According to the report published by Google and NASA after experimenting “Quantum computer D-Wave 2x” for two years, The quantum computer under experiment is more than 100 million times faster than simulated annealing running on a single core (conventional computer).
The experiments were carried out at the U.S. space agency’s Ames Research Center in California, which involved constructing proof-of-principle optimization problems and programming it into the D-Wave 2X quantum annealer. The experiment was carried out to demonstrate that quantum computers can offer runtime advantages for hard optimization problems to a specific design.

An optimization problem is when you have a process with a whole bunch of parameters you can tune that influence the outcome in complex ways.
For example:
Consider you are the manufacturer who builds a specific product, build-out of 100 components each offered by several different manufacturers. The manufacturers selling components have different prices, production rates and delivery time. The optimization problem here is to figure out what orders I should place at different manufacturers to get the best value for 100 different components to build my projected product.
For the small problems like the one discussed above the quantum annealing algorithm can yield the best results with runtime advantages. Obvious applications where this can be used would be in:
– Manufacturing
– Logistics
– Assisted R&D via simulation
– Computer-Aided Design (CAD)
– Climate science
– Robot movement & navigation

Since Quantum computers take advantage of quantum mechanics, they can theoretically be much faster and achieve the best solutions to problems efficiently through parallel processing.
Again it’s important to note that D-Wave’s Quantum computers are not capable of universal computing, they are only useful for a small number of very specific tasks. It’s still in the early stages and Google, NASA, and others are currently working hard to scale it up and make it practical.
Source: Google research blog
Download: Research paper here