Quantum convolutional neural network based on particle swarm optimization algorithm

Fig. 5. Ansatz circuit structures obtained using PSO optimization algorithm for different numbers of basic gates (Fashion MNIST). (a) $k = 3;$ (b) $k = 6;$ (c) $k = 8;$ (d) $k = 10$ (a) $k = 3;$ (b) $k = 6;$ (c) $k = 8;$ (d) $k = 10$

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Fig. 6. Ansatz circuit structures (MNIST) obtained using PSO optimization algorithm for different numbers of basic gates. (a) $k = 3;$ (b) $k = 6;$ (c) $k = 8;$ (d) $k = 10;$ (e) $k = 10$ (a) $k = 3;$ (b) $k = 6;$ (c) $k = 8;$ (d) $k = 10;$ (e) $k = 10;$

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Fig. 7. Convergence curve (Fashion MNIST), where (a), (b), (c) and (d) correspond to the cases $k = 3, 6, 8$ and $10$ , respectively ( $k$ is the dimension of the particle)

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Fig. 8. Convergence curve (MNIST), where (a), (b), (c), (d) and (e) correspond to the cases $k = 3, 6, 8, 10$ ,10 respectively

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Fig. 9. Convergence of particles in the spatial search process of PSO-QCNN model with $k = 3$

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Fig. 10. QCNN structure of optimal classification results at $k = 3$

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Table 1. Correspondence between index and quantum gate
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Table 1. Correspondence between index and quantum gate
1 2 3 4 5 6 7 8 9 10 11 12 13
$X$ $Y$ $Z$ $I$ $R_{x} (θ)$ $R_{y} (θ)$ $R_{z} (θ)$ $C N O T$ $C Y$ $C Z$ $C R_{x} (θ)$ $C R_{y} (θ)$ $C R_{z} (θ)$

Table 2. PSO⁃QCNN algorithm

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Table 2. PSO⁃QCNN algorithm

Algorithm 1: PSO⁃QCNN
The input: Size of the particle swarm $N$ , Dimensions of the search space $D$ , Initialization parameters $w, c_{1}, c_{2}, r_{1}, r_{2}$ .
The output: $α^{}$ and $θ^{}$ in Eq. (6), Optimal fitness of $F .$
The algorithm process:
1. Initialize the ansatz structure $α_{i}^{0}$ and the velocity $v_{i}^{0}$ of all particles in the particle swarm.
2. Calculate the individual extremum value $ρ_{i}^{0}$ for each particle and the group extremum $γ^{0}$ for the whole particle swarm.
3. for t in range (1, m+1):
4. Update the ansatz structure $α_{i}^{t}$ and the velocity $v_{i}^{t}$ of all particles according to Eq. (1) and Eq. (2)
5. if $α_{i}^{t}$ and $v_{i}^{t}$ are not within the specified range of values, then border processing.
// Update the individual extremum value $ρ_{i}^{t}$ and the group extremum $γ^{t}$
6. Initialize the parameter $θ^{0}$ corresponding to $α_{i}^{t}$
7. for s in range(1, n+1):
8. Run $Q (α_{i}^{t}, θ^{s - 1})$ on quantum computer.
9. Calculate the loss function $L (α_{i}^{t}, θ^{s - 1})$ .
10. Execute the gradient descent by $θ^{s} \to θ^{s - 1} - η \nabla_{θ} L (θ)$ , $η$ is the learning rate.
11. Run $Q (α_{i}^{t}, {θ_{i}^{t}}^{*})$ on quantum computer and calculate the classification accuracy $a_{c c}^{t}$ .
12. Calculate the fitness $F_{i}^{t}$ and Update $ρ_{i}^{t}$ and $γ^{t}$ .
13. $α^{} = a r g m i n_{γ} F$ , corresponding $θ$ as $θ^{}$ .
14. end

