Park, Chae-Yeun and Kastoryano, Michael J. (2020). Geometry of learning neural quantum states. Phys. Rev. Res., 2 (2). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2643-1564

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Abstract

Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground-state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learning dynamics. In this paper, we bring to light several hidden details of the algorithm by analyzing the learning landscape. In particular, the spectrum of the quantum Fisher matrix of complex restricted Boltzmann machine states exhibits a universal initial dynamics, but the converged spectrum can dramatically change across a phase transition. In contrast to the spectral properties of the quantum Fisher matrix, the actual weights of the network at convergence do not reveal much information about the system or the dynamics. Furthermore, we identify a measure of correlation in the state by analyzing entanglement in eigenvectors. We show that, generically, the learning landscape modes with least entanglement have largest eigenvalue, suggesting that correlations are encoded in large flat valleys of the learning landscape, favoring stable representations of the ground state.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Park, Chae-YeunUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Kastoryano, Michael J.UNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-332827
DOI: 10.1103/PhysRevResearch.2.023232
Journal or Publication Title: Phys. Rev. Res.
Volume: 2
Number: 2
Date: 2020
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2643-1564
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
MONTE-CARLOMultiple languages
Physics, MultidisciplinaryMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/33282

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