Figure 1.
Figure 2.
![Parity-preserving blocks (a) Toffoli-based L-block, (b) NCV-based L-block [22], (c) Toffoli-based A-block, (d) NCV-based A-block [22], and (e) Toffoli-based N2-block [33].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/695ce6067c29e05adc529c67/j_qic-2025-0030_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKGOQQI7OO%2F20260109%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260109T011148Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIA7d4YF6AI2%2B230tngo7cfZEUeGZw%2FpEJn%2F%2BZpqcHEZWAiEAgB3D94wsNTezP%2FnW9b8poswN5aH9Wso%2BAUGU5uquVesqxgUIlP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDHGzOJb%2BUBWNi2RM6CqaBTdo86n9OIwbmepCqoR6wZM3mkNnqWB7TxOf%2BFbFORZavvGN7W2J0FpPgOa2pkrdhiUaNrd9tnDgg4IFYwxp4aYIodB44WOkSlFuv4Fpqxdyzvdz%2FCP9XpgRojtUnzwhKV9sj4VjGT9wXBvarufDXU0pObVn6VAlIIDXwWtqa6VGEBBFNju%2B3sNExGe08%2FSupyUWirNw0u4C8Gi8%2BwnRf2WouMOX4M6YYw%2FudeF4as%2FiJTz2zHxuH0jYKV5txGlK3U5jJDStmNKM49Y0f5yrIc2f3nOE8HJQQTyA12VlRRbEl%2BEY7iS7SqNm0kd%2Bk%2BM5GrGOqFuRjTIWxSYDTr4UqpXI3r9%2BC%2BofKnY4VcLDeybq2PZ%2BL127qmeZOzJaMbzHHAabTYYmwnVwKYkO51iLrKpadsxKq5qbKWJOivddGzzDNIQ1TW%2BtXo9F4V9cVhgVXxlEkaUhE5dcKsgsJ%2BN8H5BGdBNpgJUtV%2FhkjmDVSaH5u9DIKb3x%2FVorbBkIhzPHLG8nb2xBqNiV5fyQpHoPbbFTQ1b1e6yovBd%2BVLemyPG1RML56I8FMYMW2vcIgzQq%2Fgfg3e2fPspDPYtzc1mHsmeCRkUiDabt%2Fic9TchFwkuoGm47pskve5bO1aJdKCqfsXdlikqHzDP097LWXEQJOdqnOF6Zd4F6QTva4XFvkMzU08E%2BqE981X2PDVA6u%2FXW5wWjrEB4Ictesnn2Iqm8pKlb7Dlcl9gtnmPT83qJIk5g%2FpbUMA1Y4bbp0jJBMgNmgFbwRnoiOH22gg8h8z%2FM7523VCiSlNqhlHoJwRou1OhQNgd3CX6Td2jcDgS079xcQ7xHoPNFBjN5FrzaHDTz2Cf1G2ZOl6OlXg%2BE9F8F6ahKXrLP6TA3YPrcjTCLhoDLBjqxAe7i0gajanxcX4bQMiWNTd8FKMJgDcdjeOxFPi9kJSLloGf9JUrug%2FaHfvIu9nfpttO9HZUy%2FI31WzqF5QiqZd8g7RiYcHeV9Hp82r4Q1700jBABB8FC9XSsQD%2BtZ2mn1jKTbdnxuK1GI%2FCc69dCFvZBQZppOcsIl3%2FLZ5xkP8Ex2D34gRo8TwcbWRY5Vpt1h4hqDFTpGxzczzFB4rq4P3jIVnobg5xSM0O7Z6KVW5NRyw%3D%3D&X-Amz-Signature=233d0f464a8ea8bb37c8d1d085a68ad9a3896efee41ffaad1e549870b800c280&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
![Orbital representation of 2×2 Vedic multiplier [54].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/695ce6067c29e05adc529c67/j_qic-2025-0030_fig_008.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKGOQQI7OO%2F20260109%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260109T011148Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIA7d4YF6AI2%2B230tngo7cfZEUeGZw%2FpEJn%2F%2BZpqcHEZWAiEAgB3D94wsNTezP%2FnW9b8poswN5aH9Wso%2BAUGU5uquVesqxgUIlP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDHGzOJb%2BUBWNi2RM6CqaBTdo86n9OIwbmepCqoR6wZM3mkNnqWB7TxOf%2BFbFORZavvGN7W2J0FpPgOa2pkrdhiUaNrd9tnDgg4IFYwxp4aYIodB44WOkSlFuv4Fpqxdyzvdz%2FCP9XpgRojtUnzwhKV9sj4VjGT9wXBvarufDXU0pObVn6VAlIIDXwWtqa6VGEBBFNju%2B3sNExGe08%2FSupyUWirNw0u4C8Gi8%2BwnRf2WouMOX4M6YYw%2FudeF4as%2FiJTz2zHxuH0jYKV5txGlK3U5jJDStmNKM49Y0f5yrIc2f3nOE8HJQQTyA12VlRRbEl%2BEY7iS7SqNm0kd%2Bk%2BM5GrGOqFuRjTIWxSYDTr4UqpXI3r9%2BC%2BofKnY4VcLDeybq2PZ%2BL127qmeZOzJaMbzHHAabTYYmwnVwKYkO51iLrKpadsxKq5qbKWJOivddGzzDNIQ1TW%2BtXo9F4V9cVhgVXxlEkaUhE5dcKsgsJ%2BN8H5BGdBNpgJUtV%2FhkjmDVSaH5u9DIKb3x%2FVorbBkIhzPHLG8nb2xBqNiV5fyQpHoPbbFTQ1b1e6yovBd%2BVLemyPG1RML56I8FMYMW2vcIgzQq%2Fgfg3e2fPspDPYtzc1mHsmeCRkUiDabt%2Fic9TchFwkuoGm47pskve5bO1aJdKCqfsXdlikqHzDP097LWXEQJOdqnOF6Zd4F6QTva4XFvkMzU08E%2BqE981X2PDVA6u%2FXW5wWjrEB4Ictesnn2Iqm8pKlb7Dlcl9gtnmPT83qJIk5g%2FpbUMA1Y4bbp0jJBMgNmgFbwRnoiOH22gg8h8z%2FM7523VCiSlNqhlHoJwRou1OhQNgd3CX6Td2jcDgS079xcQ7xHoPNFBjN5FrzaHDTz2Cf1G2ZOl6OlXg%2BE9F8F6ahKXrLP6TA3YPrcjTCLhoDLBjqxAe7i0gajanxcX4bQMiWNTd8FKMJgDcdjeOxFPi9kJSLloGf9JUrug%2FaHfvIu9nfpttO9HZUy%2FI31WzqF5QiqZd8g7RiYcHeV9Hp82r4Q1700jBABB8FC9XSsQD%2BtZ2mn1jKTbdnxuK1GI%2FCc69dCFvZBQZppOcsIl3%2FLZ5xkP8Ex2D34gRo8TwcbWRY5Vpt1h4hqDFTpGxzczzFB4rq4P3jIVnobg5xSM0O7Z6KVW5NRyw%3D%3D&X-Amz-Signature=c83f583f88edd02bcb5f58cc17ec610f02343f869bf021b8b2cc7e50e3f39410&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
![Circuit View of 4-bit RCA presented in [33].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/695ce6067c29e05adc529c67/j_qic-2025-0030_fig_013.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKGOQQI7OO%2F20260109%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260109T011148Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEMv%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIA7d4YF6AI2%2B230tngo7cfZEUeGZw%2FpEJn%2F%2BZpqcHEZWAiEAgB3D94wsNTezP%2FnW9b8poswN5aH9Wso%2BAUGU5uquVesqxgUIlP%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDHGzOJb