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Given a Hermitian operator Ĥ=〈 G|Û|G〉 that is the projection of an oracle Û by state |G〉 created with oracle Ĝ, the problem of Hamiltonian simulation is approximating the time evolution operator e^-iĤt at time t with error ϵ. We show that this can be done with query complexity O(t+(1/ϵ)/(1/ϵ)) to Ĝ,Û that is optimal, not just in asymptotic limits, but for all values t,ϵ. Furthermore, only 2 additional ancilla qubits are required in total, together with O(1) additional single and two-qubit gatesarXiv:1610.06546v2 fatcat:iilep2jp5veijli4ekyexdp5qi