  We theoretically consider solid state nuclear spins in a semiconductor
nanostructure environment as long-lived, high-fidelity quantum memory. In
particular, we calculate, in the limit of a strong applied magnetic field, the
fidelity versus time of P donor nuclear spins in random bath environments of Si
and GaAs, and the lifetime of excited intrinsic spins in polarized Si and GaAs
environments. In the former situation, the nuclear spin dephases due to
spectral diffusion induced by the dipolar interaction among nuclei in the bath.
We calculate the decay of nuclear spin quantum memory in the context of Hahn
and Carr-Purcell-Meiboom-Gill (CPMG) refocused spin echoes using a formally
exact cluster expansion technique which has previously been successful in
dealing with electron spin dephasing in a solid state nuclear spin bath. With
decoherence dominated by transverse dephasing (T2), we find it feasible to
maintain high fidelity (losses of less than 10^{-6}) quantum memory on nuclear
spins for times of the order of 100 microseconds (GaAs:P) and 1 to 2
milliseconds (natural Si:P) using CPMG pulse sequences of just a few (~2-4)
applied pulses. We also consider the complementary situation of a central
flipped intrinsic nuclear spin in a bath of completely polarized nuclear spins
where decoherence is caused by the direct flip-flop of the central spin with
spins in the bath. Exact numerical calculations that include a sufficiently
large neighborhood of surrounding nuclei show lifetimes on the order of 1-5 ms
for both GaAs and natural Si. Our calculated nuclear spin coherence times may
have significance for solid state quantum computer architectures using
localized electron spins in semiconductors where nuclear spins have been
proposed for quantum memory storage.
