AlgoLab | Limiting Trotter's infidelity

The simulation of quantum systems on quantum computers uses the Trotter approximation to translate temporal evolution into circuits. This method generates an error that increases with time and depends on the Hamiltonian of the system. The theoretical bound proposed by Childs et al. [1] guarantees the quality of the evolution, but remains too broad in practice.

This project aims to establish a more precise bound by measuring the infidelity between the exact states and those obtained by Trotterization. The idea is to construct the state that maximizes this infidelity from the extreme eigenstates of a phase operator, then to verify whether the norm of this operator can be bounded.