Trapped-Ion Quantum Logic Gates Based on Oscillating Magnetic Fields

Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.

Figure 1

Example geometry for driving ion-qubit gates with oscillating magnetic fields produced by surface-electrode traps. The trap electrodes lie in the $yz$ plane. The ion is assumed to be trapped at a distance $d_0$ above the trap plane. Oscillating currents in electrodes (a), (c), and (d) can be used to implement single-qubit rotations and entangling gates (see text). The electrode widths are $5/4d_0$ [(a),(c),(d)] and $39/40d_0$ [(b)]. We assume a uniform distribution of currents in the surface.

Figure 2

Simulation of magnetic fields resulting from surface currents in an example trap structure, viewed from above. The figure shows the frequency dependence of the field $30\mu \mathrm{m}$ above the center of the trap for the $U$-shaped current loop shown in the inset.