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Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair…
We consider the minimum vertex cover problem having applications in e.g. biochemistry and network security. Quantum annealers can find the optimum solution of such NP-hard problems, given they can be embedded on the hardware. This is often…
We present a novel formulation of structural design optimization problems specifically tailored to be solved by quantum annealing (QA). Structural design optimization aims to find the best, i.e., material-efficient yet high-performance,…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
Column generation (CG) is one of the most successful approaches for solving large-scale linear programming (LP) problems. Given an LP with a prohibitively large number of variables (i.e., columns), the idea of CG is to explicitly consider…
Quantum computers promise a qualitative speedup in solving a broad spectrum of practical optimization problems. The latter can be mapped onto the task of finding low-energy states of spin glasses, which is known to be exceedingly difficult.…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
This paper presents a generalization of a method allowing the transformation of the Elliptic Curve Discrete Logarithm Problem (ECDLP) over prime fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem. The original method…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Numerous communication networks are emerging to serve the various demands and improve the quality of service. Heterogeneous users have different requirements on quality metrics such as delay and service efficiency. Besides, the networks are…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
We demonstrate that a quantum annealer can be used to solve the NP-complete problem of graph partitioning into subgraphs containing Hamiltonian cycles of constrained length. We present a method to find a partition of a given directed graph…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…
Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and discuss the beneficial features of quantum…