  The model of local Turing machines is introduced, including classical and
quantum ones, in the framework of matrix-product states. The locality refers to
the fact that at any instance of the computation the heads of a Turing machine
have definite locations. The local Turing machines are shown to be equivalent
to the corresponding circuit models and standard models of Turing machines by
simulation methods. This work reveals the fundamental connection between
tensor-network states and information processing.
