20,932 research outputs found
Exponential data encoding for quantum supervised learning
Reliable quantum supervised learning of a multivariate function mapping
depends on the expressivity of the corresponding quantum circuit and
measurement resources. We introduce exponential-data-encoding strategies that
are hardware-efficient and optimal amongst all non-entangling Pauli-encoded
schemes, which is sufficient for a quantum circuit to express general functions
having very broad Fourier frequency spectra using only exponentially few
encoding gates. We show that such an encoding strategy not only reduces the
quantum resources, but also exhibits practical resource advantage during
training in contrast with known efficient classical strategies when
polynomial-depth training circuits are also employed. When computation
resources are constrained, we numerically demonstrate that even
exponential-data-encoding circuits with single-layer training modules can
generally express functions that lie outside the classically-expressible
region, thereby supporting the practical benefits of such a resource advantage.
Finally, we illustrate the performance of exponential encoding in learning the
potential-energy surface of the ethanol molecule and California's housing
pricesComment: 21 pages, 13 figure
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