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I was reading this lecture notes by Sevag Gharibian. He mentioned the following statement:

Large-scale universal quantum computer can be built.

I do understand what quantum computer is, but I don't know what is 'Large-scale universal' mean here. Can someone explains to me what does it mean?

Note: I don't know which tag I should put, so let me know if you know a good tag for this question.

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"Large-scale" generally means that the quantum computer's ability scales to practical instances of problems. For the case of factoring, RSA keys are usually 1024/2048/4096 bit sized: if a quantum computer could reliably factor these, it would definitely be considered "large-scale" in today's context, but, as the field develops and depending on people's individual tastes, it might change. Note that this would not just be a matter of "qubit count" as is commonly said in articles, it would also be based on the reliability and scalability of the gates acting on them, among other factors: Shor's Algorithm in theoretical principle requires around twice the number of qubits as the number of bits of the number being factored, but as things look now you'd likely need way more for error corrections, and the gate count for the circuit would still be gigantic, but if you could get it all working it could run in a realistic human timeframe unlike all known classical algorithms.

"Universal" means that it can run any quantum algorithm rather than being hard-coded for a limited set of situations. DWave's quantum computers are NOT this, which is why news stories like Google and IBM's bigger and bigger qubit records in the late two-digits are treated as significant despite DWave's claims in the thousands. DWave cannot run Shor's Algorithm or Grover's Algorithm.

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  • $\begingroup$ Thank you so much Joseph, the concept is very clear. $\endgroup$
    – user777
    Feb 21 at 17:42

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