With the slow progress of universal quantum computers, studies on the feasibility of optimization by a dedicated and quantum-annealing-based annealer are important. The quantum principle is expected to utilize the quantum tunneling effects to find the optimal solutions for the exponential-level problems while classical annealing may be affected by the initializations. This study constructs a new Quantum-Inspired Annealing (QIA) framework to explore the potentials of quantum annealing for solving Ising model with comparisons to the classical one. Through various configurations of the 1D Ising model, the new framework can achieve ground state, corresponding to the optimum of classical problems, with higher probability up to 28% versus classical counterpart (22% in case). This condition not only reveals the potential of quantum annealing for solving the Ising-like Hamiltonian, but also contributes to an improved understanding and use of the quantum annealer for various applications in the future.
With the slow progress of universal quantum computers, studies on the feasibility of optimization by a dedicated and quantum-annealing-based annealer are important. The quantum principle is expected to utilize the quantum tunneling effects to find the optimal solutions for the exponential-level problems while classical annealing may be affected by the initializations. This study constructs a new Quantum-Inspired Annealing (QIA) framework to explore the potentials of quantum annealing for solving Ising model with comparisons to the classical one. Through various configurations of the 1D Ising model, the new framework can achieve ground state, corresponding to the optimum of classical problems, with higher probability up to 28% versus classical counterpart (22% in case). This condition not only reveals the potential of quantum annealing for solving the Ising-like Hamiltonian, but also contributes to an improved understanding and use of the quantum annealer for various applications in the future.
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.
Universal quantum computers are far from achieving practical applications. The D-Wave quantum computer is initially designed for combinatorial optimizations. Therefore, exploring the potential applications of the D-Wave device in the field of cryptography is of great importance. First, although we optimize the general quantum Hamiltonian on the basis of the structure of the multiplication table (factor up to 1 005 973), this study attempts to explore the simplification of Hamiltonian derived from the binary structure of the integers to be factored. A simple factorization on 143 with four qubits is provided to verify the potential of further advancing the integer-factoring ability of the D-Wave device. Second, by using the quantum computing cryptography based on the D-Wave 2000Q system, this research further constructs a simple version of quantum-classical computing architecture and a Quantum-Inspired Simulated Annealing (QISA) framework. Good functions and a high-performance platform are introduced, and additional balanced Boolean functions with high nonlinearity and optimal algebraic immunity can be found. Further comparison between QISA and Quantum Annealing (QA) on six-variable bent functions not only shows the potential speedup of QA, but also suggests the potential of architecture to be a scalable way of D-Wave annealer toward a practical cryptography design.
Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. In addition, we also evaluate the performance of a heuristic by Selby. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue. In particular, we examine how reliably the D-Wave computer can deliver true optimum solutions and present some surprising results.
Quantum annealing (QA) algorithm is a new quantum optimization algorithm based on the classical simulated annealing (SA) algorithm. Unlike classical SA algorithm, which uses the thermal waves to search for the optimal solution, the QA algorithm uses the quantum tunneling effect to allow a quantum to penetrate a potential barrier with a higher energy than itself. Therefore, the algorithm can get rid of the local extreme values and is more likely to approach the global optimal with higher probability. In the literature, the QA algorithm has shown perfect optimization effects on combinatorial optimization problems. In this paper, the basic concepts and application fields of QA algorithm, which is the core principle of D-Wave quantum computer, are systematically reviewed. The applications of QA algorithm in cryptography, traveling salesman problem, graph coloring problem, and traffic path are discussed in detail. In addition, the direction of future research for QA algorithm is explored.
Quantum annealing is a form of quantum computing that exploits quantum effects to probabilistically solve a specific, NP-hard problem: finding the ground state of a classical, Ising-model Hamiltonian. Because physical quantum annealers are already available, there exists the pressing question of how to program such systems. That is, how can one map a computational problem into the coefficients of an Ising-model Hamiltonian for solution by quantum-annealing hardware? In this article, we address that question primarily from a practical standpoint. We survey extant software tools intended for programming D-wave annealing-based quantum processors and examine the programming model and solution technique promoted by each tool in an attempt to showcase the variety of contemporary approaches to solving computationally challenging problems on an existing annealing-based quantum computer.
Quantum annealing (QA) uses the principles of quantum mechanics for solving unconstrained optimization problems. Since its initial proposal, there has been much interest in the search for practical problems for which QA has advantage over classical algorithms. Although it is believed that quantum computers cannot in general solve NP-complete problems efficiently, there has been evidence suggesting that effects such as quantum tunneling can bring quantum speedup over classical computation for some problems in NP. In this dissertation, we consider two problems that have both theoretical and practical importance. One is the Set Cover with Pairs problem. The other is the Factorization problem. The Set Cover with Pairs (SCP) problem is a generalization of the Set Cover problem. It requires each element in a set to be covered by at least two objects instead of one as in the Set Cover problem. The SCP problem is believed to be not only NP-hard, but also hard to approximate. In this dissertation, we explicitly construct the Ising Hamiltonians whose ground states encode the solutions of SCP instances. The resulting Ising Hamiltonian has the appealing property that the control precision required for encoding an SCP instance scales only linearly with the number of objects in the covering set. The Integer Factorization problem is of great interest in the quantum community because it is difficult to solve using classical methods and its importance in cryptography. In this dissertation, we propose a general framework for solving factorization problems using quantum annealing, by mapping the framework to an Ising Hamiltonian. We develop several methods to consider the specific requirements such as control precision, spin-spin connection in the current Ising machines. We test the methods on the latest D-Wave 2000Q machine.