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      Relativistic computers and the Turing barrier

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      Applied Mathematics and Computation

      Elsevier BV

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          Inner structure of a charged black hole: An exact mass-inflation solution.

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              Is Open Access

              Quantum Computational Complexity in the Presence of Closed Timelike Curves

               Dave Bacon (2003)
              Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.
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                Author and article information

                Journal
                Applied Mathematics and Computation
                Applied Mathematics and Computation
                Elsevier BV
                00963003
                July 2006
                July 2006
                : 178
                : 1
                : 118-142
                Article
                10.1016/j.amc.2005.09.075
                © 2006

                http://www.elsevier.com/tdm/userlicense/1.0/

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