Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how can we get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with QISKIT implementation of our QIPM using quantum simulators are analyzed.

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In this paper, we study scheduling of R&D projects in which activities may to be failed due to the technological risks. We consider two introduced problems in the literature referred to as R&D Project Scheduling Problem (RDPSP) and Alternative Technologies Project Scheduling Problem (ATPSP). In both problems, the goal is maximization of the expected net present value of activities where activities are precedence related and each of them is accompanied with a cost, a duration, and a probability of technical success. In RDPSP, a project payo is obtained if all activities are succeeded, while in ATPSP, if one of activities is implemented successfully, the project payo is attained. We construct a solution representation for each of these problems and construct two population-based metaheuristics including scatter search algorithm and genetic algorithm as solution approaches. Computational experiments indicate scatter search outperforms genetic algorithm and also available exact solution algorithms.

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Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.