In this dissertation we have studied various methods that have been proposed to overcome the problem of decoherence in a quantum computer. These methods are: (1) Quantum-error correcting codes (QECC's); (2) Decoherence-free subsystem/subspace (DFS); (3) Adiabatic gate operation. In the first two methods, information is encoded in the form of a code that provides protection against certain noise and hence protect the qubit from losing information to the environment. In the third method, the gate operation is performed in such a way that the qubit is made to evolve adiabatically because of which it acquires a phase which is insensitive to the certain form of noise. Thus, because of the insensivity of the phase to the noise, the qubit is prevented from losing information to the environment. All these methods have limitations and in this work we studied these limitations. This work is divided into two parts. In the first part, we studied the performance of a 3-qubit QECC in the presence of quantized partially correlated noise, as well as 3 and 4-qubit DFS in the presence of partially correlated noise. We derived the relationship between the fidelity of the code, the initial state, coherence length of the noise and the spatial distance between the qubits. For the case of, 3-qubit QECC we found that the quantum nature of the noise enhances the infidelity of the code. For the case of, 3 and 4-qubit DFS we found that under certain conditions 3-qubit DFS code is a better code over 4-qubit code. Nonetheless, these studies provide us insights of the influence of the environment on the performance of quantum codes. In the second part, we studied the problem of the entanglement of the coherent field (that is used to turn on/off the gate) with the qubit on which gate operation is performed. The gate operation is made adiabatic by making the coherent field to change very slowly in time. The entanglement arises due to the quantum nature of the coherent field and causes faulty gate operation. Through our studies we found that by increasing the average photon number of the coherent field, the qubit can be made to stay in a coherent superposition state for short times and hence the entanglement between the coherent field and the qubit can be avoided.
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