In some theoretical sense that's right - it's easy to simulate classical circuits using quantum circuits. In a practical sense, if you want to add two 10,000 digit numbers, it's probably best to use a classical computer: you won't have neatly the overhead involved in QC.
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Thanks, this is what i thought. It depends whether "better at" is referring to efficiency or universality. That seems to keep getting confused in discussions I see on Twitter.
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It's not really universality, so much as what notion of efficiency you mean. For asymptotic complexity, ignoring polylogarithmic overheads (for error-correction & differences in implementation difficult), QCs will always be at least as efficient, & sometimes far more so.
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Basically, a classical NAND gate is pretty easily simulated by a small collection of quantum gates. And NAND is universal for classical computation. So there's at most a (small) constant overhead in gate count. But the quantum gates may be a _lot_ harder to build. So.
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Over the long run it's going to depend on what technology succeeds for quantum computing. I doubt this is a popular point of view, but I won't be entirely surprised if we end up with naturally fault-tolerant systems, and QC replaces CC. Not for a long time, though.
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