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We present a remarkable finding that a recently discovered [G. S. Uhrig,Phys. Rev. Lett. 98, 100504 (2007)] series of pulse sequences, designed tooptimally restore coherence to a qubit in the spin-boson model of decoherence,is in fact completely model-independent and generically valid for arbitrarydephasing Hamiltonians given sufficiently short delay times between pulses. Theseries maximizes qubit fidelity versus number of applied pulses forsufficiently short delay times because the series, with each additional pulse,cancels successive orders of a time expansion for the fidelity decay. The"magical" universality of this property, which was not appreciated earlier,requires that a linearly growing set of "unknowns" (the delay times) mustsimultaneously satisfy an exponentially growing set of nonlinear equations thatinvolve arbitrary dephasing Hamiltonian operators.

Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem