# Random normalised variable generation

I want to generate 8 random variables (in reality to form 4 complex numbers) such that the sum of the 8 variables squared is equal to unity. The aim of generating such numbers is to perform a quantum simulation of 4 qubits (thus the 8 parameters). I've been trying to use RandomVariate[NormalDistribution[]], but I'm not quite sure how to satisfy the constraint previously described.

• If you needed to do this by hand (and not with Carl's answer), the approach is similar. Just think of a circle. You randomly choose an angle [0,2Pi] and then you calculate the point on the circle with {Cos[phi],Sin[phi]}. This automatically has your condition. Now you extend this into 8 dimensions. – halirutan May 31 at 16:12

You can use RandomPoint of a Sphere:
SeedRandom[1]

• RandomPoint @ Sphere @ 8 is shorter. – kglr Jun 1 at 5:25