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Algoritmos cuánticos y Quantum Ant Colony Optimization

Mikel Garcia de Andoin

Published Dec 15, 2020• 0 citations
OpenAlex

Abstract

[EN] I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization. Quantum computation is on the verge of becoming the new technology for solving time- and energy-consuming problems. To make use of the full potential of quantum computers one must implement algorithms that are significantly different from the ones used on digital computers. This work serves as an introduction to both quantum computing and algorithms. Starting from the basis of the quantum physics, I expose each of the steps needed to understand the mathematics beneath this topic. Using this basis, I develope one quantum algorithm from scratch. Based on a previously proposed Quantum Ant Colony Optimization (QACO) algorithm, I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization.

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[EN] I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization. Quantum computation is on the verge of becoming the new technology for solving time- and energy-consuming problems. To make use of the full potential of quantum computers one must implement algorithms that are significantly different from the ones used on digital computers. This work serves as an introduction to both quantum computing and algorithms. Starting from the basis of the quantum physics, I expose each of the steps needed to understand the mathematics beneath this topic. Using this basis, I develope one quantum algorithm from scratch. Based on a previously proposed Quantum Ant Colony Optimization (QACO) algorithm, I propose an improved algorithm that can be implemented on a real quantum computer with a new guided exploration strategy. The benchmarks made by simulating the quantum circuit shows that the time to solve a problem using QACO could outperform greatly other classical bio-inspired algorithms, in particular the one QACO is based on, the Ant Colony Optimization.
We propose a new hybrid quantum algorithm based on the classical Ant Colony Optimization algorithm to solve NP-hard problems, in particular optimization problems. First, we discuss some previously proposed Quantum Ant Colony Optimization algorithms, and based on them, we develop an improved algorithm that can be truly implemented on near-term quantum computers. Our iterative algorithm codes only the information about the pheromones and the exploration parameter in the quantum state, while subrogating the calculation of the numerical result to a classical computer. A new guided exploration strategy is used in order to take advantage of the quantum computation power and generate new possible solutions as a superposition of states. This approach is specially useful to solve constrained optimization problems, where we can implement efficiently the exploration of new paths using Fredkin gates without having to check the correspondence of a path to a solution before the measurement of the state. As an example of a NP-hard problem, we choose to solve the Quadratic Assignment Problem. The benchmarks made by simulating the noiseless quantum circuit and the experiments made on IBM quantum computers show the validity of the algorithm.
Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithms and overcomes some limitations of the traditional ACO algorithm. However, due to the hardware resource limitations of currently available quantum computers, such as the limited number of qubits, lack of high-fidelity gating operation, and low noisy tolerance, the practical application of the QACO is quite challenging. In this paper, we introduce a hybrid quantum-classical algorithm by combining the clustering algorithm with QACO algorithm, so that this extended QACO can handle large-scale optimization problems, which makes the practical application of QACO based on available quantum computation resource possible. To verify the effectiveness and performance of the algorithm, we tested the developed QACO algorithm with the Travelling Salesman Problem (TSP) as benchmarks. The developed QACO algorithm shows better performance under multiple data set. In addition, the developed QACO algorithm also manifests the robustness to noise of calculation process, which is typically a major barrier for practical application of quantum computers. Our work shows that the combination of the clustering algorithm with QACO has effectively extended the application scenario of QACO in current NISQ era of quantum computing.
Abstract We propose a new hybrid quantum algorithm based on the classical Ant Colony Optimization algorithm to produce approximate solutions for NP-hard problems, in particular optimization problems. First, we discuss some previously proposed Quantum Ant Colony Optimization algorithms, and based on them, we develop an improved algorithm that can be truly implemented on near-term quantum computers. Our iterative algorithm codifies only the information about the pheromones and the exploration parameter in the quantum state, while subrogating the calculation of the numerical result to a classical computer. A new guided exploration strategy is used in order to take advantage of the quantum computation power and generate new possible solutions as a superposition of states. This approach is specially useful to solve constrained optimization problems, where we can implement efficiently the exploration of new paths without having to check the correspondence of a path to a solution before the measurement of the state. As an example of a NP-hard problem, we choose to solve the Quadratic Assignment Problem. The benchmarks made by simulating the noiseless quantum circuit and the experiments made on IBM quantum computers show the validity of the algorithm.
Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithm overcoming some limitations of the traditional ACO algorithm. However,due to the hardware resource limitations of currently available quantum computers, the practical application of the QACO is still not realized. In this paper, we developed a quantum-classical hybrid algorithm by combining the clustering algorithm with QACO algorithm.This extended QACO can handle large-scale optimization problems with currently available quantum computing resource. We have tested the effectiveness and performance of the extended QACO algorithm with the Travelling Salesman Problem (TSP) as benchmarks, and found the algorithm achieves better performance under multiple diverse datasets. In addition, we investigated the noise impact on the extended QACO and evaluated its operation possibility on current available noisy intermediate scale quantum(NISQ) devices. Our work shows that the combination of the clustering algorithm with QACO effectively improved its problem solving scale, which makes its practical application possible in current NISQ era of quantum computing.
The quantum ant colony algorithm (QACO) is explored as a solution to the traveling salesman problem (TSP), targeting inefficiencies such as slow convergence and local optima entrapment found in traditional ant colony optimization (ACO) methods. By integrating quantum computing elements, specifically quantum rotation gates and qubits, into the ACO framework, QACO demonstrates enhanced efficiency and faster convergence. This paper delves into the foundational principles of quantum computing and their application to refine ACO, effectively solving the TSP. An in-depth analysis is provided, showcasing QACO's advantages over traditional ACO through empirical examples. These examples illustrate QACO's potential to improve path planning for applications within the rapidly growing e-commerce and logistics sectors. The integration of quantum mechanisms facilitates a more dynamic pheromone update process, which significantly reduces the likelihood of premature convergence and enhances solution quality in complex optimization scenarios. This advancement indicates a promising direction for future research in algorithmic optimization in both theoretical and practical applications.
A quantum-inspired ant colony algorithm(QACA) for the classic graph coloring problem is proposed based upon the combination of ant colony optimization and quantum computing.The quantum bits and quantum logic gates are introduced to the ant colony algorithm(ACA),and the disadvantage of getting into the local optimum can be effectively avoided.The computational speed of the algorithm is therefore significantly improved.Series of simulation instances of the graph coloring problem are tested.And the results show that the QACA is a feasible,effective and versatile method for solving the graph coloring problem.