Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.
![The width optimization rate of different regular circuits by methods in [24,26] and our proposed ES and GHS. The labels on the x-axis are the circuit names, with the original width of the circuits in parentheses on the right. The ticks on the y-axis represent the width optimization rate.](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68642a27e88a4c302353ca35/j_qic-2025-0011_fig_010.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKO6OGLGK3%2F20260323%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260323T015703Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEKf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCqSnDvC97vv76HiPeV5HZCBc3KSW2z5VIixoUMwOXW4gIhANM2rlh2RH1VWghl994NYPvvnaIAKPKrarZYwC1BWggIKrwFCHAQAhoMOTYzMTM0Mjg5OTQwIgwAITpqVWXUwVvvcuQqmQVWT9DUI0GwsuW8MG1L0eNmjbUvt9%2F9toDDn0UWyRWn1NzC%2BnSkOWMATTeZZ8cLhZi2fksIvFhEh%2Fz6PWHzP%2B8XVdsVsgCbgUVFAG5zBOYS3cvEYxXehvft1%2FGn1H%2F9yN1zYbuClwpbsaOkbg3oEtXTk4CCwlj2upBrFwNnBM2zRLJP5CUb03mzWnPGKwvtY5ZDdPfoykWFWr%2BS5F3wSGUhcCgvYBKbhD%2F%2FH%2BepL7N6jbbsoOm1fmnO1g6kE5c0Xs%2BMe9Ekb%2FG%2FRffzNYE3umIU%2BROPx8yQ16SR0J%2BZBK%2FbeHO6yHt2tO94bBlbTzcak4mQtsngr8bqyPQvEEUOcsLi60k1ukrIewhfigTwTOaeuJ0EltDS9BOGi6TDmMtON7kGLYVBcifnT84psu%2BqvZnFMe8JND0P56snkcZQFksm5GO72h4kpxnOqHRgnK%2BXilP8f3Fu4ZlVLC20mR7Kk8D8RoRfAMqgZ%2BVyN0VTTjDaZQD5QLNyYE3622tU9x5OLZjUq1UQ1jz0tURw%2FpoAbN9YHjGdXZs8NYzYvkQlPhPrzEJV7gbM762KxURjr5rsJKqdI%2FhdCEaYk3Vi0ePHtdzo6cGzaVyzxZISZMXTqFkDCsVT0MYgi4GqeSkNtGM3IpwXOeaWEYSIlbZVfDWhJvnMUZOFtYHBfpfjQ2%2F9FGgTh5W5HN%2Fi7E4j9%2FnVYqYlzCogUYZGY7iRbkUsbrW%2BqyjyxMHG7R%2BjtEkhrJs0S3t9OJRz68vdflh3cFSUlofzlsb9QXgZg0FDdcPqUH8XQQ%2F1ecIMz0MOQH8LWwT%2B5BzrWSnfK3zU60aSctaD6cS5DcpJKZQFYi0QAnWLnIi2m1S7jFqvSF7%2FPWh07BfNtf79TjV6pgxL%2BpImUzDI8oHOBjqwAV6n5VmmE9gfEYxre9%2BaEwABovps6qHVLm2XXq8y1vqoef3I61uJIs3%2ByzctFPfwSMQmG0FsSx%2F4mp7a3ycsQxHse8AgZJwljFz7OWq1Iooz5owdq6I5a%2BLNG%2BrA3SC5vBYW%2FD6e4ye0ERQIYwBXHLrLrXaEy4wRUEoKjJXXFlhJvvthpL7ZLMG69e%2B9jE6h%2FTYWo6yadDWfwIptyp6aeZCErBlTa37K7jW1BwNAmAh1&X-Amz-Signature=04b0ab1cf0d28ecd1dfee55107f3b6606fa4d717ac98f1b4fe6d476501971b66&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 11.

Figure 12.










