Reversible Gates in
various realization
technologies
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Reversible Gates Implementation: NOT, Toffoli, Fredkin in Double-Rail & De Vos Tech, Slides of Computer Science
The realization of reversible gates, specifically not, toffoli, and fredkin gates, in double-rail and de vos technology. Detailed circuit diagrams and explanations of how these gates can be obtained from each other using cnot and swap gates. It also discusses the advantages and disadvantages of each technology.
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2012/2013
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Reversible Gates in
various realization
technologies
Double Rail
Technologies
Double-Rail Feynman Gate
- Fig. 2.2.2: Realization of Controlled-Not (Feynman) gate in
double-rail logic.
=
=
b
b
a
a
2
a
a
1
b
b
1
b
b
2
a a
b
b (^) a b
a
- a’ = (a 1 , a 2 ’) = (1,0),
- a = (a 1 ’, a 2 ) = (0,1).
Fredkin built from Toffoli and CNOT
- Fig. 2.2.3:
- Realization of Fredkin gate using Toffoli and CNOT gates.
- By surrounding the Toffoli gate (Fig. 2.2.3a) with CNOT gates (Fig. 2.2.3b) we obtain the Fredkin gate (Fig. 2.2.3c).
- Similarly the Toffoli gate can be obtained by surrounding the Fredkin gate using two CNOT gates.
- This way a Toffoli gate in double-rail logic can be realized, as shown in Fig. 2.2.4.
(a) (b) (c)
Double-rail Fredkin gate
- Fig. 2.2.5.: Detailed circuit of double-rail Fredkin gate
realized with two standard Fredkin gates with the same control.
b
b
Q
c
Q
c
R
R
b
a2 P
a1 P
Single-rail schematics for double-rail
Fredkin gate
- Fig. 2.2.6: The gate from Figure 2.2.5 in another
notation, every signal corresponds now to two wires from Figure 2.2.5.
P
Q
R
a
b c
2
2
Toffoli gate in double-rail
technology
- Fig. 2.2.8: Realization of CNOT in double-rail technology.
Signal a is represented by a1=0, a2 = 1. Signal a’ (negation of a) is represented by a1=1, a2 =0.
a
b
P
Q
P
P
a
a
b
b1 Q
Q
SWAP in double-rail
- Fig. 2.2.9: Realization of SWAP in double-rail
technology.
= =
a
a
b
b
c
c
d
d
a c
b d
2.3. DOUBLE-RAIL OPEN/CLOSE
SWITCH REVERSIBLE CMOS LOGIC
OF ALEXIS DE VOS
P
Q R
c
a b
- Fig. 2.3.1: Realization of
Fredkin gate. Notation
for De Vos double-rail
technology from Figure
a
a
c
b c
Q
Q
b
- Figure 2.3.2. Realization of
function Q in Fredkin gate using
De Vos technology.
Toffoli in De Vos Technology
- Fig. 2.3.3:
- Realization of Toffoli gate in double-rail DeVos technology.
- As we see, this is a kind of double-rail technology.
a b
a (^) b
c
p
a b
a b
c
p
CNOT gate in De Vos technology
- Figure 2.3.4. Realization of CNOT in De Vos technology.
a
a
c
c
Q
Q
a
a
Regular layout for De Vos technology
- Fig. 2.3.5: DeVos CMOS circuit layout for pass-transistor
diagram from Figure 2.3.3.
a b
a b
a b
a b
C P
C (^) P
Toffoli
2.4. CONSERVATIVE
REVERSIBLE LOGIC BASED
ON 23 SWITCHES*
b
a b
a b
a a b + a b
a
a
CONSERVATIVE REVERSIBLE LOGIC
BASED ON 23 SWITCHES*
- Fig. 2.4.1: Realization of CNOT in double-rail switch-
based technology
a
b
a b
a b
a a b
a
a b + a b
a b + a b
a a
a
b
ab