  We investigate the quantum Zeno effect as a framework for designing and
analyzing quantum algorithms for Hamiltonian simulation. We show that frequent
projective measurements of an ancilla qubit register can be used to simulate
quantum dynamics on a target qubit register with a circuit complexity similar
to randomized approaches. The classical sampling overhead in the latter
approaches is traded for ancilla qubit overhead in Zeno-based approaches. A
second-order Zeno sequence is developed to improve scaling and implementations
through unitary kicks are discussed. We show that the circuits over the
combined register can be identified as a subroutine commonly used in
post-Trotter Hamiltonian simulation methods. We build on this observation to
reveal connections between different Hamiltonian simulation algorithms.
