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Hartree-Fock on a superconducting qubit quantum computer

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Re: Hartree-Fock on a superconducting qubit quantum computer

#7

I cannot find the answer to this anywhere: what algorithms will we actually use the quantum computers for? Please skip Shor's algorithm, I understand this part. What else is there?

I get the impression no-one really knows because the potential capabilities and engineering realities knock up against the limits of what we understand. They are experimental machines that work in a way we barely understand. So maybe something really revolutionary, or maybe just more efficient Netflix recommendations.

Re: Hartree-Fock on a superconducting qubit quantum computer

#9

I cannot find the answer to this anywhere: what algorithms will we actually use the quantum computers for? Please skip Shor's algorithm, I understand this part. What else is there?

I am far from an expert, but as I understand it, Shor's factorization algorithm is a gateway to lots of fast crypto, so it's "enabling technology" for a lot of crypto and number-theoretic applications, not an end-point.

There is also Grover's search algorithm, which can retrieve items from an N-element list with fewer than N operations.

In the quantum chemistry world, there is work underway to build QC circuits that act as models for natural systems, "natively" capturing the exchange and correlation structure. I've seen model Hamiltonians for small molecules, and this work seems to be in that family also.

There are also folks who can do linear algebra on sufficiently sparse, well-conditioned matrices[1].

From what I have read, quantum computers really are very different, a good way to think about them is as super-efficient correlation-finding or correlation-generating machines. Asking "What Von Nuemann algorithm can I put on this?" is the wrong question.

If you can devise a correlation solution to your problem, then a quantum computer will be a good tool for you.

To re-disclaim, I am not an expert, I'm a reasonably technical interested bystander. For me, the "Oh, I get it!" book was Yanofsky, "Quantum Computing for Computer Scientists".

[1] https://en.wikipedia.org/wiki/Quantum_algorithm_for_linear_s...

Re: Hartree-Fock on a superconducting qubit quantum computer

#10

I cannot find the answer to this anywhere: what algorithms will we actually use the quantum computers for? Please skip Shor's algorithm, I understand this part. What else is there?

Grover's algorithm provides a quadratic speed up to any brute force search. i.e. from O(N) to O(sqrt(N)).
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