Arbitrary-order Magnus expansion is shown to have commutator-scaling error bounds and a polynomial-cost quantum circuit, yielding a time-dependent Hamiltonian simulation algorithm with O~(αbar^{1+1/p} T^{1+1/p}/ε^{1/p}) query complexity and logarithmic dependence on the Hamiltonian's time derivative
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High-order Magnus Expansion for Hamiltonian Simulation
Arbitrary-order Magnus expansion is shown to have commutator-scaling error bounds and a polynomial-cost quantum circuit, yielding a time-dependent Hamiltonian simulation algorithm with O~(αbar^{1+1/p} T^{1+1/p}/ε^{1/p}) query complexity and logarithmic dependence on the Hamiltonian's time derivative