  Entanglement purification is a crucial technique for promising the effective
entanglement channel in noisy large-scale quantum networks, yet complicated in
designing protocols in multi-degree of freedom (DoF). To execute the above
tasks easily and effectively, developing a learning framework for designing the
entanglement purification with multi-DoF is a promising way and still an open
research question. Inspired by variational quantum circuit (VQC) with
remarkable advantage in learning optimal quantum operations with near-term
quantum devices, in this paper we propose an effective VQC framework for the
entanglement purification in multi-DoF and exploit it to learn the optimal
purification protocols of the objective function which are based on
postselection. By properly introducing additional circuit lines for
representing each of the ancillary DoFs of all the particles, e.g., space and
time, the parametrized quantum circuit can effectively simulate scalable
entanglement purification. To verify our framework, the well-known protocols in
linear optics are learned well with alternative operations in low-depth quantum
circuit. Moreover, we simulate the multipair cases with multi-DoF to show the
scalability and discover one-round protocols. Our work provides an effective
way for exploring the entanglement purification protocols in multi-DoF and
multipair with near-term quantum devices.
