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Dynamics of nuclear spin measurement in a mesoscopic solid-state quantum computer

We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane, by calculating the quantum dynamics of two coupled nuclear spins on 31 P donors implanted in 28 Si. We estimate the time of the `quantum swap operation' - the minimum measurement time required for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. Our calculations show that for realistic values of the parameters this time is of the order of swap ~5 × 10-5 s. We also calculate the probability of error for typical values of the external noise.