Quantum computing with magnetically interacting atoms

We propose a scalable quantum-computing architecture based on cold atoms confined to sites of a tight optical lattice. The lattice is placed in a nonuniform magnetic field and the resulting Zeeman sublevels define qubit states. Microwave pulses tuned to space-dependent resonant frequencies are used for individual addressing. The atoms interact via magnetic-dipole interactions allowing implementation of a universal controlled-NOT gate. The resulting gate operation times for alkalis-metals are on the order of milliseconds, much faster then the anticipated decoherence times. Single qubit operations take about $10\mathrm{\mu s}$. Analysis of motional decoherence due to NOT operations is given. We also comment on the improved feasibility of the proposed architecture with complex open-shell atoms, such as Cr, Eu, and metastable alkaline-earth atoms with larger magnetic moments.

Figure 1

Zeeman effect for the ground state of ${}^{23}\mathrm{Na}$ atom. The states are labeled with the electronic and nuclear magnetic quantum numbers $M_J$ and $M_I$ in the strong-field limit. A possible choice of qubit states is shown.

Figure 2

Proposed quantum computing architecture. The atoms are confined to sites of an optical lattice. Nonuniform magnetic field is required for individual addressing of the atoms with pulses of the resonant microwave radiation.

Figure 3

Adiabaticity function $G\left(\xi \right)$, Eq. (5).