![The width optimization rate of different regular circuits by methods in [24,26] and our proposed ES and GHS. The labels on the x-axis are the circuit names, with the original width of the circuits in parentheses on the right. The ticks on the y-axis represent the width optimization rate.](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68642a27e88a4c302353ca35/j_qic-2025-0011_fig_010.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKO6OGLGK3%2F20260323%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260323T015703Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEKf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJIMEYCIQCqSnDvC97vv76HiPeV5HZCBc3KSW2z5VIixoUMwOXW4gIhANM2rlh2RH1VWghl994NYPvvnaIAKPKrarZYwC1BWggIKrwFCHAQAhoMOTYzMTM0Mjg5OTQwIgwAITpqVWXUwVvvcuQqmQVWT9DUI0GwsuW8MG1L0eNmjbUvt9%2F9toDDn0UWyRWn1NzC%2BnSkOWMATTeZZ8cLhZi2fksIvFhEh%2Fz6PWHzP%2B8XVdsVsgCbgUVFAG5zBOYS3cvEYxXehvft1%2FGn1H%2F9yN1zYbuClwpbsaOkbg3oEtXTk4CCwlj2upBrFwNnBM2zRLJP5CUb03mzWnPGKwvtY5ZDdPfoykWFWr%2BS5F3wSGUhcCgvYBKbhD%2F%2FH%2BepL7N6jbbsoOm1fmnO1g6kE5c0Xs%2BMe9Ekb%2FG%2FRffzNYE3umIU%2BROPx8yQ16SR0J%2BZBK%2FbeHO6yHt2tO94bBlbTzcak4mQtsngr8bqyPQvEEUOcsLi60k1ukrIewhfigTwTOaeuJ0EltDS9BOGi6TDmMtON7kGLYVBcifnT84psu%2BqvZnFMe8JND0P56snkcZQFksm5GO72h4kpxnOqHRgnK%2BXilP8f3Fu4ZlVLC20mR7Kk8D8RoRfAMqgZ%2BVyN0VTTjDaZQD5QLNyYE3622tU9x5OLZjUq1UQ1jz0tURw%2FpoAbN9YHjGdXZs8NYzYvkQlPhPrzEJV7gbM762KxURjr5rsJKqdI%2FhdCEaYk3Vi0ePHtdzo6cGzaVyzxZISZMXTqFkDCsVT0MYgi4GqeSkNtGM3IpwXOeaWEYSIlbZVfDWhJvnMUZOFtYHBfpfjQ2%2F9FGgTh5W5HN%2Fi7E4j9%2FnVYqYlzCogUYZGY7iRbkUsbrW%2BqyjyxMHG7R%2BjtEkhrJs0S3t9OJRz68vdflh3cFSUlofzlsb9QXgZg0FDdcPqUH8XQQ%2F1ecIMz0MOQH8LWwT%2B5BzrWSnfK3zU60aSctaD6cS5DcpJKZQFYi0QAnWLnIi2m1S7jFqvSF7%2FPWh07BfNtf79TjV6pgxL%2BpImUzDI8oHOBjqwAV6n5VmmE9gfEYxre9%2BaEwABovps6qHVLm2XXq8y1vqoef3I61uJIs3%2ByzctFPfwSMQmG0FsSx%2F4mp7a3ycsQxHse8AgZJwljFz7OWq1Iooz5owdq6I5a%2BLNG%2BrA3SC5vBYW%2FD6e4ye0ERQIYwBXHLrLrXaEy4wRUEoKjJXXFlhJvvthpL7ZLMG69e%2B9jE6h%2FTYWo6yadDWfwIptyp6aeZCErBlTa37K7jW1BwNAmAh1&X-Amz-Signature=04b0ab1cf0d28ecd1dfee55107f3b6606fa4d717ac98f1b4fe6d476501971b66&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)


© 2025 Haotian Tang, Fei Ding, Xueyun Cheng, Shuxian Zhao, Zhijin Guan, published by Cerebration Science Publishing Co., Limited
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