Decoherence of Nuclear Spin Quantum Memory in Quantum Dot

Recently an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the {\it storage} period. We calculated the maximum fidelity of writing, storing and reading operations. Our results show that nuclear spin dynamics can severely limits the performance of the proposed device for quantum information processing and storage based on nuclear spins.