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QuCumber: wavefunction reconstruction with neural networks

by Matthew J. S. Beach, Isaac De Vlugt, Anna Golubeva, Patrick Huembeli, Bohdan Kulchytskyy, Xiuzhe Luo, Roger G. Melko, Ejaaz Merali, Giacomo Torlai

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Submission summary

Authors (as registered SciPost users): Roger Melko · Ejaaz Merali
Submission information
Preprint Link:  (pdf)
Date accepted: 2019-06-05
Date submitted: 2019-05-17 02:00
Submitted by: Melko, Roger
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Artificial Intelligence
  • Quantum Physics
Approach: Computational


As we enter a new era of quantum technology, it is increasingly important to develop methods to aid in the accurate preparation of quantum states for a variety of materials, matter, and devices. Computational techniques can be used to reconstruct a state from data, however the growing number of qubits demands ongoing algorithmic advances in order to keep pace with experiments. In this paper, we present an open-source software package called QuCumber that uses machine learning to reconstruct a quantum state consistent with a set of projective measurements. QuCumber uses a restricted Boltzmann machine to efficiently represent the quantum wavefunction for a large number of qubits. New measurements can be generated from the machine to obtain physical observables not easily accessible from the original data.

List of changes

Response to report 1 "Requested Changes"

> 1- Add a small snippet on Gibbs sampling (in Glossary)

This has been added.

> 2- Typo on page 5: we have demonstrated to -> the


Response to report 2 "Requested Changes"

> 1. Define precisely (with equations not words) the mathematical problem solved by QuCumber.
> What is the RBM trial wavefuntion? What is the cost function which is optimized?

The mathematical definitions are described in a precise and self-contained way, largely in the Glossary. The trial wavefunction (the marginal distribution) and the cost function (KL divergence) are defined in equation (24) and (23) respectively. We have now referred to these equations in the main text for increased clarity and readability.

> 2. Add a short discussion of the applications of QuCumber (see the physics questions above).

We have added to the introduction and conclusion in this regard.

> 3. Define the entanglement entropy. Define its relation to the SWAP operator.
> It is also a bit strange that no actual data is shown for this quantity.

We have defined the relative quantities and included a new plot in section 2.3.3

> 4. In the introduction, clearly list the articles that explain QuCumber theory as well as those where QuCumber
> has been used to solve a physics problem.

QuCumber theory is almost completely self contained in References 5 and 6, now clearly cited in the last paragraph of the introduction. In addition, we have cited the new review [28] in the introduction which contains an extensive review of RBM theory and applications quantum physics problems.

Published as SciPost Phys. 7, 009 (2019)

Reports on this Submission

Anonymous Report 2 on 2019-5-20 (Invited Report)


The manuscript can be published in its current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
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  • grammar: -

Report 1 by Everard van Nieuwenburg on 2019-5-19 (Invited Report)


The authors have added the pieces I thought would make the submission more complete, and I remain with my conclusion that it is suitable and ready for SciPost.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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