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

We present a remarkable finding that a recently discovered [G. S. Uhrig, Phys. Rev. Lett. 98, 100504 (2007)] series of pulse sequences, designed to optimally restore coherence to a qubit in the spin-boson model of decoherence, is in fact completely model independent and generically valid for arbitrary dephasing Hamiltonians given sufficiently short delay times between pulses. The series maximizes qubit fidelity versus number of applied pulses for sufficiently 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) must simultaneously satisfy an exponentially growing set of nonlinear equations that involve arbitrary dephasing Hamiltonian operators.