# A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations

@article{Jin2021APR, title={A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations}, author={Shi Jin and Xiantao Li}, journal={ArXiv}, year={2021}, volume={abs/2109.07987} }

Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are evaluated at each time step, while the remaining terms are evaluated at random. The bound for the mean square error is obtained, together with a concentration bound. The mean square error consists of a variance term and a bias term, arising respectively from…

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