There are some basic linear algebra subroutines (Matrix inversion, finding eigenvalues & eigenvectors) that can be performed with an exponential speedup on a quantum computer in theory, that's why there is so much interest in Quantum Machine Learning. If you are asking about the current hardware level, then no, current quantum computers can not solve any practical problem faster than a classical computer.In theory classical computers are also not limited to have better solutions to problems where quantum computers claim superiority like prime factorisation or like Tang's quantum inspired classical algorithm that beats HHL for low rank matrices.
jlokier|5 years ago
Eh... those particular subroutines have polynomial time algorithms already on a classical computer.
You can't exponentially speed up something that's polynomial time already.
westurner|5 years ago