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I have a question. Gradually quantum computers will emerge someday. So, nowadays making algorithm efficient is important; I mean, making it optimal to run as fast as possible. But once quantum PC emerges does the algorithm performance improvements are still important? Cheers

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Yes. algorithm performance improvements will always be important as what people would like to compute will probably always exceed the capabilities of the computers of their time.

This holds especially for quantum computers. In 2011 it was considered a success to factor the number 21 by running Shor's factorization algorithm on a quantum computer. See

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