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Due to its significant application in reducing algorithm depth, fSim gateshave attracted a lot of attention, while one-step implementation of fSim gatesremains an unresolved issue. In this manuscript, we propose a one-stepimplementation of holonomic fSim gates in a tunable superconducting circuitbased on the three lowest energy levels. Numerical simulations demonstrate thefeasibility of our scheme. This scheme may provide a promising path towardquantum computation and simulation.

One-step implementation of nonadiabatic holonomic fSim gate in superconducting circuits