Principles and symmetries of complexity in quantum field theory

Understand

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way.

• We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems.
• Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry.
• Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems.