Ab initio simulations of the Standard Model will require thousands of qubits and millions of gates. Developing efficient quantum simulation algorithms for such settings, which will only be feasible in the era of fault-tolerant quantum computing, necessitates principles entirely different from those used in the near term. A useful guiding principle involves considering the asymptotic dependence of simulation algorithm costs on parameters such as error, evolution time, and problem size.  In this talk, I will review some recent advancements in near-optimal simulation of quantum field theories. The primary focus will be on recent work 2405.10416 involving the simulation of time evolution in the Kogut-Susskind formulation of lattice gauge theory (LGT).  Additionally, I will discuss three other projects: the application of an early-fault-tolerant near-optimal QETU state preparation algorithm to U(1) LGT (2310.13757), the construction of block encodings via quantum signal processing (WIP), and state preparation in light-front QCD (WIP).

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