Chinese Journal of Quantum Electronics, Volume. 40, Issue 5, 759(2023)
Design of quaternary quantum reversible half-adder, full-adder and parallel adder circuits
Figures & Tables(16)
Fig. 3. Quaternary quantum Feynman gate. (a) Symbolic representation of quaternary 2-qudit Feynman gate;
Fig. 4. The first part of quaternary carry output of the proposed half adder circuit.
Fig. 5. The second part of quaternary carry output of the proposed half adder circuit. (a) Realization of the quaternary carry output;
Fig. 6. The third part of quaternary carry output of the proposed half adder circuit. (a) Realization of the quaternary carry output;
Fig. 7. Symbolic representation of carry output of the proposed half adder circuit
Table 1. Truth table of quaternion 1-qudit gate
View tableView in ArticleTable 1. Truth table of quaternion 1-qudit gate
A Z(+0)=A Z(+1)=A+1 Z(+2)=A+2 Z(+3)=A+3 Z(123)=2A Z(013)=2A+1 0 0 1 2 3 0 1 1 1 0 3 2 2 3 2 2 3 0 1 3 2 3 3 2 1 0 1 0 A Z(021)=2A+2 Z(032)=2A+3 Z(132)=3A Z(012)=3A+1 Z(023)=3A+2 Z(031)=3A+3 0 2 3 0 1 2 3 1 0 1 3 2 1 0 2 1 0 1 0 3 2 3 3 2 2 3 0 1 A Z(23)=A2 Z(01)= A2+1 Z(0213)= A2+2 Z(0312)= A2+3 Z(12)=2A2 Z(0132)=2A2+1 0 0 1 2 3 0 1 1 1 0 3 2 2 3 2 3 2 1 0 1 0 3 2 3 0 1 3 2 A Z(0231)=2A2+2 Z(03)=2A2+3 Z(13)=3A2 Z(0123)=3A2+1 Z(02)=3A2+2 Z(0321)=3A2+3 0 2 3 0 1 2 3 1 0 1 3 2 1 0 2 3 2 2 3 0 1 3 1 0 1 0 3 2
Table 2. Truth table of quaternary half adder
View tableView in ArticleTable 2. Truth table of quaternary half adder
AB CS 00 00 01 01 02 02 03 03 10 01 11 02 12 03 13 10 20 02 21 03 22 10 23 11 30 03 31 10 32 11 33 12
Table 3. Comparison of hardware complexity of different quaternion reversible adders
View tableView in ArticleTable 3. Comparison of hardware complexity of different quaternion reversible adders
Hardware complexity Half adder Full adder Parallel adder Existing in [ 39 ]24ε+ 90γ 64ε+ 240γ 144ε + 540γ Proposed design 13ε+ 24γ 26ε+ 48γ 52ε+ 96γ
Table 4. Comparison of constant input of different quaternion reversible adder circuits
View tableView in ArticleTable 4. Comparison of constant input of different quaternion reversible adder circuits
Constant input Half adder Full adder Parallel adder Existing in [ 39 ]3 6 13 Existing in [ 40 ]4 5 - Proposed design 2 2 4
Table 5. Comparison of garbage output of different quaternion reversible adder circuits
View tableView in ArticleTable 5. Comparison of garbage output of different quaternion reversible adder circuits
Garbage output Half adder Full adder Parallel adder Existing in [ 39 ]3 7 14 Existing in [ 40 ]4 6 - Proposed design 2 3 5
Table 6. Comparison of quantum costs of different quaternion reversible adder circuits
View tableView in ArticleTable 6. Comparison of quantum costs of different quaternion reversible adder circuits
Quantum cost Half adder Full adder Parallel adder Existing in [ 39 ]114 304 684 Existing in [ 40 ]46 128 - Proposed design 37 74 148
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Qimei TANG. Design of quaternary quantum reversible half-adder, full-adder and parallel adder circuits[J]. Chinese Journal of Quantum Electronics, 2023, 40(5): 759
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Received: Oct. 11, 2021
Accepted: --
Published Online: Nov. 24, 2023
The Author Email: TANG Qimei (tangqimei@ahmu.edu.cn)
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