Time crystals have no direct relation to quantum computers.

Quantum computers currently are very limited, but may be able to eventually compute Fourier Transforms in an amount of time that's a polynomial function of the input size (aka polynomial time), even for large inputs. That would be really cool! There are a few other problems they can solve for which there's no known classical polynomial time algorithm, but the Quantum Fourier Transform (QFT) is the big one. AFAIK nobody has yet managed to even factor the number 21 with a quantum computer, so they're a tad impractical still. Also there's no proof that classical computers can't do everything quantum computers can do just as efficiently (i.e. that BQP ≠ P), but it is strongly suspected.

Quantum annealers like D-wave's do exist now, but solve a more limited set of problems, and can't compute the QFT. It's not certain whether they're even any faster than classical computers.

I've made several enormous simplifications above.