  Quantum process tomography conventionally uses a multitude of initial quantum
states and then performs state tomography on the process output. Here we
propose and study an alternative approach which requires only a single (or few)
known initial states together with time-delayed measurements for reconstructing
the unitary map and corresponding Hamiltonian of the time dynamics. The
overarching mathematical framework and feasibility guarantee of our method is
provided by the Takens embedding theorem. We explain in detail how the
reconstruction of a single qubit Hamiltonian works in this setting, and provide
numerical methods and experiments for general few-qubit and lattice systems
with local interactions. In particular, the method allows to find the
Hamiltonian of a two qubit system by observing only one of the qubits.
