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

TL;DR

This paper investigates measurement-induced landscape transitions in hybrid variational quantum circuits, revealing a universal transition point and the emergence of coding barren plateaus where information persists despite vanishing gradients.

Contribution

It distinguishes measurement-induced landscape transitions from phase transitions and introduces the concept of coding barren plateaus in variational quantum algorithms.

Findings

Identifies a universal measurement-induced landscape transition at p_c^{MILT} ≈ 0.2

Shows non-zero quantum-classical mutual information persists in certain regimes

Demonstrates measurement-induced coding barren plateaus with vanishing gradients but available information.

Abstract

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. The results are evidence for a universal measurement-induced landscape transition (MILT) at $p_c^{\text{MILT}} \approx 0.2 < p_c^{\text{MIPT}}$ and that throughout $0<p<p_c^{\text{MILT}}$, there is a finite quantum-classical channel mutual information in the limit of a large number of qubits. Unlike the barren plateau without measurements, a non-zero rate of measurements induces a coding barren plateau where, typically, information about the parameters is available to a local cost function despite a vanishing gradient.