Quantum Natural Gradient

Quantum Natural Gradient

This PennyLane tutorial introduces the quantum natural gradient, an advanced optimization method that often trains variational quantum circuits faster and more reliably than ordinary gradient descent. Standard gradient descent treats all parameters as living in a flat Euclidean space, but the space of quantum states has a curved geometry; the natural gradient accounts for this by rescaling the gradient with the inverse of a metric tensor, the Fubini-Study metric (the quantum geometric tensor), so that each update step moves a fixed distance in state space rather than parameter space. This makes progress more uniform and helps the optimizer navigate flat or ill-conditioned regions of the landscape. The tutorial explains the geometric intuition, shows how to compute the metric tensor for a parameterized circuit in PennyLane (including its block-diagonal approximation), and uses PennyLane's built-in quantum-natural-gradient optimizer to train a variational circuit, comparing its convergence against vanilla gradient descent on the same problem. By connecting optimization to the geometry of quantum states, the tutorial gives both the theory and the practical tooling for faster variational training in PennyLane.

Run it

pip install -r requirements.txt
python demo.py

Source and license

Imported from demonstrations_v2/tutorial_quantum_natural_gradient/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.