Variational Quantum Algorithm (VQA) is a kind of quantum algorithm corresponding to classical machine learning. Unlike the square speed up of Grover's algorithm, the circuit in VQA does not seem to guarantee being faster than classical machine learning. So, is VQA faster than classical machine learning? If not, why is there a lot of research in this field?

  • $\begingroup$ VQA is not really just classical machine learning... but even so, to classicallysimulate a general circuit of n qubits and measure it will be very difficult when n is large... of course there are circuits that are easily simulable classically, but for the problems of interest in VQA, the circuits that require to obtain meaningful solutions are not easily simulable classically. $\endgroup$
    – KAJ226
    Commented Jun 14, 2021 at 7:45
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    $\begingroup$ @narip ok, i see. Note exact diagonalization for electronic structure problem is very expensive... it scales exponentially with the system size. With VQE you do have a polynomial scale up. There are problems like Barren Plateaus that have been brought up but that should not be the case for quantum chemistry problems. People in chemistry use variational technique with billion of parameters with no issue... you just have to use the right chemistry motivated Ansatze, and there have been a lot of work developed on that. I don't see much potential of VQA outside of quantum chemistry problems tho... $\endgroup$
    – KAJ226
    Commented Jun 14, 2021 at 14:31
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    $\begingroup$ @narip These reviews might be helpful: arxiv.org/pdf/1808.10402.pdf and arxiv.org/pdf/1812.09976.pdf Also note that with $n$ qubits, you have access to a wavefunction in dimension of $2^n$... this is what make QC promising in this aspect. The reviews I linked will talked about how you design Ansatze that can promise good solution to the electronic structure problem... but these reviews are rather old... there have been a lot more development into this area since. $\endgroup$
    – KAJ226
    Commented Jun 14, 2021 at 16:57
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    $\begingroup$ Adding to the links @KAJ226 provided, this paper analyzes some more recents techniques of VQE. $\endgroup$
    – epelaez
    Commented Jun 14, 2021 at 18:11
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    $\begingroup$ I highly recommend this lecture that discusses a recent paper that tries to answer your question youtube.com/watch?v=aU8XBjG5tAw $\endgroup$ Commented Jun 29, 2021 at 17:13


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