Cayley Table — click any cell to see product details
Color by phase:
+real
-real
+imag
-imag
Pauli matrices:
I = [[1,0],[0,1]]
X = [[0,1],[1,0]]
Y = [[0,-i],[i,0]]
Z = [[1,0],[0,-1]]
Key identities:
XY = iZ
YZ = iX
ZX = iY
X² = Y² = Z² = I
XYZ = iI
Commutation:
[Xᵢ,Xⱼ]=0 (same)
{X,Y}=0 (diff)
Anticommute: XY=-YX
Click a cell:
Shows A·B = result
P_n (n qubits):
|P_n| = 4^(n+1)
P_2: 64 elements
Tensor product:
(A⊗B)(C⊗D) = (AC)⊗(BD)