  Boson sampling solves a classically intractable problem by sampling from a
probability distribution given by matrix permanents. We propose a scalable
implementation of Boson sampling using local transverse phonon modes of trapped
ions to encode the Bosons. The proposed scheme allows deterministic preparation
and high-efficiency readout of the Bosons in the Fock states and universal mode
mixing. With the state-of-the-art trapped ion technology, it is feasible to
realize Boson sampling with tens of Bosons by this scheme, which would
outperform the most powerful classical computers and constitute an effective
disproof of the famous extended Church-Turing thesis.
