  We propose dynamical control schemes for Hamiltonian simulation in many-body
quantum systems that avoid instantaneous control operations and rely solely on
realistic bounded-strength control Hamiltonians. Each simulation protocol
consists of periodic repetitions of a basic control block, constructed as a
suitable modification of an "Eulerian decoupling cycle," that would otherwise
implement a trivial (zero) target Hamiltonian. For an open quantum system
coupled to an uncontrollable environment, our approach may be employed to
engineer an effective evolution that simulates a target Hamiltonian on the
system, while suppressing unwanted decoherence to the leading order. We present
illustrative applications to both closed- and open-system simulation settings,
with emphasis on simulation of non-local (two-body) Hamiltonians using only
local (one-body) controls. In particular, we provide simulation schemes
applicable to Heisenberg-coupled spin chains exposed to general linear
decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian
starting from Ising-coupled qubits, as potentially relevant to the dynamical
generation of a topologically protected quantum memory. Additional implications
for quantum information processing are discussed.
