Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

Algorithm 1

Quantum_Minimum_Length (QML).

Input: Quantum Gate Library 𝐿

Output:  max𝑙,𝑁[0…max𝑙],𝑆[0…max𝑙]

1: 𝑆[0]={cmp∶𝜋_𝑒},𝑗=0,𝑁[0]=1

2: while  𝑁[𝑗]≠0  do

3: 𝑗=𝑗+1,𝑆[𝑗]=∅

4: for each node Node x in 𝑆[𝑗−1]  do

5:  𝑐=Node𝑥.cpm

6:  for  𝑣=0to1  do

7:   if  𝑣=1  then

8:    𝑐=𝑐⁻¹

9:   end if

10:    for each gate 𝑔 in 𝐿  do

11:    𝑝=𝑐∘𝜋(𝑔),𝜋=GetMin(𝑝,𝜎,𝑏)

12:    if  𝜋∉⋃^𝑗_𝑖=0𝑆[𝑖]  then

13:     𝑆[𝑗]=𝑆[𝑗]∪gate∶𝑔,cpm∶𝜋,lnpm∶

            𝜎,binv∶𝑏,pcpm∶𝑝,

            pbinv∶𝑣

14:     if memory overflow error then

15:      free𝑆[𝑗],𝑗=𝑗−1,goto23

16:     end if

17:    end if

18:   end for

19:  end for

20: end for

21: 𝑁[𝑗]=∑_{𝐺∈𝑆[𝑗]}⋃_{𝑖∈𝑆𝐹,𝑏∈𝑆𝐵}𝑅_𝑏(𝑃_𝜎𝑖(𝐺))

22: end while

23: max𝑙=𝑗