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One of the most significant hurdles to be overcome on the path to practicalquantum information processors is dealing with quantum errors. Dynamicaldecoupling is a particularly promising approach that complements conventionalquantum error correction by eliminating some correlated errors without theoverhead of additional qubits. In practice, the control pulses used fordecoupling are imperfect and thus introduce errors which can accumulate aftermany pulses. These instrumental errors can destroy the quantum state. Here weexamine several dynamical decoupling sequences, and their concatenatedvariants, using electron spin resonance of donor electron spins in a $^{28}$Sicrystal. All of the sequences cancel phase noise arising from slowlyfluctuating magnetic fields in our spectrometer, but only those sequences basedupon alternating $\pi$-rotations about the X- and Y-axes in the rotating frame(XYXY sequences) demonstrate the ability to store an arbitrary quantum state.By comparing the experimental results with a detailed theoretical analysis wedemonstrate that the superior performance of XYXY sequences arises from thefact that they are self-correcting for the dominant instrumental pulse errorsin magnetic resonance experiments. We further find that concatenated sequencesperform better than the periodic variants, maintaining near 100% fidelities forspin states even after several hundred control pulses. Intuitively, one wouldexpect the instrumental error to increase with the number of pulses in thesequence but we show that the dominant first-order error does not increase whenconcatenating the XYXY sequence.

Dynamical Decoupling in the Presence of Realistic Pulse Errors