5,550 research outputs found
Entanglement-guided architectures of machine learning by quantum tensor network
It is a fundamental, but still elusive question whether the schemes based on
quantum mechanics, in particular on quantum entanglement, can be used for
classical information processing and machine learning. Even partial answer to
this question would bring important insights to both fields of machine learning
and quantum mechanics. In this work, we implement simple numerical experiments,
related to pattern/images classification, in which we represent the classifiers
by many-qubit quantum states written in the matrix product states (MPS).
Classical machine learning algorithm is applied to these quantum states to
learn the classical data. We explicitly show how quantum entanglement (i.e.,
single-site and bipartite entanglement) can emerge in such represented images.
Entanglement characterizes here the importance of data, and such information
are practically used to guide the architecture of MPS, and improve the
efficiency. The number of needed qubits can be reduced to less than 1/10 of the
original number, which is within the access of the state-of-the-art quantum
computers. We expect such numerical experiments could open new paths in
charactering classical machine learning algorithms, and at the same time shed
lights on the generic quantum simulations/computations of machine learning
tasks.Comment: 10 pages, 5 figure
Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpi\'nski gasket
The anisotropic antiferromagnetic Ising model on the fractal Sierpi\'{n}ski
gasket is intensively studied, and a number of exotic properties are disclosed.
The ground state phase diagram in the plane of magnetic field-interaction of
the system is obtained. The thermodynamic properties of the three plateau
phases are probed by exploring the temperature-dependence of magnetization,
specific heat, susceptibility and spin-spin correlations. No phase transitions
are observed in this model. In the absence of a magnetic field, the unusual
temperature dependence of the spin correlation length is obtained with JJ, and an interesting crossover behavior between different
phases at JJ is unveiled, whose dynamics can be described by the
JJ-dependence of the specific heat, susceptibility and spin
correlation functions. The exotic spin-spin correlation patterns that share the
same special rotational symmetry as that of the Sierpi\'{n}ski gasket are
obtained in both the plateau disordered phase and the plateau
partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated
to study the thermodynamics of the fractal Sierpi\'{n}ski gasket with
Heisenberg interactions. We find that the unusual temperature dependence of the
correlation length remains intact in a small quantum fluctuation.Comment: 9 pages, 12 figure
Kosterlitz-Thouless phase transition and reentrance in an anisotropic 3-state Potts model on the generalized Kagome lattice
The unusual reentrant phenomenon is observed in the anisotropic 3-state Potts
model on a gen- eralized Kagome lattice. By employing the linearized tensor
renormalization group method, we find that the reentrance can appear in the
region not only under a partial ordered phase as commonly known but also a
phase without a local order parameter, which is uncovered to fall into the uni-
versality of the Kosterlitz-Thouless (KT) type. The region of the reentrance
depends strongly on the ratios of the next nearest couplings {\alpha} = J2 /|J1
| and {\beta} = J3 /|J1 |. The phase diagrams in the plane of temperature
versus {\beta} for different {\alpha} are obtained. Through massive
calculations, it is also revealed that the quasi-entanglement entropy can be
used to accurately detect the KT transition temperature
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