We demonstrate the possibility of realizing a neural network in a chain of trapped ions. We show that the system allows for robust distributed classical information storage and its storage capacity, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. Identifying the qubits with configurations of spins that echo the lowest vibrational modes of the system, we perform error resistant universal quantum information processing. Single and two-qubit gates are implemented by applying appropriate axial and transverse magnetic fields.

© 2007 Optical Society of America

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