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.Comment: Published in PRL, revise