Classification of data with a qudit, a geometric approach
- URL: http://arxiv.org/abs/2307.14060v1
- Date: Wed, 26 Jul 2023 09:13:43 GMT
- Title: Classification of data with a qudit, a geometric approach
- Authors: A. Mandilara, B. Dellen, U. Jaekel, T. Valtinos, D. Syvridis
- Abstract summary: We propose a model for data classification using isolated quantum $d$-level systems or else qudits.
We show that this geometrically inspired qudit model for classification is able to solve nonlinear classification problems using a small number of parameters only and without requiring entangling operations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a model for data classification using isolated quantum $d$-level
systems or else qudits. The procedure consists of an encoding phase where
classical data are mapped on the surface of the qudit's Bloch hyper-sphere via
rotation encoding, followed by a rotation of the sphere and a projective
measurement. The rotation is adjustable in order to control the operator to be
measured, while additional weights are introduced in the encoding phase
adjusting the mapping on the Bloch's hyper-surface. During the training phase,
a cost function based on the average expectation value of the observable is
minimized using gradient descent thereby adjusting the weights. Using examples
and performing a numerical estimation of lossless memory dimension, we
demonstrate that this geometrically inspired qudit model for classification is
able to solve nonlinear classification problems using a small number of
parameters only and without requiring entangling operations.
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