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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

This is not the current version.

Submission summary

As Contributors: Andreas Baumbach · Stefanie Czischek
Arxiv Link: (pdf)
Date submitted: 2021-02-22 14:29
Submitted by: Czischek, Stefanie
Submitted to: SciPost Physics
Academic field: Physics
  • Neural and Evolutionary Computing
  • Quantum Physics
Approaches: Experimental, Computational


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 neural-network 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 spike-based BrainScaleS hardware allowing us to represent few-qubit maximally entangled quantum states with high fidelities. Extracted Bell correlations for pure and mixed two-qubit states convey that non-classical features are captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.

Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission 2008.01039v5 on 26 October 2021

Reports on this Submission

Anonymous Report 2 on 2021-7-5 (Invited Report)


1) Relevant first step in the simulation of quantum states using neuromorphic hardware.

2) Very clear and exhaustive presentation of the results.


1) The statements on the future developments of neuromorphic hardware are not always clearly justified.


I have read the paper with interest. The idea is innovative and the overall implementation and description of the experiment is commendable. I am certainly inclined to recommend the paper for publication on SciPost Physics. Still, I have some doubts regarding the comparison between the hardware and the software implementations of the algorithm. In section 2 the following statement is made regarding the training algorithm:

"This otherwise prohibitively compute-intensive method was made possible by the accelerated hardware dynamics and allows a much better approximation of the DKL gradient than the more conventional contrastive divergence update scheme"

I find this statement rather vague as no quantitative comparison between the hardware and software implementations is made in this perspective. A somehow more detailed discussion of this issue is given in Appendix D, but I still find this discussion insufficient. As far as I understood the authors claim that the hardware allows to optimally sample from the complete distributions and, therefore, the sampling does not need to be approximated as in the conventional contrastive divergence approach.

However, when an explicit comparison between the hardware and software implementations is presented (in Appendix B) no comment is made on the relevance of such approximation (which I believe is not made in the software implementation discussed in Sec. B) . I believe that the paper will benefit by a more extensive discussion on the relevance of the contrastive divergence approximation and on the benefit granted by the possibility of avoiding it in the hardware realisation.

Requested changes

1) Extend the discussion on the contrastive divergence approximation and connect this discussion with the specific comparison between hardware and software implementations made in Appendix B.

  • validity: good
  • significance: good
  • originality: high
  • clarity: top
  • formatting: good
  • grammar: excellent

Anonymous Report 1 on 2021-3-19 (Invited Report)


Interdisciplinary work connecting neuromorphic chips and representations of quantum states.


Easily accessible explanation of the functionality of the neurmorphic chip missing.


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 non-classical 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.

  • validity: good
  • significance: good
  • originality: high
  • clarity: ok
  • formatting: excellent
  • grammar: excellent

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