877 research outputs found
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
Mainstream machine-learning techniques such as deep learning and
probabilistic programming rely heavily on sampling from generally intractable
probability distributions. There is increasing interest in the potential
advantages of using quantum computing technologies as sampling engines to speed
up these tasks or to make them more effective. However, some pressing
challenges in state-of-the-art quantum annealers have to be overcome before we
can assess their actual performance. The sparse connectivity, resulting from
the local interaction between quantum bits in physical hardware
implementations, is considered the most severe limitation to the quality of
constructing powerful generative unsupervised machine-learning models. Here we
use embedding techniques to add redundancy to data sets, allowing us to
increase the modeling capacity of quantum annealers. We illustrate our findings
by training hardware-embedded graphical models on a binarized data set of
handwritten digits and two synthetic data sets in experiments with up to 940
quantum bits. Our model can be trained in quantum hardware without full
knowledge of the effective parameters specifying the corresponding quantum
Gibbs-like distribution; therefore, this approach avoids the need to infer the
effective temperature at each iteration, speeding up learning; it also
mitigates the effect of noise in the control parameters, making it robust to
deviations from the reference Gibbs distribution. Our approach demonstrates the
feasibility of using quantum annealers for implementing generative models, and
it provides a suitable framework for benchmarking these quantum technologies on
machine-learning-related tasks.Comment: 17 pages, 8 figures. Minor further revisions. As published in Phys.
Rev.
Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
Machine learning has the potential to become an important tool in quantum
error correction as it allows the decoder to adapt to the error distribution of
a quantum chip. An additional motivation for using neural networks is the fact
that they can be evaluated by dedicated hardware which is very fast and
consumes little power. Machine learning has been previously applied to decode
the surface code. However, these approaches are not scalable as the training
has to be redone for every system size which becomes increasingly difficult. In
this work the existence of local decoders for higher dimensional codes leads us
to use a low-depth convolutional neural network to locally assign a likelihood
of error on each qubit. For noiseless syndrome measurements, numerical
simulations show that the decoder has a threshold of around when
applied to the 4D toric code. When the syndrome measurements are noisy, the
decoder performs better for larger code sizes when the error probability is
low. We also give theoretical and numerical analysis to show how a
convolutional neural network is different from the 1-nearest neighbor
algorithm, which is a baseline machine learning method
Unsupervised Generative Modeling Using Matrix Product States
Generative modeling, which learns joint probability distribution from data
and generates samples according to it, is an important task in machine learning
and artificial intelligence. Inspired by probabilistic interpretation of
quantum physics, we propose a generative model using matrix product states,
which is a tensor network originally proposed for describing (particularly
one-dimensional) entangled quantum states. Our model enjoys efficient learning
analogous to the density matrix renormalization group method, which allows
dynamically adjusting dimensions of the tensors and offers an efficient direct
sampling approach for generative tasks. We apply our method to generative
modeling of several standard datasets including the Bars and Stripes, random
binary patterns and the MNIST handwritten digits to illustrate the abilities,
features and drawbacks of our model over popular generative models such as
Hopfield model, Boltzmann machines and generative adversarial networks. Our
work sheds light on many interesting directions of future exploration on the
development of quantum-inspired algorithms for unsupervised machine learning,
which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page:
https://congzlwag.github.io/UnsupGenModbyMPS
Quantum Approaches to Data Science and Data Analytics
In this thesis are explored different research directions related to both the use of classical data analysis techniques for the study of quantum systems and the employment of quantum computing to speed up hard Machine Learning task
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