Quantum Mining
1.Can quantum computing improve Bitcoin mining?
2.Would a D-Wave 2 with 512 qbits be faster than the fastest ASIC when mining bitcoins?
There are two different things here:
D-Wave machines are ASICs. They only solve certain particular problems. It is not really clear they take advantage of quantum effects or that they perform better than a classical ASIC working on the same problem would. In any case, they would be quantum ASICs, not general purpose quantum computers.
Mining can be improved using Grover's algorithm (http://en.wikipedia.org/wiki/Grover%27s_algorithm). When you mine, you basically have a black box that you feed with guesses and the box answers whether you have "won" the block or not. The number of possible answers is your difficulty. It is easy to produce by chance an even number, not so easy to produce a multiple of 5743.
Imagine you have a quantum computer and a classical computer each with a black box which takes the same time to check your guess. Each guess has a probability of being right equal to (#right answers)/(#total possible answers).
In a classical computer you just try one by one. On average you need about (#total possible answers)/(#right answers) tries to hit a block. In a quantum computer or a quantum ASIC implementing Grover's algorithm, you only need to use the black box (what they call the "oracle") the square root of (#right answers)/(#total possible answers) times. There are some other factors, but roughly you get a quadratic advantage.
Of course you never get this kind of fair comparison. I wouldn't really worry about quantum mining for a long time. Even if it were faster, it would probably be much more expensive. Think that you can always mine faster with more expensive equipment. You could mine faster with a supercomputer, but, at the cost they come, you better use it for something else.
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