Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.
Combinatorial optimization problems pose significant computational challenges across various fields, from logistics to cryptography. Traditional computational methods often struggle with their exponential complexity, motivating exploration into alternative paradigms such as quantum computing. In this paper, we investigate the application of photonic quantum computing to solve combinatorial optimization problems. Leveraging the principles of quantum mechanics, we demonstrate how photonic quantum computers can efficiently explore solution spaces and identify optimal solutions for a range of combinatorial problems. We provide an overview of quantum algorithms tailored for combinatorial optimization for different quantum architectures (boson sampling, quantum annealing and gate-based quantum computing). Additionally, we discuss the advantages and challenges of implementing those algorithms on photonic quantum hardware. Through experiments run on an 8-qumode photonic quantum device, as well as numerical simulations, we evaluate the performance of photonic quantum computers in solving representative combinatorial optimization problems, such as the Max-Cut problem and the Job Shop Scheduling Problem.
Quantum computers are increasingly being integrated into classical computing environments, particularly within supercomputing and data centers, where they serve as accelerators for solving a wide range of specific problems. Previous research has indicated that quantum computers have the potential to resolve optimization problems with theoretically lower computational complexity than classical algorithms. However, in practical scenarios, even minor instances of these problems often require substantial computational resources, enhanced quality quantum hardware, and the results may not always be optimal. In this paper, we highlight the importance of hybrid systems, combining quantum and classical computations to address growing problem sizes and computational demands. We focus on optimization problems using hardware and software-enhanced quantum computers operational within a novel quantum–classical hybrid setup, incorporating GPUs and photonic quantum computers. The study specifically addresses combinatorial optimization problems, such as the Max-Cut and the Job Shop Scheduling Problem, in addition to selected machine learning classification use cases. Notably, the quantum algorithm in Max-Cut optimization outperformed complete solution searches, especially for larger problem instances. For the Job-Shop Scheduling Problem, we made a significant advancement by successfully solving substantially larger instances compared to our previous previous work. Furthermore, selected hybrid neural networks incorporating quantum layers showed improved stability, though without a clear quality advantage over classical models. The paper also highlights the rapid progress and technological achievements in both hardware and software used in near-term photonic quantum computers, suggesting a promising future for quantum–classical hybrid systems in useful applications.
Optimization algorithms for combinatorial problems play a critical role in a wide range of applications, from logistics and scheduling to cryptography and artificial intelligence. Traditional classical methods, such as simulated annealing, genetic algorithms, and branch-and-bound techniques, have been widely employed to solve these problems, but they often face limitations in terms of computational efficiency and scalability as problem complexity grows. In recent years, quantum computing has emerged as a promising alternative, with quantum annealing offering a novel approach to solving combinatorial optimization problems. This study provides a comparative analysis of quantum annealing and classical optimization methods, highlighting their respective strengths and limitations. We explore how quantum annealing, through leveraging quantum tunnelling and superposition, has the potential to outperform classical algorithms in specific problem domains and Noisy Mean Field Annealing (NMFA) is used to comparisons of all algorithms. Benchmarking various combinatorial problems, such as the Traveling Salesman Problem (TSP), Max-Cut, Knapsack, and Quadratic Assignment Problem (QAP), this paper discusses performance metrics, computational time, and scalability. The findings suggest that while classical methods remain robust and practical for many real-world problems, quantum annealing holds significant promise, especially as quantum hardware continues to mature. However, there remain challenges in terms of noise, coherence, and problem mapping, which currently limit the full realization of quantum annealing's potential. This study offers insights into the future directions of optimization techniques and the evolving role of quantum computing in solving complex combinatorial problems.
Quantum computing has emerged as a transformative paradigm with the potential to revolutionize computational tasks previously deemed intractable for classical computers. This paper explores the application of quantum computing algorithms in solving optimization problems, a cornerstone of numerous fields including logistics, finance, machine learning, and operations research. Quantum computers harness quantum mechanical phenomena such as superposition and entanglement to perform computations in ways fundamentally different from classical computers. This enables quantum algorithms to explore vast solution spaces simultaneously, offering potential exponential speedups over classical algorithms for certain optimization tasks. The abstract focuses on reviewing prominent quantum algorithms tailored for optimization, such as Grover's algorithm and quantum annealing approaches like those developed by D-Wave Systems. These algorithms target diverse optimization challenges including combinatorial optimization, portfolio optimization, and scheduling problems. We discuss their theoretical underpinnings, computational complexities, and practical implementations on current and near-term quantum hardware.
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.
Quantum computing offers new possibilities for solving combinatorial optimization problems with rapidly growing search spaces. Among emerging hardware platforms, photonic quantum computers based on boson sampling provide a promising approach for sampling-based optimization methods. In this work, we investigate the application of the Binary Bosonic Solver, a hybrid quantum-classical algorithm designed for photonic quantum processors, to the binary portfolio optimization problem derived from the classical mean-variance framework. In addition to evaluating the feasibility of solving such problems on photonic quantum hardware, we analyze the behavior of the Binary Bosonic Solver algorithm under different architectural and optimization parameters, including interferometer loop configurations and gradient estimation methods. Benchmark instances are generated using historical financial market data, and experiments are performed both on a photonic quantum computer simulator and on the ORCA PT-1 photonic quantum processor installed at Poznan Supercomputing and Networking Center, with results compared to those obtained using a classical optimization algorithm. The results demonstrate that portfolio optimization can be successfully executed on current photonic quantum hardware and that the Binary Bosonic Solver algorithm consistently produces feasible and high-quality solutions, highlighting the practical potential of photonic quantum computing for combinatorial optimization problems.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.