Generating Toffoli Networks from ESOP Expressions

Yasaman SanaeeWinter 2009

University of New Brunswick

2

Outline

• Motivation• Background

– Reversible Logic– ESOP-based Toffoli gate cascade

• Our method– Shared ESOP cubes– Make Shared Toffoli Gate Cascade– Templates

• Future Work and Conclusion

3

Motivation

• Launder and Bennett

• Reversible Logic Applications

1) Quantum Computing/Computers

2) Optical Computing

3) Low Power CMOS

• How make a circuit from a logical function?

4

Reversible Logic

• Reversible Functions

000

100

101

110

001

010

111

011

111

011

101

001

110

010

100

000321 fffcba

cbcaf

cbcabaf

cbcabaf

3

2

1

Circuita

b

c

f3

f2

f1

5

Reversible Logic

• Reversible Gates • Toffoli Gates• Cascade of Gates• ESOP cubes

01101

1011

1100

3.

2.

3.

p

o

i

cube

6

Our Method

• Find shared cubes• Reorder ESOP• Generate Shared

Toffoli gates

e

typeesop

o

i

.

010110

101101

101100

011011

011010

100001

101000

.

3.

3.

e

typeesop

o

i

.

101000

101100

101101

.

3.

3.2x1x

3x

1o2o3o

7

Our Method

• Reduce the number of Toffoli gates and Quantum Cost

• Converge

• High number of Not gates

• Solution? Template Matching

8

Our Method

21

Template 21

Circuit

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Future Work and Conclusion

Future Works:• Template Matching Works for small number of

input and outputs• Some Transformation to reduce the number of

NOTsConclusion• Converge Method to generate Toffoli gate cascade

(even large number of input and output )• Optimization (Template Matching)• Experimental Results

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Questions?