Implementation of quantum gate operations using a dynamic learning algorithm
Garigipati, Rudrayya Chowdary
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Quantum circuits can be implemented by breaking them into a series of elementary gates, and several methods have been proposed to decompose a quantum circuit into elementary gate operations. The total number of gates required to implement the circuit is called the gate count, which gives a measure of the computational overhead of the circuit. In order to take advantage of the quantum effects of a quantum system, it is desired that all gate operations required to implement the quantum circuit be performed before the system loses its coherence. However, as the complexity of a quantum circuit increases, the gate count increases, and it becomes difficult to implement the circuit before losing its coherence. Therefore, strategies need to be designed that minimize the total gate count, and hence, the total time of operation relative to the system. Quantum gate operations can be realized by finding the parameters of the system Hamiltonian. (The Hamiltonian represents total energy of the system). This can be done by equating the matrix representations for the desired gate operations to the unitary transformation under the Hamiltonian. Here, we proposed a method for finding system parameters for implementing gate operations along a linear array of qubits. A dynamic learning algorithm has been used as a tool for finding the system parameters to implement the desired gate operations directly wherein gate operation need not be decomposed into a sequence of elementary gate operations belonging to a universal set. Therefore, the main advantage of this scheme is that the computational overhead of a quantum circuit can be reduced. Moreover since all qubits are involved in the gate operation, and no qubits are idle, our scheme also eliminates other problems like relative phases, which are picked up due to individual qubit precessions during idle times. Another advantage is that all the parameters found using this scheme are scalable and, therefore, can be adjusted to the requirements of a given experimental realization.
Thesis (Ph.D.)-- Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science