Finally a proof that quantum computers outperform classical computers
for a certain class of problems? Thoughts?

"Quantum computers are expected to be better at solving certain
computational problems than classical computers. This expectation is
based on (well-founded) conjectures in computational complexity
theory, but rigorous comparisons between the capabilities of quantum
and classical algorithms are difficult to perform. Bravyi et al.
proved theoretically that whereas the number of “steps” needed by
parallel quantum circuits to solve certain linear algebra problems was
independent of the problem size, this number grew logarithmically with
size for analogous classical circuits (see the Perspective by
Montanaro). This so-called quantum advantage stems from the quantum
correlations present in quantum circuits that cannot be reproduced in
analogous classical circuits."

http://science.sciencemag.org/content/362/6412/308

Cheers,
Telmo.

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