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In Iris Cong et. al. (2019) they propose a Quantum Convolutional Neural Network that utilizes mid-circuit measurements to control an error-correcting ansatz $V_j$. This is the equivalent of a pooling layer and is used to reduce the dimensionality of the state.

I'm trying to wrap my head around it, and I have a few questions:

  • What's the motivation for error correction in this context, and why should it improve the results?
  • It's unclear from the paper which $V_j$ pooling ansatz they use, but I found two implementations using two different schemas this and this. Is there a reason why those specific ansatz are used? And how can I select one for my specific application?

Any suggestions or pointers to further material are welcome.

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  • $\begingroup$ To answer your first bullet point - error correction is always useful in all contexts of quantum algorithms because in principle they eliminate noise in the system and causes the output of your quantum circuits to be more robust $\endgroup$ Nov 29, 2023 at 19:38
  • $\begingroup$ Thanks for the comment, I agree that error correction is beneficial on its own. My question, however, was more related to the correction of non-determinism. In section "QCNN Circuit Model" they mention how "such a QCNN does not generally produce deterministic measurement outcomes" and how they use measurements to apply correction unitaries. Do you have any comments on that? $\endgroup$ Dec 1, 2023 at 15:21
  • $\begingroup$ So most quantum circuits (QCNN or otherwise) do not produce deterministic measurement outcomes. This is because quantum circuits produce states that represent probability distributions. So with quantum circuits you either a) want to create a specific distribution that you then sample from or b) want find a deterministic value so you create a distribution with as much weight as possible on that value with hopefully negligible weights on other values. In both these cases, added noise messes this up and creates a different distribution than the one you want. Error correction can prevent that. $\endgroup$ Dec 2, 2023 at 21:32
  • $\begingroup$ I see, it's clearer now. My doubt then is whether in this paper they use correction as a way of removing non-determinism arising from the traced-out qubits, or merely as a way of reducing noise. $\endgroup$ Dec 11, 2023 at 14:55
  • $\begingroup$ Hmm OK I'm a bit confused now. I'm almost certain that they don't use error correction in the paper. Do they maybe use another technique that has a similar sounding name? Could you point to the part of the paper that discusses whichever error reduction technique they are mentioning? $\endgroup$ Dec 20, 2023 at 13:53

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