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Acta Physica Sinica

Application of quantum approximate optimization algorithm to mission planning of command and control organization

Yijun Zhang, Xiao-Dong Mu, Xiaowen Liu, Xingyu Wang, Chen Dong, Tianyi Wu, Kai Li

Published Jan 1, 2021• 3 citations
Publisher

Abstract

The mission planning problem in command and control organization can be mapped into a combinatorial optimization problem with many variables and is difficult to solve. The traditional heuristic list planning method faces the problems of high time complexity and poor real-time response. For the mission planning problem in command and control organization, a quantum circuit solution scheme is proposed based on quantum approximate optimization algorithm in this work. Firstly, the mission planning problem is transformed into a typical combinatorial optimization problem, the exact coverage problem. Then, by constructing the corresponding mathematical model, the final state Hamiltonian expression of the quantum approximate optimization algorithm for the exact coverage problem is derived. The quantum circuit based on the quantum approximate optimization algorithm is designed. Finally the parameters in the quantum logic gate are optimized by the momentum gradient descent algorithm, and the simulation experiment is carried out by using the quantum software development environment of the Origin Quantum Computing Company. The simulation results show that the quantum circuit scheme can be used to solve the mission planning problem, reduce the time complexity of the algorithm, and improve the resource utilization to a certain extent. This work lays the foundation for further application of quantum algorithm to solving the mission planning problem in command and control organization.

DOI
10.7498/aps.70.20211028

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The mission planning problem in command and control organization can be mapped into a combinatorial optimization problem with many variables and is difficult to solve. The traditional heuristic list planning method faces the problems of high time complexity and poor real-time response. For the mission planning problem in command and control organization, a quantum circuit solution scheme is proposed based on quantum approximate optimization algorithm in this work. Firstly, the mission planning problem is transformed into a typical combinatorial optimization problem, the exact coverage problem. Then, by constructing the corresponding mathematical model, the final state Hamiltonian expression of the quantum approximate optimization algorithm for the exact coverage problem is derived. The quantum circuit based on the quantum approximate optimization algorithm is designed. Finally the parameters in the quantum logic gate are optimized by the momentum gradient descent algorithm, and the simulation experiment is carried out by using the quantum software development environment of the Origin Quantum Computing Company. The simulation results show that the quantum circuit scheme can be used to solve the mission planning problem, reduce the time complexity of the algorithm, and improve the resource utilization to a certain extent. This work lays the foundation for further application of quantum algorithm to solving the mission planning problem in command and control organization.
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Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a satellite. The ever-growing amount of satellites in orbit underscores the need to operate them efficiently, which requires solving many instances of the problem in short periods of time. However, current classical algorithms often fail to find the global optimum or take too long to execute. Here, we approach the problem from a quantum computing point of view, which offers a promising alternative that could lead to significant improvements in solution quality or execution speed in the future. To this end, we study a planning problem with a variety of intricate constraints and discuss methods to encode them for quantum computers. Additionally, we experimentally assess the performance of quantum annealing and the quantum approximate optimization algorithm on a realistic and diverse dataset. Our results identify key aspects like graph connectivity and constraint structure that influence the performance of the methods. We explore the limits of today’s quantum algorithms and hardware, providing bounds on the problems that can be currently solved successfully and showing how the solution degrades as the complexity grows. This work aims to serve as a baseline for further research in the field and establish realistic expectations on current quantum optimization capabilities.
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Combinatorial optimization has wide and high-value applications in many fields of science and industry, but solving general combinatorial optimization problems is non-deterministic polynomial time (NP) hard. Many such problems can be mapped onto the ground-state-search problems of the Ising model. Here, an iterative quantum algorithm based on quantum gradient descent to solve combinatorial optimization problems is introduced, where the initial state of a quantum register evolves over several iterations to a good approximation of the Ising-Hamiltonian ground state. We verified the effectiveness of the proposed algorithm in solving the MaxCut problem for different types of undirected graphs by numerical simulations, and analyzed the robustness of the algorithm to errors by simulating random error and Gaussian error. We compared the performance of the algorithm with the quantum approximate optimization algorithm, and the results indicate that the proposed algorithm has comparable convergence performance. We also verified the feasibility of the algorithm by conducting experiments on a real quantum computer through the quantum cloud platform. Our work provides a potential method for solving combinatorial optimization problems on future quantum devices without the use of complex classical optimization loops.
Quantum optimization which is the use of quantum computers and algorithms for solving complex optimization problems, is one of the topics in quantum computing with the highest potential. Two types of approaches are generally used to solve combinatorial optimization problems with quantum computers: exact methods such as the Grover’s search algorithm, and meta-heuristics such as the Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA). Exact methods and variational methods like QAOA make use of universal gate-based quantum computers, such as the ones developed by the IBM company.Quantum annealing is designed for analogic quantum computers developed by D-Wave. Solving a combinatorial optimization problem with heuristics generally requires a transformation of the problem to a format suitable for the quantum computer. While some existing frameworks can cope with Constrained Quadratic Models (CQM), Quadratic Unconstrained Binary Optimization (QUBO) is the best option to map an optimization problem to a quantum computer or simulator. We consider in this paper the job shop scheduling problem.