Friday, Aug 31, 1:30pm, 6C-442
The Quantum Boltzmann Machine
Bert Kappen,
Donders Institute, Radboud University Nijmegen,
Gatsby Computational Neuroscience Unit UCL London
We propose to generalise classical maximum likelihood learning 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 learning a
quantum Hamiltonian from quantum statistics using this approach. For the
anti-ferromagnetic Heisenberg and XYZ model we recover the true ground
state wave function and Hamiltonian. The second contribution is to apply
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
cases. We give an example how the QBM can learn a strongly non-linear
problem such as the parity problem. The solution shows entanglement,
quantified by the entanglement entropy.
https://arxiv.org/abs/1803.11278
Bio:
http://www.snn.ru.nl/~bertk/biograph2
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