Maximal Entropy Formalism and the Restricted Boltzmann Machine

• URL: http://arxiv.org/abs/2504.03634v1
• Date: Fri, 04 Apr 2025 17:57:20 GMT
• Title: Maximal Entropy Formalism and the Restricted Boltzmann Machine
• Authors: Vinit Singh, Rishabh Gupta, Manas Sajjan, Francoise Remacle, Raphael D. Levine, Sabre Kais,
• Abstract summary: We introduce Restricted Boltzmann Machines (RBMs) as probabilistic models to approximate quantum states.<n>We employ quantum sampling techniques to enhance RBM training, enabling scalable and high-fidelity quantum state reconstruction.<n>Our method applies to the general and previously unaddressed case of reconstructing arbitrary mixed quantum states from incomplete and potentially non-commuting sets of expectations.
• Score: 1.7563879056963012
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 corresponds to RBM parameters. We integrate RBMs into quantum state tomography (QST) 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 non-commuting sets of expectations of observables while still ensuring maximal entropy.

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