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A353196
Number of stabilizer states on n qubits.
1
6, 60, 1080, 36720, 2423520, 315057600, 81284860800, 41780418451200, 42866709330931200, 87876754128408960000, 360118938418219918080000, 2950814581398894008747520000, 48352047730802277227336862720000
OFFSET
1,1
COMMENTS
A stabilizer state is a quantum state on n qubits prepared by applying a series of Hadamard, CNOT, and S gates to the all-zero state. There are only a finite number of such states for any n.
FORMULA
a(n) = 2^n*Product_{i=1..n} (2^i+1).
a(n) = A000079(n)*A028362(n+1).
EXAMPLE
For n = 1, the a(1) = 6 states are |0>, |1>, |+>, |->, |i>, and |-i>.
PROG
(Python)
def a(n):
ans = 2 ** n
for i in range(1, n+1):
ans *= 2 ** i + 1
return ans
(Python)
from math import prod
def A353196(n): return prod((1<<i)+1 for i in range(1, n+1)) << n # Chai Wah Wu, Jun 20 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
James Rayman, Apr 29 2022
STATUS
approved