  We study the use of the quantum wavelet transform to extract efficiently
information about the multifractal exponents for multifractal quantum states.
We show that, combined with quantum simulation algorithms, it enables to build
quantum algorithms for multifractal exponents with a polynomial gain compared
to classical simulations. Numerical results indicate that a rough estimate of
fractality could be obtained exponentially fast. Our findings are relevant e.g.
for quantum simulations of multifractal quantum maps and of the Anderson model
at the metal-insulator transition.
