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Neural Network Quantum State Tomography.

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A Quantum Calculator Used for Many-body Eigenstate Reconstruction

QuCumber is a program that reconstructs an unknown quantum wavefunction from a set of measurements. The measurements should consist of binary counts; for example, the occupation of an atomic orbital, or angular momentum eigenvalue of a qubit. These measurements form a training set, which is used to train a stochastic neural network called a Restricted Boltzmann Machine. Once trained, the neural network is a reconstructed representation of the unknown wavefunction underlying the measurement data. It can be used for generative modelling, i.e. producing new instances of measurements, and to calculate estimators not contained in the original data set.

QuCumber is developed by the Perimeter Institute Quantum Intelligence Lab (PIQuIL).


QuCumber implements unsupervised generative modelling with a two-layer RBM. Each layer is a number of binary stochastic variables (with values 0 or 1). The size of the visible layer corresponds to the input data, i.e. the number of qubits. The size of the hidden layer is a hyperparameter, varied to systematically control representation error.

Currently, quantum state reconstruction/tomography can be performed on both pure and mixed states. Pure state reconstruction can be further broken down into positive or complex wavefunction reconstruction. In the case of a positive wavefunction, data is only required in one basis. For complex wavefunctions as well as mixed states, measurement data in additional bases will be required to train the state.


Documentation can be found here.

See "QuCumber: wavefunction reconstruction with neural networks"

Getting Started

These instructions will get you a copy of the project up and running on your local machine for development and testing purposes.


If you're on Windows, you will have to install PyTorch manually; instructions can be found on their website:

You can install the latest stable version of QuCumber, along with its dependencies, using pip:

pip install qucumber

If, for some reason, pip fails to install PyTorch, you can find installation instructions on their website. Once that's done you should be able to install QuCumber through pip as above.

QuCumber supports Python 3.6 and newer stable versions.

Installing the bleeding-edge version

If you'd like to install the most upto date, but potentially unstable version, you can clone the repository's master branch and then build from source like so:

git clone
cd ./QuCumber
python install


Please read for details on how to contribute to the project, and the process for submitting pull requests to us.


QuCumber is licensed under the Apache License Version 2.0, this includes almost all files in this repo. However, some miscellaneous files may be licensed differently. See LICENSE for more details.


    title={{QuCumber: wavefunction reconstruction with neural networks}},
    author={Matthew J. S. Beach and Isaac De Vlugt and Anna Golubeva and Patrick Huembeli and Bohdan Kulchytskyy and Xiuzhe Luo and Roger G. Melko and Ejaaz Merali and Giacomo Torlai},
    journal={SciPost Phys.},


  • We thank M. Albergo, G. Carleo, J. Carrasquilla, D. Sehayek, and L. Hayward Sierens for many helpful discussions.

  • We thank the Perimeter Institute for the continuing support of PIQuIL.

  • Thanks to Nick Mercer for creating our awesome logo. You can check out more of Nick's work by visiting his portfolio on Behance!

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