Nuclear spins as quantum memory in semiconductor nanostructures

We theoretically consider the possibility of using 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 of P donor nuclear spins as a function of time 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; in the interest of the high fidelity requirements necessary for fault-tolerant quantum computing, we consider the initial quantum memory decay caused by a non-Markovian bath. We calculate this nuclear spin memory time 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 (T-2), 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 mu s (GaAs:P) and 1 to 2 ms (natural Si:P) using CPMG pulse sequences of just a few (similar to 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.