Quantum Adiabatic Evolution for Global Optimization in Big Data

To my Parents who taught me how the clock of patience ticks and Professor Mario Rasetti for his guidance

Everything and everyone is interconnected through an invisible web of stories. Whether we are aware of it or not, we are all in a silent conversation. Do no harm. Practice compassion. And do not gossip behind anyone’s back-not even a seemingly innocent remark! The words that come out of our mouths do not vanish but are perpetually stored in infinite space, and they will come back to us in due time. One man’s pain will hurt us all. One man’s joy will make everyone smile.–Shams of Tabriz (Forty Rules of Love) Acknowledgments ……..And when (Solomon) saw it truly before him, he exclaimed:“This is [an outcome] of my Sustainers bounty, to test me as to whether I am grateful or ungrateful! However, he who is grateful [to God] is but grateful for his own good; and he who is ungrateful [should know that], verily, my Sustainers is self-sufficient, most generous in giving!” –from the story of the Queen of Saba, Quran, 27:40

There is an association of a long journey that evolved gradually, passing through the different and undistinguished phases. The tradition of morality and philosophy of ethics revives me to pay sincere gratitude to all those who have been very instrumental so far in this untamed voyage of my thesis. I would like to thank my mother for taming my wild intellect to order during the darkness and failures and my father for having belief in my hard work. I am highly thankful to my supervisor Dr Jamal Abdul Nasir, IIUI Pakistan for supervising and guiding me in difficult times. I don’t have words to thank and manifest in literal bounds of language the admiration for Prof Mario Rasetti, ISI Foundation in Italy for guiding me and continuously interacting on the evolution of my thoughts. I feel pleased to thank Dr Mir Faizal at University of Lethbridge, Alberta Canada for his academic suggestions. I am also thankful to my collaborator Dr Wail Mardini from Jordan University of Science and Technology for his valuable scientific thoughts. I would like to thank Charles Bennett IBM Fellow from Harvard University for suggesting me institutions for implementation of my idea. I am thankful to Jamia Millia Islamia, New Delhi, IIT Roorkee and Aligarh Muslim University for assisting me for carrying out simulations in the lab and its reductions. I am also thankful to Dr Qin Zhao at National University of Singapore for her encouraging and emotional support. Dr Andrei Kirilyuk at Institute of Metal Physics, Ukraine, Dr Kazuharu Bamba at Fukushima University, Japan, Junaid ul Haq at Jamia Millia Islamia, Muhammad Anas at IIT Kharagpur, and Syed Masood at IIUI for their suggestions and perspectives.

Lastly I am thankful once again to my mother and grandmothers for shaping instinctive and imaginative nature of my intellect via long continuous moulding and my father and my uncle for his support has helped much in continuation of my thesis work.

Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated ‘free will’ having dynamic and non linear nature. This hardness of big data has not yet been reduced to any physical in Hamiltonian formalism, neither any quantum formulation of big data has initiated. Additionally there is no specific simulator for optimization of this ‘quantum space’. We reduced big data based on its characteristics, conceptually driven by quantum field theory and utilizing the physics of condensed matter theory. It is reduced to a complex non linear dynamic system in Hamiltonian formalism. The model is formulated from the dynamics and evolution of single datum, eventually defining the global properties and evolution of collective data space via action, partition function, green’s propagators in almost polynomially solvable O (n logn) complexity. It is an initiation towards new understanding of information with epistemological shift. The simulation was carried out by mapping the dye laser parameters with the conditions of Quantum Adiabatic Evolution for global optimization. Energy and pulse width are mapped to the time-gap condition in terms of transition time, stability factor and adiabatic conditions. The algorithm was designed based on five main stages Reduction, Mapping, Evolution, Optimization and Simulation phase. The simulated results show that the time complexity of our algorithm for global optimization via quantum adiabatic evolution is almost O (logn). During simulation the excitation of rhodium atom is taken as a realizable qubit. Pertin