Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation

TL;DR

This paper presents a self-learning measurement-based feedback protocol for variational quantum state preparation, improving efficiency and scalability by overcoming local minima and enabling the discovery of new protocols.

Contribution

It introduces a novel feedback-enhanced variational approach that extends beyond unitary methods, demonstrating scalability and the ability to find new quantum state preparation strategies.

Findings

Achieved high-fidelity AKLT state preparation using feedback.

Overcame local minima through parameter update adjustments.

Demonstrated scalability with neural network feedback mechanisms.

Abstract

This work introduces a self-learning protocol that incorporates measurement and feedback into variational quantum circuits for efficient quantum state preparation. By combining projective measurements with conditional feedback, the protocol learns state preparation strategies that extend beyond unitary-only methods, leveraging measurement-based shortcuts to reduce circuit depth. Using the spin-1 Affleck-Kennedy-Lieb-Tasaki state as a benchmark, the protocol learns high-fidelity state preparation by overcoming a family of measurement induced local minima through adjustments of parameter update frequencies and ancilla regularization. Despite these efforts, optimization remains challenging due to the highly non-convex landscapes inherent to variational circuits. The approach is extended to larger systems using translationally invariant ans\"atze and recurrent neural networks for feedback, demonstrating scalability. Additionally, the successful preparation of a specific AKLT state with desired edge modes highlights the potential to discover new state preparation protocols where none currently exist. These results indicate that integrating measurement and feedback into variational quantum algorithms provides a promising framework for quantum state preparation.