Fast incomplete decoherence of nuclear spins in a quantum Hall ferromagnet

A scenario of the quantum computing process based on the manipulation of a large number of nuclear spins in quantum Hall (QH) ferromagnets 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 constraint on the level of decoherence is set by this fluctuation effect. For GaAs multiple-quantum-well structures we find a coherence level not smaller than $1–{10}^{-9},$ which is safely above the danger level of quantum error correction methods.