Theorem demonstrates that CNNs can always be trained on quantum computers | Hacker News Reader

Theorem demonstrates that CNNs can always be trained on quantum computers

discover.lanl.gov

38 pointssizzle9 comments

Slightly unrelated, but does anyone think we'll ever discover a closed-form solution to neural network optimization? If you think about it, the network is known, the initial weights are known, the training data is known, and the objective function is known. All of the work spent "training" is spent computing the solution to an optimization problem that could (theoretically) have a closed-form solution.

Since we can't find general closed form solutions for simpler equations such as 5th order polynomials, general closed form NN solvers (vs optimizers) do not look likely.

However, constraints on the general class of polynomials of 5th order and higher can result in subclasses that are solvable in closed form.

So there may be a long tail of closed form solvable classes of NN architectures waiting to be discovered.

Whether non-trivial closed-form subclasses of neural networks exist, and whether any of those classes is actually useful ... seems an area worth exploring.

Digressing back to qc..

If you look at how Shor's algorithm works, it's more like manipulating some kind of embeded values (that we have no direct access to) eg via Hadamard gates and eventually collapsing the entanglement into the solution.

So maybe we can have something closed-form-ish that solves NN by arranging some q gates some way

Suggested background music: "if I were a rich man" https://youtu.be/j5fCqKbSC7M

If I had a quantum computer, I could do all these wonderful things... it's interesting theoretical research but we do not have the machines yet.

IONQ hitting Stockmarket this month

When does their quantum computer hit the shelves?

You can use it any time you want (on Amazon Braket)

Is it faster to run on the actual hardware or in the simulation mode?

I am very suspicious of free lunches; almost surely this means the expressibility of QCNNs is limited (as opposed to a sufficient depth VQE)?

(Disclaimer: I didn't Google for known results w.r.t. the expressibility of QCNNs)

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