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Is there any way to get an equivalent of computing power of quantum computers in terms of computing power of common computers? I mean, how many teraflops (or so) can a quantum computer compute? How can I calculate that equivalence? I think it depends on the architecture, like a x64 in common computer, and a 512-qubit.

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  • $\begingroup$ The actual power does of course depend on the specific machine. Why do you think "count operations per second" is no longer a good metric? (It assumes you can actually build a quantum computer, obviously, but until then the question for processing power is moot, anyway.) $\endgroup$ – Raphael Jan 28 '14 at 8:21
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this is a very difficult/subtle/controversial question at the heart of current research that even topnotch scientists are having a lot of trouble answering precisely. there are two main lines of QM computer development:

  • adiabatic QM computing, this is the Dwave computer that is up to 512 qubits, but it doesnt operate using "qbit transport" which is the main line of scientific research

  • "standard" QM computing transports qbits so their spins can interact as laid out in "quantum circuits". there is a lot of theoretical research on this topic but physics researchers are apparently still far from actually implementing (physically building/realizing) this type of computing.

unfortunately in both cases there are other further issues:

  • theoretically, can one get a speedup based on the mathematics/physics of quantum computing? see eg proof of speedup with [adiabatic] qm computing tcs.se

  • in practice, after one builds the computer, and one applies various systems, eg error correction being one of the main ones, and decoherence being one of the main challenges to overcome, how efficient will it be? will there be any speedup over conventional computing?

  • QM algorithms run completely differently, they are not based on binary logic! so therefore there is not yet any way to determine what the "equivalent" or "corresponding" qm algorithm is to a "classical" algorithm that is under consideration. the best we can do is try to optimize the performance of both & see what happens but that is obviously not satisfactory and somewhat dependent on human factors.

so the best answer right now is "nobody can really say right now". or, the best quantum computer in the world, Dwave, (apparently costing in \$ millions per unit, and over $100M research so far) is now shown in scientific papers to be slower than desktop computers when algorithms are optimized on those computers. or, "its an open question subject to cutting edge international research". there are many posts in Aaronsons blog on the subject. see also

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  • $\begingroup$ ps the good news is that there is far more insight into these questions than just a year ago, and now google/nasa/lockheed martin have Dwave machines & scientists crunching hard on these questions... $\endgroup$ – vzn Jan 28 '14 at 3:29

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