The goal of the quantum learner is to learn a unitary ${\mathit{V}}_{{x}}$ that can accurately predict the output of the target unitary ${\mathit{U}}_{{x}}$ under a fixed observable $\mathit{O}$, where the subscript ${x}$ refers to the quantum system in which the operator $\mathit{O}$ act on. The learning process is as follows. (a) A total number of $\mathit{N}$ entangled bipartite quantum states living in Hilbert space ${\mathcal{H}}_{{x}}\otimes {\mathcal{H}}_{\mathcal{R}}$ ($\mathcal{R}$ denotes the reference system) are taken as inputs, dubbed entangled data. (b) Quantum learner proceeds incoherent learning. The entangled data separately interacts with the target unitary ${\mathit{U}}_{{x}}$ (agnostic) and the candidate hypothesis ${\mathit{V}}_{{x}}$ extracted from the same Hypothesis set $\mathit{H}$. (c) The quantum learner is restricted to leverage the finite measured outcomes of the observable O on the output states of ${\mathit{U}}_{{x}}$ and ${\mathit{V}}_{{x}}$ to conduct learning. (d) A classical computer is exploited to infer ${\mathit{V}}^{\mathit{*}}$ that best estimates ${\mathit{U}}_{{x}}$ according to the measurement outcomes. For example, in the case of variational quantum algorithms, the classical computer serves as an optimizer to update the tunable parameters of the ansatz ${\mathit{V}}_{{x}}$ . (e) The learned unitary ${\mathit{V}}^{\mathit{*}}$ is used to predict the output of unseen quantum states in Hilbert space ${\mathcal{H}}_{{x}}$ under the evolution of the target unitary ${\mathit{U}}_{{x}}$ and the measurement of $\mathit{O}$. A large Schmidt rank $\mathit{r}$ can enhance the prediction accuracy when combined with a large number of measurements $\mathit{m}$, but may lead to a decrease in accuracy when m is small.