# Period of a Multivariable Function using Quantum Computing

consider a function

$$f(x_1,x_2...x_n)$$

I am told it is possible to compute the period of the function as a vector

$$<l_1,l_2...l_n>$$ where each l denotes the period of the function for that corresponding variable using a generalization of the fourier transform.

My question is:

Is the time complexity of running the multivariable version of the quantum fourier transform still polynomial in the bit complexity of a function being evaluated?