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SUMMARY:Joint CMSP/QLS Seminar: The Quantum Boltzmann Machine
DTSTART;VALUE=DATE-TIME:20181115T130000Z
DTEND;VALUE=DATE-TIME:20181115T140000Z
DTSTAMP;VALUE=DATE-TIME:20190219T231223Z
UID:indico-event-8773@ictp.it
DESCRIPTION:\n We propose to generalise classical maximum likelihood learn
ing to density matrices. As the objective function\, we propose a quantum
likelihood that is related to the cross entropy between density matrices.
We apply this learning criterion to the quantum Boltzmann machine (QBM)\,
previously proposed by Amin et al.. We demonstrate for the first time lear
ning a quantum Hamiltonian from quantum statistics using this approach. Fo
r the anti-ferromagnetic Heisenberg and XYZ model we recover the true grou
nd state wave function and Hamiltonian. The second contribution is to appl
y quantum learning to learn from classical data. Quantum learning uses in
addition to the classical statistics also quantum statistics for learning.
These statistics may violate the Bell inequality\, as in the quantum case
. Maximizing the quantum likelihood yields results that are significantly
more accurate than the classical maximum likelihood approach in several ca
ses. We give an example how the QBM can learn a strongly non-linear proble
m such as the parity problem. The solution shows entanglement\, quantified
by the entanglement entropy.https://arxiv.org/abs/1803.11278\n \n \n\
nhttp://indico.ictp.it/event/8773/
LOCATION:ICTP Central Area\, 2nd floor\, old SISSA building
URL:http://indico.ictp.it/event/8773/
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