Simulated quantum computation of global minima

Finding the optimal solution to a complex optimisation problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations N reduced from O(N) in classical simulation to O(N1/2) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimisation to treat larger systems.