Simulated quantum computation of global minima

Abstract

Finding the optimal solution to a complex optimization 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( √ N ) in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.

Implementation of quantum logic gates using polar molecules in pendular states

“…Quantum computers take direct advantage of superposition and entanglement to perform computations. Because quantum algorithms compute in ways which classical computers cannot, for certain problems they provide exponential speedups over their classical counterparts [1][2][3][4][5][6][7][8]. That prospect has fostered a variety of proposals suggesting means to implement such a device [5,9,10].…”

Group leaders optimization algorithm

“…Recently, in a promising new direction, we demonstrate that a modified Grovers quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits [40]. 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 Grovers algorithm.…”

“…It reduces the computational time of a brute force search from O(N ) to O( √ N). The algorithm can be described in four steps [39,40]: • Apply the first operator U f which is defined as:…”

Quantum Computing Approach to Nonrelativistic and Relativistic Molecular Energy Calculations

“…Aspuru-Guzik et al in their seminal article [12] reduced the number of quantum bits (qubits) needed by the Abrams and Lloyd's algorithm [10] and applied it to molecular ground state energy calculations. Since these two pioneering works, other papers involving energy calculations of excited states [13], quantum chemical dynamics [14], calculations of molecular properties and geometry optimizations [15], state preparations [16,17] or global minima search [18] were published. The list of all chemical applications for quantum computers is quite rich and an interested reader can find a comprehensive review in [19].…”

“…The overall scaling of the algorithm is given by the scaling of a single controlled action of the unitary propagator without repetitions enforced by the Trotter approximation (18). These repetitions increase only the prefactor to the polynomial scaling, not the scaling itself.…”