Would the P vs. NP problem become trivial as a result of the development of universal quantum computers?

If someone were to build a universal quantum computer, would that have any implications on the problem of P vs. NP?

No, there will be absolutely no implication, for several reasons:

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The P vs. NP problem is about classical computation rather than quantum computation. Even if quantum computers could solve NP-hard problems in polynomial time (which we don't expect them to be able to do), it could still be the case that classical computers cannot solve them in polynomial time.

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Universal quantum computers, in a theoretical sense, are (to the best of my knowledge) already known to exist. These are just the quantum analogs of universal Turing machines: they can execute any given quantum "program".

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Both quantum computation and the P vs. NP problem are theoretical notions. What someone can construct in the physical world has absolutely no bearing on anything having to do with them.

Lieuwe Vinkhuijzen gave a different interpretation of your question:


Will quantum computers be able to solve NP-complete problems efficiently?

The expected answer is: no. So even in this sense, physical quantum computers won't enable us to solve NP-complete problems at will.

StackExchange Computer Science Q#73864, answer score: 41