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%I #21 Jun 20 2022 14:45:27
%S 6,60,1080,36720,2423520,315057600,81284860800,41780418451200,
%T 42866709330931200,87876754128408960000,360118938418219918080000,
%U 2950814581398894008747520000,48352047730802277227336862720000
%N Number of stabilizer states on n qubits.
%C 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.
%H D. Gross, <a href="https://arxiv.org/abs/quant-ph/0602001">Hudson's Theorem for finite-dimensional quantum systems</a>, arXiv:quant-ph/0602001, 2006-2007.
%F a(n) = 2^n*Product_{i=1..n} (2^i+1).
%F a(n) = A000079(n)*A028362(n+1).
%e For n = 1, the a(1) = 6 states are |0>, |1>, |+>, |->, |i>, and |-i>.
%o (Python)
%o def a(n):
%o ans = 2 ** n
%o for i in range(1, n+1):
%o ans *= 2 ** i + 1
%o return ans
%o (Python)
%o from math import prod
%o def A353196(n): return prod((1<<i)+1 for i in range(1,n+1)) << n # _Chai Wah Wu_, Jun 20 2022
%Y Cf. A000079, A003956, A028362.
%K nonn,easy
%O 1,1
%A _James Rayman_, Apr 29 2022
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