Universal discriminative quantum neural networks
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.
 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.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Universal discriminative quantum neural networks
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.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 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.
assistant
 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.