Quantum algorithms for production and scheduling optimization

Abstract

Quantum computing has become an emerging field of interest due to its computational efficiency in solving combinatorial optimization problems. This rapid-growing paradigm of computation harnesses the principles of quantum mechanics such as superposition and entanglement, to converge towards an optimum solution faster than classical computation. In our advanced developing era, we are facing challenges of storing and processing exponentially growing data. Quantum computation has proven its value in rectifying such issues by its ability of storing large sizes of data and processing them in a parallel manner. One of the widely used quantum optimization algorithms is the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm. In this paper, we use an active learning-based Bayesian optimization approach to identify appropriate quantum circuit parameters. A variety of industrial processes are modeled using combinatorial optimization with the ultimate objective of either the improving overall efficiency or minimizing the total cost. However, these problems are known to be computationally intractable. In the realm of combinatorial optimization, a single-machine scheduling problem with multiple jobs and operations is notoriously a hard problem. In this paper, we discuss the application of QAOA and active learning approach to solve a single-machine scheduling problem, and compare the solution obtained using classical analysis. Another one of the common problems is solving linear systems of equations, in which there are already many existing classical algorithms that can be implemented. A linear system of equations is a vital concept in the realm of science and engineering. As the field of data analytics grow tremendously, the sizes of datasets can be computationally expensive and time consuming. Hence, quantum linear regression algorithms such as the HHL algorithm can supply exponential speedups to solve these questions. To prove the flexibility and breadth of such quantum applications, this paper will also discuss how a quantum linear regression algorithm can be used to solve production scheduling problems.