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A practical applicable quantum-classical hybrid ant colony algorithm for the NISQ era

Qian Qiu, Liang Zhang, Mohan Wu, Qichun Sun, Xiaogang Li, Da-Chuang Li, Hua Xu

TL;DR

This work shows that the combination of the clustering algorithm with QACO effectively improved its problem-solving scale, which makes its practical application possible in the current NISQ era of quantum computing.

Abstract

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.

A practical applicable quantum-classical hybrid ant colony algorithm for the NISQ era

TL;DR

This work shows that the combination of the clustering algorithm with QACO effectively improved its problem-solving scale, which makes its practical application possible in the current NISQ era of quantum computing.

Abstract

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.

Paper Structure

This paper contains 9 sections, 4 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. ACO and K-means Clustering algorithms
  3. Ant Colony Optimization Algorithm
  4. K-means Clustering
  5. Quantum Ant Colony Optimization with K-means clustering method
  6. Experimental Results
  7. Conclusions and future work
  8. Acknowledgements
  9. References

Figures (4)

  • Figure 1: The path search quantum circuit. In this diagram, $q0$ indicates the auxiliary qubit (ancilla) which make the solution to mutate in the certain condition controlled by Ry gate and c0 denotes classical bits. Meanwhile, $q1_{0}$-$q1_{n}$ denote n+1 qubits for points in the combinatorial optimization problems.
  • Figure 2: The work flow of the extended QACO algorithm
  • Figure 3: The best path of the algorithm for solving ulysses-16 and bayg-29: First line:(left) QACO for ulysses-16 (right) ACO for ulysses-16; Second line: (left) QACO for bayg-29 (right) ACO for bayg-29
  • Figure 4: The deviation of different noises: (a) Bit-flip Noise (b) Thermal Relaxation Noise