  Data representation is crucial for the success of machine learning models. In
the context of quantum machine learning with near-term quantum computers,
equally important considerations of how to efficiently input (encode) data and
effectively deal with noise arise. In this work, we study data encodings for
binary quantum classification and investigate their properties both with and
without noise. For the common classifier we consider, we show that encodings
determine the classes of learnable decision boundaries as well as the set of
points which retain the same classification in the presence of noise. After
defining the notion of a robust data encoding, we prove several results on
robustness for different channels, discuss the existence of robust encodings,
and prove an upper bound on the number of robust points in terms of fidelities
between noisy and noiseless states. Numerical results for several example
implementations are provided to reinforce our findings.
