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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.
We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediat
Clift and Murfet (2019) introduced a naive Bayesian smooth relaxation of Turing machines motivated by work in differential linear logic; this was subsequently used to endow spaces of program codes of bounded length with a smooth manifold structure vi
An {omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {omega}-languages, i.e. the class of {omega}-languages accepted by Turing machines with a Buchi acceptance condition, which is also the class
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
This note introduces a generalization to the setting of infinite-time computation of the busy beaver problem from classical computability theory, and proves some results concerning the growth rate of an associated function. In our view, these results