  We introduce an error resilient distributed computing method based on an
extension of the channel polarization phenomenon to distributed algorithms. The
method leverages an algorithmic split operation that transforms two identical
compute nodes to slow and fast workers, which parallels the channel split
operation in Polar Codes. This operation preserves the average runtime,
analogous to the conservation of Shannon capacity in channel polarization. By
leveraging a recursive construction in a similar spirit to the Fast Fourier
Transform, this method synthesizes virtual compute nodes with dispersed return
time distributions, which we call computational polarization. We show that the
runtime distributions form a functional martingale processes, identify their
limiting distributions in closed-form expressions together with non-asymptotic
convergence rates, and prove strong convergence results in Banach spaces. We
provide an information-theoretic lower bound on the overall runtime of any
coded computation method and show that the computational polarization approach
asymptotically achieves the optimal runtime for computing linear functions. An
important advantage is the near linear time decoding procedure, which is
significantly cheaper than Maximum Distance Separable codes.
