Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

Algorithm 2

Minimal_Quantum_Representation (MQR).

Input: Quantum Gate Library 𝐿, minimal permutation 𝑝,

   circuit length 𝑙

Output: Circuit of minimal permutation 𝑝 with mini-length

1: compute 𝑆[0…max𝑙] as in QML(𝐿) for the first time;

2: 𝑖=𝑙,mynode[𝑖]=𝑠[𝑖].find(𝑝)

3: pcpm𝑥=mynode[𝑖].pcpm

4: while  𝑖>1  do

5: 𝑖=𝑖−1

6: mynode[𝑖]=𝑆[𝑖].find(pcpm𝑥)

7: pcpm𝑥=mynode[𝑖].pcpm

8: end while

9: 𝜎=mynode[1].lnpm,𝑏=mynode[1].binv

10: 𝐺₁=𝑃_𝜎𝑅_𝑏(mynode[1].gate)

11: for  𝑖=2 to 𝑙  do

12: 𝜎=mynode[𝑖].lnpm,𝑏=mynode[𝑖].binv

13: 𝑐=mynode[𝑖].pbinv,𝑔=mynode[𝑖].gate

14: 𝐺_𝑖=𝑅_𝑏𝑃_𝜎𝑅_𝑐𝐺_𝑖−1𝑔

15: end for

16: return  𝐺_𝑙