Quantum simulation of second-quantized Hamiltonians in compact encoding

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