Fast incomplete decoherence of nuclear spins in a 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 � = 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. PACS numbers: A growing number of models for quantum information processing (or Quantum Computing-QC) has been recently proposed 1 , some of which were successfully tested experimentally in devices consisting of a few qbits.The scaling up of these toy devices to the desired large number of quantum gates seems at present a formidable challenge. Of special interest are the models based on the manipulation of nuclear spins in semiconducting