  Theoretically understanding and experimentally characterizing and modifying
the underlying Hamiltonian of a quantum system is of utmost importance in
achieving high-fidelity quantum gates for quantum computing. In this work, we
explore the use of dynamical decoupling (DD) in characterizing undesired
two-qubit couplings as well as the underlying single-qubit decoherence, and in
suppressing them. We develop a syncopated dynamical decoupling technique which
protects against decoherence and selectively targets unwanted two-qubit
interactions, overcoming both significant hurdles to achieving precise quantum
control and realizing quantum computing on many hardware prototypes. On a
transmon-qubit-based superconducting quantum device, we identify separate white
and $1/f$ noise components underlying the single-qubit decoherence and a static
ZZ coupling between pairs of qubits. We suppress these errors using syncopated
dynamical decoupling in two-qubit benchmarking experiments and significantly
boost performance in a realistic algorithmic quantum circuit.
