Variational quantum circuit learning of entanglement purification in multiple degrees of freedom

TL;DR

This paper introduces a variational quantum circuit framework to learn and optimize entanglement purification protocols across multiple degrees of freedom, demonstrating scalability and effectiveness on near-term quantum devices.

Contribution

The paper proposes a novel VQC-based approach for designing entanglement purification protocols in multi-DoF systems, enabling scalable and efficient learning of optimal quantum operations.

Findings

Successfully learned known linear optics protocols with low-depth circuits

Demonstrated scalability to multipair multi-DoF cases

Discovered one-round purification protocols

Abstract

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.