Reconstructing quantum states with generative models

Abstract

A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an experimentally friendly method for density matrix reconstruction based on deep neural-network generative models. The learning procedure comes with a built-in approximate certificate of the reconstruction and makes no assumptions on the state under scrutiny, making it both reliable and unconditional. It can efficiently handle a broad class of complex systems including prototypical states in quantum information, as well as ground states of local spin models common to condensed matter physics. The key insight is to reduce the state tomography task to an unsupervised learning problem of the statistics of an informationally complete set of quantum measurements. This constitutes a modern machine learning approach to the validation of large quantum devices, which may prove relevant as a neural-network ansatz over mixed states suitable for variational optimization.

29 pages, 9 figures. Includes appendix. Some typos in the description of the POVMs have been fixed. The numerically generated measurements, the implementation of the generative models, and the code to numerically generate the data sets used in this manuscript are available at https://github.com/carrasqu/POVM_GENMODEL

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