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A highly anticipated use of quantum computers is the simulation of complexquantum systems including molecules and other many-body systems. One promisingmethod involves directly applying a linear combination of unitaries (LCU) toapproximate a Taylor series by truncating after some order. Here we present anadaptation of that method, optimized for Hamiltonians with terms of widelyvarying magnitude, as is commonly the case in electronic structurecalculations. We show that it is more efficient to apply LCU using a truncationthat retains larger magnitude terms as determined by an iterative procedure. Weobtain bounds on the simulation error for this generalized truncated Taylormethod, and for a range of molecular simulations, we report these bounds aswell as exact numerical results. We find that our adaptive method can typicallyimprove the simulation accuracy by an order of magnitude, for a given circuitdepth.

Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries