  Quantum machine learning (QML) leverages quantum states for data encoding,
with key approaches being explicit models that use parameterized quantum
circuits and implicit models that use quantum kernels. Implicit models often
have lower training errors but face issues such as overfitting and high
prediction costs, while explicit models can struggle with complex training and
barren plateaus. We propose a quantum-classical hybrid algorithm to create an
explicit quantum surrogate (EQS) for trained implicit models. This involves
diagonalizing an observable from the implicit model and constructing a
corresponding quantum circuit using an extended automatic quantum circuit
encoding (AQCE) algorithm. The EQS framework reduces prediction costs,
mitigates barren plateau issues, and combines the strengths of both QML
approaches.
