Symmetric derivatives of parametrized quantum circuits

Understand

Symmetries are crucial for tailoring parametrized quantum circuits to applications, due to their capability to capture the essence of physical systems.

• In this work, we shift the focus away from incorporating symmetries in the circuit design and towards symmetry-aware training of variational quantum algorithms.
• For this, we introduce the concept of projected derivatives of parametrized quantum circuits, in particular the equivariant and covariant derivatives.
• We show that the covariant derivative gives rise to the quantum Fisher information and quantum natural gradient.