Supervised Learning with Quantum Computers by Maria Schuld & Francesco Petruccione

Author:Maria Schuld & Francesco Petruccione
Language: eng
Format: epub
ISBN: 9783319964249
Publisher: Springer International Publishing

5.1 Basis Encoding

Assume we are given a binary dataset where each pattern is a binary string of the form with for . We can prepare a superposition of basis states that qubit-wise correspond to the binary input patterns,

(5.1)

For example, given two binary inputs , where features are encoded with a binary precision of , we can write them as binary patterns . These patterns can be associated with basis states , and the full data superposition reads

(5.2)

The amplitude vector corresponding to State (5.1) has entries for basis states that are associated with a binary pattern from the dataset, and zero entries otherwise. For Eq. (5.2), the amplitude vector is given by

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