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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: (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:
Editor-in-charge assigned

Submission & Refereeing History

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Submission 2008.01039v3 on 22 February 2021

Reports on this Submission

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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