Trapped-ion qutrit spin molecule quantum computer

We present a qutrit quantum computer design using trapped ions in the presence of a magnetic field gradient. The magnetic field gradient induces a "spin-spin" type coupling, similar to the J-coupling observed in molecules, between the qutrits which allows conditional quantum logic to take place. We describe in some detail, how one can execute specific one and two qutrit quantum gates, required for universal qutrit quantum computing.