally, we incorporate a local search method to ensure this Lagrangian relaxation based quantum algorithm achieves an optimal solution. We use the proposed parallelized quantum annealing algorithm to solve optimal scheduling problems in network function virtualization networks. The problem is expressed in a linear optimization model that is NP-hard. Our proposed algorithm presents excellent time performance in solving this virtualized network functions scheduling problem, compared with the Lagrangian relaxation based classical algorithm.
Quantum computing is commonly considered one highly efficient computing method with the potential to revolutionize computation technology and solve problems that are currently unsolvable. However, due to the limitation of hardware equipment and an immature experimental base, quantum technology is still in its early stages and is far from achieving the expected performance, especially in solving large-scale complex problems. To break through these barriers, we propose a parallelized quantum annealing algorithm based on Lagrangian relaxation. The proposed algorithm divides the large-scale problem into several small problems and then employs multiple quantum computers to solve them. Our proposed approach overcomes the limited number of qubits and allows quantum computing to solve largescale optimization problems. Additionally, we incorporate a local search method to ensure this Lagrangian relaxation based quantum algorithm achieves an optimal solution. We use the proposed parallelized quantum annealing algorithm to solve optimal scheduling problems in network function virtualization networks. The problem is expressed in a linear optimization model that is NP-hard. Our proposed algorithm presents excellent time performance in solving this virtualized network functions scheduling problem, compared with the Lagrangian relaxation based classical algorithm.
Network function virtualization (NFV) is a crucial technology for the 5G network development because it can improve the flexibility of employing hardware and reduce the construction of base stations. There are vast service chains in NFV to meet users’ requests, which are composed of a sequence of network functions. These virtual network functions (VNFs) are implemented in virtual machines by software and virtual environment. How to deploy VMs to process VNFs of the service chains as soon as possible when users’ requests are received is very challenging to solve by traditional algorithms on a large scale. Compared with traditional algorithms, quantum computing has better computational performance because of quantum parallelism. We build an integer linear programming model of the VNF scheduling problem with the objective of minimizing delays, and transfer it into the quadratic unconstrained binary optimization (QUBO) model. Our proposed heuristic algorithm employs a quantum annealer to solve the model. Finally, we evaluate the computational results and explore the feasibility of leveraging quantum computing to solve the VNF scheduling problem.
As more and more controllable devices equiped in the smart grid, the inceasing scale of binary virables brings time-consuming dimension explosion problems to traditional optimizations problems. As a parallel computing method, quantum computing is valuable for exploration to accelerate the optimization computation. The classic quantum annealer (QA) only can be used for quadratic unconstraint binary optimization (QUBO) problems. This paper is to explore a novel algorithm based on the quantum annealer for grid partition problems. It is a typical large-scale Integer Quadratic Programming (IQP) problems. The proposed quantum algorithm attemped to apply Lagrangian relaxation (LR) and alternating direction method of multipliers (ADMM), to transform an IQP problem to general format of QUBO problems. Some numerical cases of the grid partition are discussed to compare the performance of the proposed algorithm with some typical methods, thus verifing the feasibility and performance of this ADMM-QA algorithm.
In planning and scheduling, large-scale optimization problems often have complex limits and a lot of factors, which makes them hard to answer with standard methods. Quantum annealing has become a hopeful way to deal with these problems because it can quickly look into a lot of possible solutions. This essay looks into how quantum annealing might be used to solve optimization problems in transportation and scheduling, with a focus on how it could be used for route planning, inventory management, and arranging workers. To do these optimization jobs, quantum annealing is used. This is a quantum computing method that gets the global minimum of a cost function. We use the D-Wave quantum annealer in this method. It turns the problem's limits and objective function into a quadratic unconstrained binary optimization (QUBO) model. The quantum annealer then works on this model to find the best answers. The suggested method combines traditional preparation methods with quantum annealing to get the best results for big schedule and transportation issues. We use quantum annealing to solve difficult multi-objective optimization problems, like reducing shipping time, cost, and resource use all at the same time. Preliminary results show that quantum annealing can make solutions much better and use computers much more efficiently than traditional methods for optimizing supplies and schedules. Quantum annealing works especially well with problems that have a lot of dimensions. It can provide scalable answers that sometimes work better than standard methods.
Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific state. This study introduces multi-tasking quantum annealing (MTQA), a method that enables the parallel processing of multiple optimization problems by embedding them into spatially distinct regions on quantum hardware. MTQA is evaluated using two NP-hard problems: the minimum vertex cover problem (MVCP) and the graph partitioning problem (GPP). This parallel approach optimizes quantum resource utilization by concurrently utilizing idle qubits. The findings demonstrate that MTQA achieves a solution quality comparable to single-problem quantum annealing and classical simulated annealing (SA), while notably reducing the time-to-solution (TTS) metrics. Eigenspectrum analysis further theoretically supports the hypothesis that parallel embedding preserves quantum coherence and does not increase computational complexity by efficiently utilizing available quantum hardware (e.g., qubits and couplers). MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
Large-scale logistic networks present a formidable challenge to traditional optimization techniques. The sheer number of variables and constraints involved—including vehicle routing, shipment scheduling, warehouse operations, and inventory management—often leads to computational bottlenecks, hindering efficient network design and operation. This paper investigates the application of quantum-inspired optimization algorithms to address these challenges. Specifically, we explore the potential of algorithms mimicking quantum phenomena, such as quantum annealing and quantum walks, to efficiently solve complex routing and scheduling problems within large logistic networks. Our approach leverages the inherent parallelism and ability of these algorithms to navigate complex solution spaces, offering a promising alternative to classical methods. We demonstrate the feasibility and potential benefits of this strategy through a theoretical framework and illustrative examples, highlighting the advantages of quantum-inspired optimization for improving the performance of large-scale logistic networks.