  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.
