Research On The Construction Method Of Quantum Fault-tolerant Encoded Gates For Quantum Stabilizer Code

Quantum fault-tolerant encoded gates could reduce the inevitable coupling of physical qubitsto the noisy environment, and it is the foundation of achieving reliable quantum computation andlong-time quantum communication. The research on quantum fault-tolerant encoded gates hasimportant theoretical significance and reference value to physically realizing quantum computer,and it has been one of the hot topics in quantum communication and quantum computation.In this thesis, two construction methods of quantum fault-tolerant encoded gates are proposedfor stabilizer codes based on measurement and teleportation. The first one is based on measurement.Since measurement can change the normalizer of the stabilizer code, a larger code0is encodedfor the stabilizer code, and the appropriate measuring operators and correcting operators areperformed on the to change the logical operators of the stabilizer code gradually, thefault-tolerant encoded gate can be obtained while the stabilizer is kept unchanged.The other method is based on teleportation. In the construction, quantum teleportation is usedto get the teleported code and the teleported code is applied to imaginary encoded gate. Then theimaginary encoded gate is moved forward. Thus, the quantum fault-tolerant encoded gate could beobtained based on teleportation. In this construction method, the difficulty to construct encoded gatecould be reduced to prepare a special ancillary state.Hadamard gate, phase gate and Control-X gate can generate the whole C2group (Cliffordgroup), so that they can implement the six types unitary transformation on stabilizer code. Thethesis not only present the two construction methods of the quantum fault-tolerant encoded gate, butalso verify the two construction methods by constructing circuits of the encoded phase gate, theendoded Hadamard gate and the encoded CNOT gate. The overhead of the constructed encodedgates are analyzed and compared with that using the method in reference [20]. The results show thatthe measuring construction method is obviously reduced, and the teleportation constructing methoddecreases the overhead when constructing one-qubit gates. For the endoded Hadamard gate, the measurment method has reduced64*n physical quantum gates,6encoded block0and5ancillablock Cat; The teleportation method has decreased60*n physical quantum gates,5encoded blockand5ancilla block.