Quantum Adiabatic Evolution for Global Optimization in Big Data

Abstract

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. We reduced big data based on its characteristics, conceptually driven by quantum field theory and utilizing the physics of condensed matter theory in a complex nonlinear dynamic system: Quantum Topological Field Theory of Data. 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 propagators in almost polynomially solvable O(nlogn) complexity. The simulated results show that the time complexity of our algorithm for global optimization via quantum adiabatic evolution is almost in O(logn) Our algorithm first mines the space via greedy approach and makes a list of all ground state Hamiltonians, then utilizing the tunnelling property of quantum mechanics optimizes the algorithm unlike up hill and iterative techniques and doesnot let algorithm to get localized in local minima or sharp valley due to adiabatic evolution of the system. The loss in quantumness, non realizable, no clone, noise, decoherence, splitting of energy states due to electric and magnetic fields, variant to perturbations and less lifetime makes it inefficient for practical implementation. The inefficiencies of qubit can be overcome via property that remains invariant to perturbation and Cartesian independent having well defined mathematical structure. It can be well addressed via topological field theory of data.