[en] The connection between the maximum entropy (MaxEnt) formalism and restricted Boltzmann machines (RBMs) is natural as both give rise to a Boltzmann-like distribution with constraints enforced by Lagrange multipliers, which correspond to RBM parameters. We integrate RBMs into quantum state tomography by using them as probabilistic models to approximate quantum states while satisfying MaxEnt constraints. Additionally, we employ polynomially efficient quantum sampling techniques to enhance RBM training, enabling scalable and high-fidelity quantum state reconstruction. This approach provides a computationally efficient framework for applying RBMs to MaxEnt-based quantum tomography. Furthermore, our method applies to the general and previously unaddressed case of reconstructing arbitrary mixed quantum states from incomplete and potentially noncommuting sets of expectations of observables while still ensuring maximal entropy.
Disciplines :
Chemistry
Author, co-author :
Singh, Vinit; Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27606, United States
Gupta, Rishabh; Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
Sajjan, Manas; Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27606, United States
Remacle, Françoise ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique
Levine, Raphael D; The Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Kais, Sabre ; Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27606, United States
Language :
English
Title :
Maximal Entropy Formalism and the Restricted Boltzmann Machine.
S.K. would like to acknowledge that this material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Energy Frontier Research Centers program under Award Number DE-SC0025620.
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