CNN Convolutional layer optimisation based on quantum evolutionary algorithm

Figures & data

Table 1. Probabilities of binary strings for qubit individual $〈\begin{array}{ccccc}0.3& & 0.1& & 0.8\end{array}〉$.

Binary string $\mathit{b}$	Probability
“000”	$(1-{0.3}^2)\times (1-{0.1}^2)\times (1-{0.8}^2)\cong 0.3243$
“001”	$(1-{0.3}^2)\times (1-{0.1}^2)\times {0.8}^2\cong 0.5766$
“010”	$(1-{0.3}^2)\times {0.1}^2\times (1-{0.8}^2)\cong 0.0033$
“011”	$(1-{0.3}^2)\times {0.1}^2\times {0.8}^2\cong 0.0058$
“100”	${0.3}^2\times (1-{0.1}^2)\times (1-{0.8}^2)\cong 0.0321$
“101”	${0.3}^2\times (1-{0.1}^2)\times {0.8}^2\cong 0.0570$
“110”	${0.3}^2\times {0.1}^2\times (1-{0.8}^2)\cong 0.0003$
“111”	${0.3}^2\times {0.1}^2\times {0.8}^2\cong 0.0006$

Figure 1. Plot of qubit update.

Figure 2. Quantum convolution unit.

Figure 3. VGG-19 and quantum VGG-19 (“N×N conv, n + ReLU” represents a convolutional layer containing n N×N filters and a rectified linear unit, “max pool, /2” represents a max pooling with a stride of 2, and “fc, 10+softmax + Classification” represents a fully connected layers with a 10-class softmax output).

Figure 4. Quantum CNN training process.

Table 2. Comparison of original VGG-19 and quantum VGG-19 (average result of 5 runs).

	Number of layers	Test accuracy	Number of layers after training
VGG-19	19	90.5%	19
Quantum VGG-19		91.9%	7.2

Figure 5. Quantum VGG-19 optimisation result.

Figure 6. Retrain the weights under the architecture of Figure 5.

Figure 7. Multi-layer CNN architecture.

Figure 8. Quantum multilayer CNN architecture.

Figure 9. Comparison of test accuracy and number of layers.

Table 3. Comparison of original CNN and quantum CNN (average result of 5 runs).

	Original layer	Test accuracy	Number of layers after training
CNN20	20	89.8%	20
Quantum CNN20		91.5%	11.0
CNN32	32	88.9%	32
Quantum CNN32		91.8%	15.4
CNN44	44	86.9%	44
Quantum CNN44		91.5%	17.0
CNN56	56	83.4%	56
Quantum CNN56		91.0%	18.2