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Replying to @MelMitchell1
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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Replying to @michael_nielsen @MelMitchell1
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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Replying to @michael_nielsen @MelMitchell1
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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(Let me emphasize: that last tweet is very speculative!)
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