Variational-toolbox-based separability detection of multiqubit states

TL;DR

This paper introduces variational toolboxes and adaptive strategies to detect the k-separability of multiqubit states using optimal parametrized quantum circuits, providing insights into state properties beyond state reproduction.

Contribution

It presents a novel variational toolbox approach for identifying k-separability in pure and mixed states, with adaptive optimization reducing parameter complexity for low-rank states.

Findings

Successfully detects k-separability in various states

Controls fewer parameters for low-rank states

Validated through numerical demonstrations

Abstract

Parametrized quantum circuits (PQCs) are crucial in variational quantum algorithms. While it is commonly believed that the optimal PQC is solely used to reproduce the target state, we here reveal that the optimal PQC can also provide valuable insights into the state's properties. We propose variational toolboxes to identify the $k$-separability of pure states, with or without preparation noise, by checking the structure within the optimal PQCs. Additionally, we introduce adaptive optimization strategies to detect the $k$-separability of mixed states. Compared to fixed PQCs, our approach controls fewer parameters for low-rank states. Finally, we validate our methods through numerical demonstrations for various states.