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Exact Generation of Quantum States by the Dynamics of Spin Chains

Moradi, Morteza | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53913 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid
  7. Abstract:
  8. One of the most popular topics in quantum information is the transfer of quantum states by the evolution of spin chains. To transfer quantum information one must transfer an arbitrary quantum state from one point to another in a spin network. The common idea for this is to use the coupling strengths of adjacent spins and apply a specific local magnetic field to the spin chains. In many of these chains, the state transfer is not done complete and the fidelity between the final state and the initial state is less than one. Recently, chains with a special Hamiltonian have been designed by which a desired state can be placed on one side of the chain and after a specific time, the state can be completely transferred to the other side of the chain. In these chains, the coupling strength between adjacent spins must be unequal or local magnetic fields must be applied to the Hamiltonian of the chain, while the implementation of such manipulations requires advanced laboratory equipment in practice. Another issue that has been considered is the production of quantum states by the evolution of spin chains, which has been solved approximately and numerically in recent years, but so far no exact analytical solution has been provided. In this dissertation, the conditions required to achieve an desired overlap of states with an upward spin have been studied analytically and accurately. Indeed, we designed a quasi-one-dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left-hand site to any specified single particle state on the whole chain. We have also obtained the rate of fidelity deviation due to the amount of laboratory error in the implementation of local interventions, and finally as two important examples, we study the W states and Gaussian states of arbitrary width
  9. Keywords:
  10. Spin Chain ; State Transfer ; Qubit ; Hamiltonian Path ; Fidelity ; Coupling Strentgh

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