9,724 research outputs found
Quantum kernels with squeezed-state encoding for machine learning
Kernel methods are powerful for machine learning, as they can represent data
in feature spaces that similarities between samples may be faithfully captured.
Recently, it is realized that machine learning enhanced by quantum computing is
closely related to kernel methods, where the exponentially large Hilbert space
turns to be a feature space more expressive than classical ones. In this paper,
we generalize quantum kernel methods by encoding data into continuous-variable
quantum states, which can benefit from the infinite-dimensional Hilbert space
of continuous variables. Specially, we propose squeezed-state encoding, in
which data is encoded as either in the amplitude or the phase. The kernels can
be calculated on a quantum computer and then are combined with classical
machine learning, e.g. support vector machine, for training and predicting
tasks. Their comparisons with other classical kernels are also addressed.
Lastly, we discuss physical implementations of squeezed-state encoding for
machine learning in quantum platforms such as trapped ions.Comment: 5 pages, 4 figure
Quantum Kerr Learning
Quantum machine learning is a rapidly evolving field of research that could
facilitate important applications for quantum computing and also significantly
impact data-driven sciences. In our work, based on various arguments from
complexity theory and physics, we demonstrate that a single Kerr mode can
provide some "quantum enhancements" when dealing with kernel-based methods.
Using kernel properties, neural tangent kernel theory, first-order perturbation
theory of the Kerr non-linearity, and non-perturbative numerical simulations,
we show that quantum enhancements could happen in terms of convergence time and
generalization error. Furthermore, we make explicit indications on how
higher-dimensional input data could be considered. Finally, we propose an
experimental protocol, that we call \emph{quantum Kerr learning}, based on
circuit QED.Comment: 20 pages, many figures. v2: significant updates, author adde
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