Is quantum annealing faster than simulated annealing/genetic/other state-of-the-art optimization algorithms?

Question

Forgive me wise men for my simple words, for I am but a noob.

There's the idea of quantum annealing being used to solve optimization problems in terms of a QUBO problem for D-Wave's quantum algorithm. I understand that the advantage of quantum annealing as opposed to classical simulated annealing is that quantum annealing allows the particle/search point to tunnel through high barriers with probability as a function of barrier width, instead of having to climb all the way over the barrier (which in some cases wouldn't be possible because there wouldn't be enough energy). This is my understanding from here: http://en.wikipedia.org/wiki/Quantum_annealing

If quantum annealing is better than simulated annealing in this fundamental way, would it not be faster to implement QA instead of SA or GA's for solving optimization problems on a classical computer? If so, why aren't people using it? Or are they, and I'm just unaware (in which case I'd love to see references)?

D-Wave seems to be banking on the practicality of their quantum computer, not so much insane accuracy or other more "scientific" pursuits. If it just so happens that D-Wave's computers aren't really quantum, shouldn't we be able to find a fast classically implemented quantum annealing algorithm to compete with the quantumly implemented version also?

Answer 1

Quantum annealing essentially offers a square-root speed-up over classical simulated annealing in many circumstances. So, yes, it is potentially a faster approach for some optimization problems, but the speed-up isn't enough to make most hard problems tractable.

Unfortunately, you cannot efficiently simulate quantum annealing classically, because any approaches we know of require you to keep track of the state of the system, which requires keeping track of exponentially many parameters (the amplitude of each possible classical state). Thus any attempt to simulate quantum annealing incurs a huge overhead which kills any advantage.