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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/2008.01039v5 (pdf)
Date accepted: 2021-12-16
Date submitted: 2021-10-26 15:01
Submitted by: Czischek, Stefanie
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Neural and Evolutionary Computing
  • Quantum Physics
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 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. Bell correlations of pure and mixed two-qubit states are well captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.

Published as SciPost Phys. 12, 039 (2022)



Author comments upon resubmission

We thank the editor and the referees for considering our revised manuscript. In our revised manuscript, which we resubmit herewith, we have addressed the concerns of the second referee. We are convinced that our paper now meets the acceptance criteria of SciPost Physics. Below we provide a point-by-point response to the referee reports.

*Reply to Report 1*

We thank the referee for his positive feedback and for suggesting the publication of our manuscript.

*Reply to Report 2*

We thank the referee for the positive evaluation of our manuscript and for pointing out the ambiguity which could be seen in the statement (on p. 9) that our work is “demonstrating that intrinsic quantum features can be captured by a classical spiking network”. We indeed do not mean to imply that the classical neuromorphic system is subject to genuine quantum correlations itself. To make clearer that the hardware rather encodes entangled quantum states, we rewrote the sentence cited by the referee, as well as similar formulations in the text, as detailed in the list of changes.

List of changes

- Last sentence of the abstract, p. 1:
Replace “Extracted Bell correlations for pure and mixed two-qubit states convey that non-classical features are captured by the analog hardware, …” by “Bell correlations of pure and mixed two-qubit states are well captured by the analog hardware, …”

- Last sentence of Section 1, p. 2:
Replace “With this substrate, we demonstrate an approximate representation of quantum states with classical spiking neural networks that is sufficiently precise for encoding genuine quantum correlations.” by “With this substrate, we demonstrate an approximate representation of quantum states with classical spiking neural networks that is sufficiently precise for encoding states with genuine quantum correlations.”

- Third paragraph of Section 3, p. 6:
Replace “The correlations encoded by the trained spiking network clearly exceed the classicality bound …” by “The correlations in the quantum states encoded as probability distributions by the trained spiking network clearly exceed the classicality bound …”

- First paragraph of Section 6, p. 9:
Replace “In particular non-classical Bell correlations can be encoded faithfully, demonstrating that intrinsic quantum features can be captured by a classical spiking network.” by “In particular states with non-classical Bell correlations can be encoded faithfully, demonstrating that the representation of quantum states on a classical spiking network can capture their intrinsic quantum features.”

Submission & Refereeing History

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Resubmission 2008.01039v5 on 26 October 2021

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