  A key component of a quantum machine learning model operating on classical
inputs is the design of an embedding circuit mapping inputs to a quantum state.
This paper studies a transfer learning setting in which classical-to-quantum
embedding is carried out by an arbitrary parametric quantum circuit that is
pre-trained based on data from a source task. At run time, a binary quantum
classifier of the embedding is optimized based on data from the target task of
interest. The average excess risk, i.e., the optimality gap, of the resulting
classifier depends on how (dis)similar the source and target tasks are. We
introduce a new measure of (dis)similarity between the binary quantum
classification tasks via the trace distances. An upper bound on the optimality
gap is derived in terms of the proposed task (dis)similarity measure, two
R$\'e$nyi mutual information terms between classical input and quantum
embedding under source and target tasks, as well as a measure of complexity of
the combined space of quantum embeddings and classifiers under the source task.
The theoretical results are validated on a simple binary classification
example.
