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We make a numerical study of decoherence on the teleportation algorithm implemented in a linear chain of three nuclear spins system. We study different types of environments, and we determine the associated decoherence time as a function of the dissipative parameter. We found that the dissipation parameter to get a well defined quantum gates (without significant decoherence) must be within the range of γ≤4×10-4 for not thermalized case, which was determined by using the purity parameter calculated at the end of the algorithm. For the thermalized case the decoherence is stablished for very small dissipation parameter, making almost not possible to implement this algorithm for not zero temperature.
By removing a 12C atom from the tetrahedral
configuration of the diamond, replacing it by a 13C atom, and repeating
this in a linear direction, it is possible to have a linear chain of nuclear
spins one half and to build a solid state quantum computer. One qubit rotation,
controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are
obtained immediately from this configuration. CNOT and CCNOT quantum gates are
used to determined the design parameters of this quantum computer.
We make an observation about Galilean transformation on a 1-D mass variable system which leads us to the right way to deal with mass variable systems. Then using this observation, we study two-body gravitational problem where the mass of one of the bodies varies and suffers a damping-antidamping effect due to star wind during its motion. For this system, a constant of motion, a Lagrangian and a Hamiltonian are given for the radial motion, and the period of the body is studied using the constant of motion of the system. Our theoretical results are applied to Halley’s Comet.