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Renormalized Circuit Complexity
Arpan Bhattacharyya1,2, Pratik Nandy3, Aninda Sinha3
1Indian Institute of Technology, Gandhinagar, Gujarat 382355, India.
Abstract:
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 radial coordinate. The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given.
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