Measurement-Induced Landscape Transitions and Coding Barren Plateaus in Hybrid Variational Quantum Circuits

Understand

The entanglement-induced barren plateau is an exponential vanishing of the parameter gradients with system size that limits the practical application of variational quantum algorithms (VQA).

• A landscape transition from barren plateau to no-barren plateau was recently observed in monitored quantum circuits, hypothesized to coincide with the measurement-induced phase transition (MIPT) that separates the area-law states from the volume-law states.
• We argue from an information theory perspective that these are different transitions.
• This hypothesis is supported by a numerical study that includes cost-gradient variances, visualizations of the optimization runs and cost-landscape, and a quantum-classical channel mutual information measure.