Table 6 The distribution of the number of equivalence classes across Clifford circuits over 2, 3, 4, 5, and 6 qubits.

From: 6-qubit optimal Clifford circuits

CNOT count Qubits

2

3

4

5

6

0

1

1

1

1

1

1

1

1

1

1

1

2

1

3

4

4

4

3

1

8

20

22

23

4

 

10

112

183

198

5

 

3

525

1958

2549

6

 

1

1230

22,257

42,883

7

  

453

223,723

824,723

8

  

16

1,441,124

16,086,167

9

  

1

2,471,855

294,266,642

10

   

161,458

4,399,997,085

11

   

72

40,791,942,327

12

   

1

92,804,759,960

13

    

5,666,221,415

14

    

8,281

15

    

3

Total

4

27

2363

4,322,659

143,974,152,262

Back to article page