  We present exact numerical calculations of supercurrent density, inductance,
and impurity-induced flux noise of cylindrical superconducting wires in the
nonlocal Pippard regime, which occurs when the Pippard coherence length is
larger than the London penetration depth. In this regime the supercurrent
density displays a peak away from the surface, and changes sign inside the
superconductor, signalling a breakdown of the usual approximation of local
London electrodynamics with a renormalized penetration depth. Our calculations
show that the internal inductance and the bulk flux noise power is enhanced in
nonlocal superconductors. In contrast, the kinetic inductance is reduced and
the surface flux noise remains the same. As a result, impurity spins in the
bulk may dominate the flux noise in superconducting qubits in the Pippard
regime, such as the ones using aluminum superconductors with large electron
mean free path.
