Paper:
Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network.

Review:
Neural Network Cost Landscapes as Quantum States
The authors describe a method where a deep learning framework can be quantised, this is done by considering the two state form of a Bloch sphere/qubit and mapping binary neural network. onto the quantum object creating a quantum binary neural network
I have to say I liked the paper, it is indeed novel and I haven’t seen this anywhere else. More then that, it addresses the quantum aspects of deep learning which has only recently started getting so much attention rather the regular machine learning algorithms. And such I think it’s a good fit for ICLR.
With that I have a few concerns/ nitpicking issues I would like the authors to address if possible
1. While authors show basically a discreet network (much like Soudry’s work) there has also been recently a show of continues variable networks (https://arxiv.org/pdf/1806.06871.pdf), how does your scaling compare to that ? Could one think of this is the continuum limit (albeit you showed a *very* small system) of your model ?
2. As a general style remark there is a lot of introduction on quantum information and I wondering if authors could just reference classical text such as Isaac Chuang, Michael Nielsen or for the CS flavour Classical and Quantum Computation  ? I would have liked to see all 3.1,3.2 maybe in an appendix and a lot more details on the experiments and setup for example 
3. At the end of section 3.2 authors mention the lack of correspondence principle in some quantum systems, I would be happy for a refinement in the aspect of quantum computing that is true and also in general quantum mechanics but there is a huge body of work and an entire field dedicated to just that, settling the difference in correspondence principle and it’s meaning (for example Chaos and the semiclassical limit of quantum mechanics (is the moon there when somebody looks?) by Michael Berry. While this is defiantly far from a deal breaker I would be happy for a bit more clarification on subtle difference. My guess is that authors are referring to the fact that an essential part of quantum computing is the lack of correspondence that can also be taken advantage of for quantum parallelism/ quantum speed ups ? Same for the last paragraph of 3.1.
4. In the method section  all of this procedure is described for a fault tolerant machine, can you say something about coupling to error correction codes for near term quantum devices ?
5. On the same note, there is a feeling that non linearities are swept under the rug, do you have a hunch how can one use non linear activation functions ? (General question, you don’t really have to answer and can take the fifth )
6. In the problem statement (4.2)  x is in fact the binary representation of the qubit state ?
7. In your method Fig. 2, should there be some sort of measurements ?
8. Can you elaborate what exactly goes into the U gates and how are they constructed in Fig.2 ? Or is it some  oracle model that can do all the actions 
9. You report a quadratic speedup, is there some relationship to random walk  is this in fact a case of a RW search over the parameter space ?