Universal discriminative quantum neural networks

Abstract: Quantum mechanics fundamentally forbids deterministic discrimination of quantum states and processes. However, the ability to optimally distinguish various classes of quantum data is an important primitive in quantum information science. In this work, we trained near-term quantum circuits to classify data represented by quantum states using the Adam stochastic optimization algorithm. This is achieved by iterative interactions of a classical device with a quantum processor to discover the parameters of an unknown non-unitary quantum circuit. This circuit learns to simulate the unknown structure of a generalized quantum measurement, or positive-operator valued measure (POVM), that is required to optimally distinguish possible distributions of quantum inputs. Notably we used universal circuit topologies, with a theoretically motivated circuit design which guaranteed that our circuits can perform arbitrary input-output mappings. Our numerical simulations showed that quantum circuits could be trained to discriminate among various pure and mixed quantum states, exhibiting a trade-off between minimizing erroneous and inconclusive outcomes with comparable performance to theoretically optimal POVMs. We trained the circuit on different classes of quantum data and evaluated the generalization error on unseen quantum data. This generalization power hence distinguishes our work from standard circuit optimization and provides an example of quantum machine learning for a task that has inherently no classical analogue. 

Reviews and author responses:

Authors give a method to perform a full quantum problem of classifying unknown mixed quantum states. This is an important topic but the paper is ok and I think the test case is a bit lacking.

The theory  is sound and the math is good. The only question I have is how does this hold on a real quantum computer such as IBMQ/rigetti quantum computing etc.. or even under a noisy simulator 

Although the paper is sounds and it is a good idea, the presentation is a bit lacking. There are several typos and formatting problems, such as excess spaces and some sort of hex code (9b8d) in the abstract which I am guessing is left over from the NIPS template.
Two other things is that usually in double blind review one should not leave the emails with affiliation and one should anonymize the Acknowledgements as well.

Summary of paper:
The authors partially integrate a neural network into classical approaches to classify the state of a quantum circuit. The model is not actually clear in what it is doing, but there are some trained weights somewhere. They allow for an "uncertainty" prediction by giving one more node than there are classification targets, corresponding to a less-penalized uncertain prediction. They evaluate their model on numerical simulations.

Strengths:
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Weaknesses:
- The neural network architecture is entirely standard with nothing new.
- The paper is poorly written and very hard to follow.
- The focus is almost exclusively on the application, and yet the application is not explained effectively.
- The implication of the results and usefulness is not elaborated.
- The particular contributions are not clear.

Suggested Revisions:
- What is the 9b8d in the first sentence of the abstract?
- "...been developed to address the question [of] whether quantum mechanics..."
- "...for all the dataset[s] in Table 1..."

Unfortunately, while this is interesting work, the authors emails are listed on the first page and the acknowledgments are very revealing. I am a big fan of Google, UCL, and the Royal Society, and this strongly biases my view of the work. 

My biased review:

- the paper is interesting, and should go to another venue. I do not think the authors will get benefit from presenting this work at ICLR (there is a tiny quantum focus).

- how is the cost function justified? I'd be curious to see how the authors derived it. Right now above Eq 2.4 it seems like it is heuristic to balance successful/erroneous/inconclusive rates. If it is a heuristic, the paper should clearly state this. 

- using simple examples of quantum data and quantum states would go a long way towards helping me understand the problem setup (Eq 2.1). It took me a while to grok this.

- The acronym POVM is never defined. 

Meta-review: The paper needs work to improve clarity and strengthen the technical message. Also, the authors broke the policy of anonymous submission which disqualifies the paper.

Decision: rejected-papers