Multiple-pulse sequences for precise transmitter phase alignment

Bootstrap tomography of the pulses for quantum control

Long-time dynamical decoupling and quantum control of qubits require high-precision control pulses. Full characterization (quantum tomography) of imperfect pulses presents a bootstrap problem: tomography requires initial states of a qubit which cannot be prepared without perfect pulses. We present a protocol for pulse error analysis, specifically tailored for a wide range of the single solid-state electron spins. Using a single electron spin of a nitrogen-vacancy center in diamond, we experimentally verify the correctness of the protocol, and demonstrate its usefulness for quantum control tasks.