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Quantum Error Correction and Fault-Tolerant Quantum Computation

Bagheri Mehrab, Mohsen | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46886 (04)
  4. University: Sharif University of Technology
  5. Department: physics
  6. Advisor(s): Karimipour, Vahid
  7. Abstract:
  8. Quantum states are highly susceptible to noise and can lose their coherence easily. Thus, for the large-scale quantum algorithms results to be valid, it is necessary to use an error correction process to eliminate the errors. The theory of quantum error correction provides a comprehensive methodology for protecting quantum states against noise. In this theory, by adding ancilla qubits and carefully encoding, quantum states are prepared such that they can be robust to a great extent against errors. To perform a scalable quantum computation, we face an even more daunting task. If our quantum gates are imperfect, everything we do will add to the error. So the quantum error correction could be ineffective. The theory of fault-tolerant quantum computation tells us how to perform elementary operations on encoded states without compromising the code’s ability to correct the errors. According to this theory, if all of the elementary operations are constructed with an error rate below some threshold error rate, the scalable quantum computation will be possible. In this thesis, the theory of quantum error correction, fault-tolerant quantum computation and fault-tolerant quantum error correction methods are investigated completely. Moreover, a general relation for the threshold accuracy is presented which is independent of the type of coding, assuming that the noisy process is local and Markovian
  9. Keywords:
  10. Quantum Coding Theory ; Fault-tolerant Quantum Error Correction Methods ; Fault-tolerant Quantum Computation ; Noisy Gadgets Analysis ; Markovian Noise Model ; Quantum Accuracy Threshold ; Local Noise Model

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