Constructing quantum circuits for maximally entangled multi-qubit states using the genetic algorithm

Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.