Decoherence from qubit-qubit dipolar interaction in an all silicon quantum computer

Abstract

The qubit-qubit dipolar interaction arises with the very presence of the nuclear qubits in an all--silicon quantum computer (ASQC). Since such interaction depends on the qubit spatial separation noise is induced on entanglement through a damping contribution to the density matrix. A closed condition of ``robustness'' against decoherence is found. The term ``robustness'' is defined unambiguosly. The existence of at least two exceptional coherent states is infered. The preparation of such states is within the range of present technological capabilities. Thus, the harmful effects of decoherence coming from the dipolar interaction can be diminished considerably. An approximate condition against decoherence, to leading order in 1/(qubit separation)[3], is derived. By expanding the time evolution operator in a series of Chebyshev polynomials an approximated expression for the density matrix, whose precision is of order $10^{-4}$, is also found. From this expression, a next-to-leading order approximation for the condition of robustness against decoherence is derived.