2,206 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
Characterizing the quantum field theory vacuum using temporal Matrix Product states
In this paper we construct the continuous Matrix Product State (MPS)
representation of the vacuum of the field theory corresponding to the
continuous limit of an Ising model. We do this by exploiting the observation
made by Hastings and Mahajan in [Phys. Rev. A \textbf{91}, 032306 (2015)] that
the Euclidean time evolution generates a continuous MPS along the time
direction. We exploit this fact, together with the emerging Lorentz invariance
at the critical point in order to identify the matrix product representation of
the quantum field theory (QFT) vacuum with the continuous MPS in the time
direction (tMPS). We explicitly construct the tMPS and check these statements
by comparing the physical properties of the tMPS with those of the standard
ground MPS. We furthermore identify the QFT that the tMPS encodes with the
field theory emerging from taking the continuous limit of a weakly perturbed
Ising model by a parallel field first analyzed by Zamolodchikov.Comment: The results presented in this paper are a significant expansion of
arXiv:1608.0654
Tensor networks for interpretable and efficient quantum-inspired machine learning
It is a critical challenge to simultaneously gain high interpretability and
efficiency with the current schemes of deep machine learning (ML). Tensor
network (TN), which is a well-established mathematical tool originating from
quantum mechanics, has shown its unique advantages on developing efficient
``white-box'' ML schemes. Here, we give a brief review on the inspiring
progresses made in TN-based ML. On one hand, interpretability of TN ML is
accommodated with the solid theoretical foundation based on quantum information
and many-body physics. On the other hand, high efficiency can be rendered from
the powerful TN representations and the advanced computational techniques
developed in quantum many-body physics. With the fast development on quantum
computers, TN is expected to conceive novel schemes runnable on quantum
hardware, heading towards the ``quantum artificial intelligence'' in the
forthcoming future.Comment: 12 pages, 3 figure
- …