Tesis de Maestría / master Thesis
Testing the Efficiency of Digital Simulation of Quantum Walks on IBM’s Q platform - towards quantum experimental algorithms
Registro en:
Sedas, L. (2019). Testing the Efficiency of Digital Simulation of Quantum Walks on IBM’s Q platform - towards quantum experimental algorithms (Unpublished master dissertation). Monterrey, Nuevo León, México
Autor
Sedas, Luis Ángel
Institución
Resumen
This thesis presents several quantum circuit implementations of discrete and continuous quantum walks in cycle graphs. Quantum walks have become an important tool for developing quantum algorithms, that is why this work is a contribution to the area of quantum computation, specially for scientist who want to test their developed algorithms, in a real quantum device as the IBM-Q Experience platform.
We give a complete suite of quantum gates that are needed to simulate quantum walks and quantum walk-based algorithms. Since some of these quantum gates are not elementary, we show how to decompose them into fundamental quantum gates available at Qiskit, an open-source quantum computing software development framework created by IBM. This is an important contribution towards the development of a professional platform for simulating and testing quantum algorithms. We found that the decomposition of unitary gates, related to quantum walks, into elementary gates is not very well documented in the literature.
We studied the efficiency of both, the number of qubits and logic gates needed for each circuit, and the correctness of the results of each experiment by comparing the theoretical expected output state with the output generated by quantum simulators. Implementations of both discrete and continuous quantum walks in quantum circuits rely heavily on controlled gates, that when decomposed into fundamental gates add a high number of quantum gates and depth.
Experiments were performed on a real quantum device, but results showed that the quantum computer is not good enough when executing these quantum circuits, due to the depth of the circuits and the high amount of CNOT gates required. We tested different implementations and optimization methods for the simplification of the quantum circuits, were we find that resources grow linearly w.r.t the number of qubits, and the minimum amount of gates required for the discrete case in C8 was 144 quantum gates with a depth of 111, which is the reason of the error between the simulations and the implementations in the quantum device.