  We describe methods for simulating general second-quantized Hamiltonians
using the compact encoding, in which qubit states encode only the occupied
modes in physical occupation number basis states. These methods apply to
second-quantized Hamiltonians composed of a constant number of interactions,
i.e., linear combinations of ladder operator monomials of fixed form. Compact
encoding leads to qubit requirements that are optimal up to logarithmic
factors. We show how to use sparse Hamiltonian simulation methods for
second-quantized Hamiltonians in compact encoding, give explicit
implementations for the required oracles, and analyze the methods. We also
describe several example applications including the free boson and fermion
theories, the $\phi^4$-theory, and the massive Yukawa model, all in both
equal-time and light-front quantization. Our methods provide a general-purpose
tool for simulating second-quantized Hamiltonians, with optimal or near-optimal
scaling with error and model parameters.
