3. Features of quantum computer:
Super position
Interference
Entanglement
Measurement
4.
5.
6.
7. Quantum vs Classical
Quantum Computation
Bijective or Reversible
Input and output vectors have same bit-width
No information loss
Classical Computation
Irreversible
Different input and output bit-width
Loss of information
8. Need for reversibility
Fundamental physics dictates that energy
must be dissipated when information is
erased, in the amount KT ln2 per bit erased,
where K is Boltzmann constant(k=1.38x1023JK-1) and T is absolute temperature in K
14. Reed Muller Reversible Logic
Synthesis(RMRLS)
Any Boolean function can be described by an
exclusive-OR sum-of-products (ESOP) expression
ex: for a boolean expression y= a+b’c
SOP=a+b’c
ESOP=a a’b’c
Two types of expressions:
PPRM :All variables are un-complemented
PPRM=abc ac bc
a c
FPRM:Either x or x’ appear throughout
FPRM=a’b’c a’
1
15. Reed Muller Reversible Logic
Synthesis (cont..)
Synthesis flow
Find factors for any outptut a0 without literal a (target)
Build a node in a search tree, where:
#PPRM terms is reduced by Toffoli gate
Create a child node
Insert the node into Priority Queue (PQ)
EX: a0 = a bc 1 ac
Valid factors :bc,1
Target : a
Sort Priority queue
Priority α # PPRM terms eliminated
Pop the queue ,repeat above steps
16.
17.
18.
19. Decision Diagram Synthesis
Boolean functions are represented by a DD
(Decision Diagrams)
DD:acyclic graph G=(V, E) where
decompositions are applied to each node v ϵ V
Shannon decomposition(S) : f=xi’.fxi=0
xi.fxi=1
Positive Davio decomposition(pD): f=xi’.fxi=0
xi.fxi=2
Negative Davio decomposition(nD): f=xi’.fxi=1
xi.fxi=2
fxi=0 and fxi=1
f
=f
are co-factors w.r.t. xi’ and xi
f
20. Decision Diagram Synthesis
(DDS)
Synthesis flow
Build DD(Decision Diagrams)
Depth first search
Map each gate to Toffoli gate
Note:
DDS method automatically transforms an
irreversible specification into reversible
23. RMRLS vs DDS
RMRLS
DDS
Pros
Fewer qubits(lines)
Low quantum cost
Low synthesis time
Able to synthesize large
circuits
Can synthesize
irreversible specifications
Cons
High synthesis time
Only able to synthesize small circuits
Large no. of garbage
outputs
24. Reed-Muller Decision Diagram
Synthesis (RMDSS)
Hybrid of RMRLS and DDS
A flexible and efficient reversible circuit
synthesizer
Qubits can be traded off for QC
User defined time limit
28. References
D. P. Di Vincenzo, “Quantum Computation,”
Science, 270, 1995, pp. 255-256.
K. Iwama, Y. Kambayashi, S. Yamashita,
“Transformation Rules for Designing CNOTBased Quantum Circuits,” Design Automation
Conference,2002, pp.419-424.
P. A. M. Dirac, The Principles of Quantum
Mechanics, Oxford University Press, 1st
Edition, 1930.
