Delocalization border and onset of chaos in a model of quantum computation- art. no. 056226

We study the properties of spectra and eigenfunctions for a chain of 1/2 sp ins (qubits) in an external time-dependent magnetic field and under the con ditions of nonselective excitation (when the amplitude of the magnetic fiel d is large). This model is known as a possible candidate for experimental r ealization of quantum computation. We present the theory for finding deloca lization transitions and show that for the interaction between nearest qubi ts, the transition is very different from that in quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the th reshold for the onset of quantum chaos due to the interqubit interaction de creases with an increase of the number of qubits. Contrary to this expectat ion, for a magnetic field with constant gradient we have found that chaos b order does not depend on the number of qubits. We give analytical estimates that explain this effect, together with numerical data supporting our anal ysis. Random models with long-range interactions have been studied as well. In particular, we show that in this case the delocalization and quantum ch aos borders coincide.