Barren Plateaus in Quantum Neural Networks

Barren Plateaus in Quantum Neural Networks

This PennyLane tutorial investigates barren plateaus, one of the most important obstacles to training quantum neural networks, following the landmark analysis by McClean and collaborators. A barren plateau is a region of the optimization landscape where the cost function's gradients vanish exponentially with the number of qubits, so that for large, randomly-initialized, sufficiently-expressive circuits the landscape becomes almost flat and gradient-based training stalls, the quantum analogue of (and arguably worse than) classical vanishing gradients. The tutorial makes the phenomenon concrete and measurable: using PennyLane, it constructs random parameterized circuits of increasing width, samples the variance of the cost gradient across many random initializations, and shows empirically that this variance shrinks exponentially as the number of qubits grows. It explains why this happens (the concentration of measure for random circuits) and discusses the practical implications for ansatz design and initialization. By demonstrating barren plateaus directly and quantitatively, the tutorial gives practitioners the understanding they need to recognize and avoid this failure mode when building trainable quantum models, and motivates the mitigation strategies (local cost functions, structured ansaetze) explored in other PennyLane demos.

Run it

pip install -r requirements.txt
python demo.py

Source and license

Imported from demonstrations_v2/tutorial_barren_plateaus/demo.py in PennyLaneAI/demos at c52c0abeb5122218aa96b38eea848864cce7323f, under the Apache License 2.0. Original authors: Xanadu and the PennyLane community. The upstream LICENSE is included alongside this example.