Réseau de neurones artificiels quantiques pour un diagnostic rapide et précis de quatre maladies tropicales
Jean-Pierre Tchapet Njafa · HAL (Le Centre pour la Communication Scientifique Directe) · 2017
This thesis presents a model of Quantum Associative Memory (QAM), that we will call QAMDiagnos and that can be a helpful tool for physicians for the diagnosis of four tropical diseases (malaria, typhoid fever, yellow fever and dengue) which have several similar signs and symptoms. The memory can distinguish between a single infection from a polyinfection. Our model is a combination of improved versions of the original linear quantum search algorithm made by Ventura for QAM and the non-linear quantum search algorithm of Abrams and Lloyd. For the linear algorithm, we introduce two modifications of the query that optimized data retrieval of correct multi-patterns simultaneously for any rate of the number of the recognition pattern states on the total basis states. For the non-linear algorithm, we propose a simplified and generalised version of Rigui Zhou \al which includes the quantum matrix with the binary decision diagram put forth by David Rosenbaum in the Abrams and Lloyd's non-linear search quantum algorithm. Our model has the avantage to give the possibility to retrieve one of the sought states in multi-values retrieving scheme when a measurement is done on the first register in $\mathcal{O}(c-r)$ time complexity. It is better than the Grover's algorithm and its modified form which need $\mathcal{O}(\sqrt{\frac{2^n}{m}})$ steps when they are used as the retrieval algorithm in a QAM. $n$ is the number of qubits of the first register and $m$ the number of $x$ values for which $f(x)=1$; $f$ is a function computed by the oracle, which takes a value between $0$ and $2^n-1$ and returns values $0$ or $1$. As the nonlinearity makes the system highly susceptible to the noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM shows a fidelity of about $0.7$ whatever the number of qubits existing in the first register, thus demonstrating the robustness of our model.The database of the QAMDiagnos application contains signs and symptoms of the four retained tropical diseases. A multi-platform graphical user interface (Android, Linux, MS Windows) has been developed to make QAMDiagnos user-friendly. From the given simulation results, it appears that the efficiency of recognition is good when particular signs and symptoms of a disease are inserted given that the linear algorithm is the main algorithm. The non-linear algorithm helps confirm or correct the diagnosis or suggest some tratment advice to the physician. So, the application QAMDiagnos is a tool for medical diagnosis sensitive and a low-cost that enables rapid and accurate detection of the four tropical diseases, and therefore a rapid and effective medical care.