چكيده به لاتين
In this dissertation, various aspects of Quantum Computations have been exhibited. In the beginning, the related physical concepts to Quantum Information Processing including quantum superpostions, entangles and mixed quantum systems, quantum interference, etc. have been discussed. Next, Divincenzo Criteria have been studied to ascertain whether or not a candidate physical system is capable of perfoming quantum computations. After a succinct comparision between some of the most significant suggested physical systems for quantum information processing, superconducting qubits and circuits which, overall, are the most promising proposal have been chosen to be studied in detail. Different types of superconducting qubits, their respective Hamiltonians, and diverse approaches to their coupling have been reported meticulously. Then, Transmon which is one of the newest samples of supeconducting qubits have been analyzed precisely. We have evaluated its Hamiltonian and using some approximations, we have written its two-level demonstration. In addition, in this dissertation, we have talked about quantum costs of quantum circuits and their relative parameters. Next, we have discussed a very important quantum algorithm, namely Grover’s Algorithm. We have innovated two improvements in implementation of Grover’s algorithm. The first, improvement, is based on removing the ancillary qubits which are added for decomposition of Multi-Polar Multi-Control gates into liberaries of simpler gates like Toffoli using the kthroot of quantum gates and a recursive relation which orders the elements of the subsequent subcircuit. In the second improvement, the sign-holder qubit in the Grover’s algorithm is turned into a date qubit with still preserving the property of determining the sign of the system’s quantum state. With the aforementioned improvements, we have enhanced the number of entries on which a quantum device would be able to run the Grover’s algorithm and get the result exponentially. Indeed, the techniques introduced in this dissertation, enable the circuit designer to reduce the number of ancillary qubits to any desired number down to zero and utilize the saved qubits in information processing. In addition, we have elucidated the principal ideas of Grover’s algorithm and also traditional implementation schemes of the algorithm before we present our own method. Moreover, a real run of a small two-qubit sample of the algorithm on IBM quantum computer is performed and reported.
Keywords: Quantum Computations, Superconducting Qubits, Transmon, Grover’s Algorithm, Improvements
