Abstract:

Quantum computer use phenomena like superposition and entanglement that empower them to perform faster and can solve some problems more efficiently than on classical computers. For many problems, there is a quantum algorithm which is faster and gives better results than classical algorithm. But there are some restrictions to use these powerful and efficient algorithms on quantum computers. One of the restrictions is that current quantum computers have very few qubits. We are working on reducing required qubits to implement quantum algorithm. In the first part of thesis, we implement a scalable version of quantum order-finding algorithm for factoring the integer 35 and 77, where n qubit control register is replaced by only one qubit which is used several times. This involves the iterative quantum phase estimation to minimize the qubits resulting in less noise. We implement the algorithm on IBM quantum processors using only 5 qubits for N = 35 and 7 qubits for N = 77. This method could be used to minimize the qubits for other algorithms as well.