Fast Incomplete Decoherence of Nuclear Spins in Quantum Hall Ferromagnet

A scenario of quantum computing process based on the manipulation of a large number of nuclear spins in Quantum Hall (QH) ferromagnet is presented. It is found that vacuum quantum fluctuations in the QH ferromagnetic ground state at filling factor $\nu =1$, associated with the virtual excitations of spin waves, lead to fast incomplete decoherence of the nuclear spins. A fundamental upper bound on the length of the computer memory is set by this fluctuation effect.