cp's OEIS Frontend

A353196 Number of stabilizer states on n qubits.

%I A353196 #26 Aug 17 2025 11:17:59
%S A353196 6,60,1080,36720,2423520,315057600,81284860800,41780418451200,
%T A353196 42866709330931200,87876754128408960000,360118938418219918080000,
%U A353196 2950814581398894008747520000,48352047730802277227336862720000,1584496604138390624739828991334400000
%N A353196 Number of stabilizer states on n qubits.
%C A353196 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 A353196 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 A353196 a(n) = 2^n*Product_{i=1..n} (2^i+1).
%F A353196 a(n) = A000079(n)*A028362(n+1).
%F A353196 a(n) ~ c * 2^(n*(n+3)/2) where c = Product_{k>=1} (1 + 1/2^k) = A079555. - _Amiram Eldar_, Aug 17 2025
%e A353196 For n = 1, the a(1) = 6 states are |0>, |1>, |+>, |->, |i>, and |-i>.
%t A353196 Table[2^n * QPochhammer[-2, 2, n], {n, 13}] (* _Amiram Eldar_, Aug 17 2025 *)
%o A353196 (Python)
%o A353196 def a(n):
%o A353196     ans = 2 ** n
%o A353196     for i in range(1, n+1):
%o A353196         ans *= 2 ** i + 1
%o A353196     return ans
%o A353196 (Python)
%o A353196 from math import prod
%o A353196 def A353196(n): return prod((1<<i)+1 for i in range(1,n+1)) << n # _Chai Wah Wu_, Jun 20 2022
%Y A353196 Cf. A000079, A003956, A028362.
%K A353196 nonn,easy
%O A353196 1,1
%A A353196 _James Rayman_, Apr 29 2022