Renormalized Circuit Complexity

Understand

We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit.

• This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal.
• The optimized ST iteration order is correlated with the error tolerance and plays the role of an anti-de Sitter (AdS) radial coordinate.
• The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given.