Givens Rotations for Quantum Chemistry

Givens Rotations for Quantum Chemistry

This PennyLane tutorial explains Givens rotations, the natural building blocks for constructing quantum circuits that prepare molecular states in quantum chemistry, and shows why they are the right primitive for the job. In chemistry, the relevant quantum states conserve the number of electrons, so the gates that build them should preserve particle number; Givens rotations are exactly the particle-conserving operations that rotate amplitude between electronic configurations with the same number of electrons (single excitations), and their generalizations handle double excitations. The tutorial builds intuition for how a circuit of Givens rotations explores the fixed-particle-number subspace, connects them to the excitation operators used in chemistry ansaetze such as unitary coupled cluster, and shows how PennyLane provides single- and double-excitation gates that implement these rotations directly. It demonstrates constructing a state-preparation circuit from these gates, preparing a target electronic state, and understanding the structure this imposes on the accessible states. By grounding chemistry ansatz design in the concrete and physically-motivated language of Givens rotations, the tutorial gives a clear, foundational understanding of how particle-conserving circuits are built in PennyLane.

Run it

pip install -r requirements.txt
python demo.py

Source and license

Imported from demonstrations_v2/tutorial_givens_rotations/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.