The hamiltonian simulation is to simulate the dynamics of the system, given some Hamiltonian. The conventional way of the Hamiltonian simulation is the Trotter decomposition. We discretize the simulated time to small time steps, like the classical Runge–Kutta method. Although if we increase the steps of the discretization, we can in principle reduce the algorithmic error, the physical error like dephasing increases linearly to the number of the Trotter steps. Therefore, there are an optimised number of the Trotter steps, and accordingly the restricted accuracy of the Hamiltonian simulation.
In this work, we showed that we can enhance the accuracy of the simulation by using several data points obtained from several numbers of Trotter of steps and extrapolation, estimating the error-free value we hope to obtain. This method significantly improves the performance of the Hamiltonian simulation, especially when combined with the recently proposed error mitigation technique for physical errors.
Our work was recently published in Physical Review A!
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.012334