%2BUBWNi2RM6CqaBTdo86n9OIwbmepCqoR6wZM3mkNnqWB7TxOf%2BFbFORZavvGN7W2J0FpPgOa2pkrdhiUaNrd9tnDgg4IFYwxp4aYIodB44WOkSlFuv4Fpqxdyzvdz%2FCP9XpgRojtUnzwhKV9sj4VjGT9wXBvarufDXU0pObVn6VAlIIDXwWtqa6VGEBBFNju%2B3sNExGe08%2FSupyUWirNw0u4C8Gi8%2BwnRf2WouMOX4M6YYw%2FudeF4as%2FiJTz2zHxuH0jYKV5txGlK3U5jJDStmNKM49Y0f5yrIc2f3nOE8HJQQTyA12VlRRbEl%2BEY7iS7SqNm0kd%2Bk%2BM5GrGOqFuRjTIWxSYDTr4UqpXI3r9%2BC%2BofKnY4VcLDeybq2PZ%2BL127qmeZOzJaMbzHHAabTYYmwnVwKYkO51iLrKpadsxKq5qbKWJOivddGzzDNIQ1TW%2BtXo9F4V9cVhgVXxlEkaUhE5dcKsgsJ%2BN8H5BGdBNpgJUtV%2FhkjmDVSaH5u9DIKb3x%2FVorbBkIhzPHLG8nb2xBqNiV5fyQpHoPbbFTQ1b1e6yovBd%2BVLemyPG1RML56I8FMYMW2vcIgzQq%2Fgfg3e2fPspDPYtzc1mHsmeCRkUiDabt%2Fic9TchFwkuoGm47pskve5bO1aJdKCqfsXdlikqHzDP097LWXEQJOdqnOF6Zd4F6QTva4XFvkMzU08E%2BqE981X2PDVA6u%2FXW5wWjrEB4Ictesnn2Iqm8pKlb7Dlcl9gtnmPT83qJIk5g%2FpbUMA1Y4bbp0jJBMgNmgFbwRnoiOH22gg8h8z%2FM7523VCiSlNqhlHoJwRou1OhQNgd3CX6Td2jcDgS079xcQ7xHoPNFBjN5FrzaHDTz2Cf1G2ZOl6OlXg%2BE9F8F6ahKXrLP6TA3YPrcjTCLhoDLBjqxAe7i0gajanxcX4bQMiWNTd8FKMJgDcdjeOxFPi9kJSLloGf9JUrug%2FaHfvIu9nfpttO9HZUy%2FI31WzqF5QiqZd8g7RiYcHeV9Hp82r4Q1700jBABB8FC9XSsQD%2BtZ2mn1jKTbdnxuK1GI%2FCc69dCFvZBQZppOcsIl3%2FLZ5xkP8Ex2D34gRo8TwcbWRY5Vpt1h4hqDFTpGxzczzFB4rq4P3jIVnobg5xSM0O7Z6KVW5NRyw%3D%3D&X-Amz-Signature=1d277fbaaff1ae366cc365c7331e209170a79d8a61093106a9aa471c7b90d7e8&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
A comparison of various 2×2 Vedic multipliers_
| Designs | CI | QC | GC | GO | CNOT-V/V+ count |
|---|---|---|---|---|---|
| In [29] | 16 | 42 | 10 | 16 | 50 |
| In [30]#1 | 16 | 40 | 10 | 16 | 50 |
| In [30]#2 | 10 | 34 | 7 | 10 | 44 |
| In [30]#3 | 9 | 31 | 7 | 9 | 39 |
| In [31] | 8 | 30 | 6 | 8 | 37 |
| In [32] | 8 | 29 | 5 | 8 | 37 |
| In [33] | 7 | 27 | 5 | 7 | 35 |
| Proposed | 6 | 25 | 3 | 6 | 33 |
| imp% in [29] | 62.50 | 40.47 | 70.00 | 62.50 | 34.00 |
| imp% in [30]#1 | 62.50 | 37.50 | 70.00 | 62.50 | 34.00 |
| imp% in [30]#2 | 40.00 | 26.47 | 57.14 | 40.00 | 25.00 |
| imp% in [30]#3 | 33.33 | 19.35 | 57.14 | 33.33 | 15.38 |
| imp% in [31] | 25.00 | 16.66 | 50.00 | 25.00 | 10.81 |
| imp% in [32] | 25.00 | 13.79 | 40.00 | 25.00 | 10.81 |
| imp% in [33] | 14.28 | 7.40 | 40.00 | 14.28 | 5.71 |
| Average saving | 37.51 | 23.09 | 54.89 | 37.51 | 19.38 |