Information in entangled dynamic quantum networks

We present a simple method of obtaining a completely entangled lattice of qubits, using a modified form of the controlled-NOT quantum gates connecting nearest neighbors, which we have studied earlier. In this fully entangled case, for computational economy a slightly modified form of the c-NOT gate is used, which inverts the phase as well as the state of the controlled qubit when the controlling qubit is excited. It too gives a manifestly unitary transition matrix for each updating of the network, while keeping all the numbers produced in the operations real. The dynamics leads to a completely entangled state of the qubits. Simulation shows a surprising property of the dynamics of the network, viz. the possibility of obtaining the initial state by a method of back-projecting the complicated entangled states that evolve after many updatings of the entire network. We prove that it is not possible for a sequence of unitary operators working on a net to make it move from an aperiodic regime to a periodic one, unlike some classical cases where phase-locking happens in course of evolution. However, we show that it is possible to introduce periodic orbits to sets of initial states, which may be useful in forming dynamic pattern recognition systems.