Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation

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 ansätze 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.

Technical info

In the files you will find the resulting data and libraries needed to reproduce the plots for the paper Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation. Note that the simulation data is in the JLD2 format, which can be read either directly in Julia or by any hdf5 compatible library.