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Spiking neuromorphic chip learns entangled quantum states
by Stefanie Czischek, Andreas Baumbach, Sebastian Billaudelle, Benjamin Cramer, Lukas Kades, Jan M. Pawlowski, Markus K. Oberthaler, Johannes Schemmel, Mihai A. Petrovici, Thomas Gasenzer, Martin Gärttner
Submission summary
As Contributors:  Andreas Baumbach · Stefanie Czischek 
Arxiv Link:  https://arxiv.org/abs/2008.01039v3 (pdf) 
Date submitted:  20210222 14:29 
Submitted by:  Czischek, Stefanie 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approaches:  Experimental, Computational 
Abstract
The approximation of quantum states with artificial neural networks has gained a lot of attention during the last years. Meanwhile, analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neuralnetwork architectures for the profit of generative applications. This encourages employing such hardware systems as platforms for simulations of quantum systems. Here we report on the realization of a prototype using the latest spikebased BrainScaleS hardware allowing us to represent fewqubit maximally entangled quantum states with high fidelities. Extracted Bell correlations for pure and mixed twoqubit states convey that nonclassical features are captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.
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Reports on this Submission
Anonymous Report 1 on 2021319 Invited Report
Strengths
Interdisciplinary work connecting neuromorphic chips and representations of quantum states.
Weaknesses
Easily accessible explanation of the functionality of the neurmorphic chip missing.
Report
The paper presents an approach to represent quantum states with the help of a neural network that is implemented in a neuromorphic chip in hardware. The concept shares some similarities with numerical approaches that use software coded neural networks for this applications, see e.g. [29,30], but uses a neural network that is implemented in hardware.
There are some aspects that should be clarified better.
1) As I understand it, the expansion coefficients of a quantum state in a chosen bases are here represented by neurons of the neural network. What is not clear to me is how phases of the coefficients are taken into account. The expansion coefficients are generally complex numbers. However for a physical implementation of the network I would expect real coefficients. is this expectation too naive? How is this taken care of? In this context I also not a misleading (even wrong) statement in the introduction "any quantum state can be mapped to a probability distribution". This is in conflict with the notion that such mapping can't hold for nonclassical states, where e.g. the Wigner function becomes negative. An example are Fock states.
2) The connections and differences to approaches with software coded restricted Boltzmann machines as discussed in refs [29,30] should be discussed in more detail. In this context I also note that the software coded restricted Boltzmann machines have also been developed for mixed states as are considered here. I also note that the network isn't called restricted Boltzmann machine here although this is the usual name for it.
3) My understanding is that the employed chip works purely classically. This should be stated explicitly.
4) In addition, for the interdisciplinary nature of the work, an explanation of the employed chip addressed to laymen would be highly appreciated.