Table 3. Accuracy comparison of different QCNN models with different numbers of base gates (Fashion MNIST)
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Table 3. Accuracy comparison of different QCNN models with different numbers of base gates (Fashion MNIST)
Dimension $k$ of particles Classification accuracy
HKP-QCNN/% GPZ-QCNN/% PSO-QCNN/%
3 90.9 90.77 94.45
6 90.7 91.62 94.6
8 90.4 - 94.7
10 89.9 89.7 94.7

Table 4. Accuracy comparison of different QCNN models with results for different numbers of base gates (MNIST)
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Table 4. Accuracy comparison of different QCNN models with results for different numbers of base gates (MNIST)
Dimension $k$ of particles Classification accuracy
HKP-QCNN/% GPZ-QCNN/% PSO-QCNN/%
3 96.8 95.25 98.77
6 97.8 92.72 98.96
8 97.2 - 99.05
10 98.3 95.91 99.05

Table 5. Accuracy comparison of different QCNN models with different numbers of parameters (Fashion MNIST)
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Table 5. Accuracy comparison of different QCNN models with different numbers of parameters (Fashion MNIST)
Number of parameters for QCNN Classification accuracy
HKP-QCNN/% GPZ-QCNN/% PSO-QCNN/%
9 - - 94.7
12 90.9 90.77 94.6
18 90.1 89.57 94.7
36 89.9 89.7 -

Table 6. Accuracy comparison of different QCNN models with different numbers of parameters (MNIST)
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Table 6. Accuracy comparison of different QCNN models with different numbers of parameters (MNIST)
Number of parameters for QCNN Classification accuracy
HKP-QCNN/% GPZ-QCNN/% PSO-QCNN/%
12 96.8 95.25 98.77
15 - - 99.05
18 93.8 97.31 99.05
30 - - 99.05
36 98.3 95.91 -

Table 7. Comparison of classification accuracy between PSOQ⁃CNN model and CNN model
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Table 7. Comparison of classification accuracy between PSOQ⁃CNN model and CNN model
Model Classification Accuracy
Fashion MNIST/% MNIST/%
CNN 87.67 86.32
PSO-QCNN 94.6 ( $k = 6$ ) 99.05 ( $k = 8$ )
PSO-QCNN 94.7 ( $k = 10$ ) 99.05 ( $k = 10$ )

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Jiawen ZHANG, Binbin CAI, Song LIN. Quantum convolutional neural network based on particle swarm optimization algorithm[J]. Chinese Journal of Quantum Electronics, 2025, 42(1): 123

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Paper Information

Category: Quantum Computing

Received: Feb. 28, 2024

Accepted: --

Published Online: Mar. 13, 2025

The Author Email: ZHANG Jiawen (gamung123@163.com)

DOI:10.3969/j.issn.1007-5461.2025.01.012

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Correspondence between index and quantum gate

Table 1. Correspondence between index and quantum gate

Table 2. PSO⁃QCNN algorithm

Table 2. PSO⁃QCNN algorithm

Table 3. Accuracy comparison of different QCNN models with different numbers of base gates (Fashion MNIST)

Table 3. Accuracy comparison of different QCNN models with different numbers of base gates (Fashion MNIST)

Table 4. Accuracy comparison of different QCNN models with results for different numbers of base gates (MNIST)

Table 4. Accuracy comparison of different QCNN models with results for different numbers of base gates (MNIST)

Table 5. Accuracy comparison of different QCNN models with different numbers of parameters (Fashion MNIST)

Table 5. Accuracy comparison of different QCNN models with different numbers of parameters (Fashion MNIST)

Table 6. Accuracy comparison of different QCNN models with different numbers of parameters (MNIST)

Table 6. Accuracy comparison of different QCNN models with different numbers of parameters (MNIST)

Table 7. Comparison of classification accuracy between PSOQ⁃CNN model and CNN model

Table 7. Comparison of classification accuracy between PSOQ⁃CNN model and CNN model