Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays

We propose an architecture and methodology for large-scale quantum simulations using hyperfine states of trapped ions in an arbitrary-layout microtrap array with laserless interactions. An ion is trapped at each site, and the electrode structure provides for the application of single and pairwise evolution operators using only locally created microwave and radio-frequency fields. The avoidance of short-lived atomic levels during evolution effectively eliminates errors due to spontaneous scattering; this may allow scaling of quantum simulators based on trapped ions to much larger systems than currently estimated. Such a configuration may also be particularly appropriate for one-way quantum computing with trapped-ion cluster states.

Figure 1

(Color online) Rendering of section of surface trap array and microcoils. Leads are not shown, and the electrodes shown are only a representative subset of those required. Ions may be trapped directly above loops, or trap electrodes and coils may be offset so ions can be trapped above any point in a microcoil unit cell. For field calculations, coils are treated as complete circular current loops.

Figure 2

(Color online) Force on an ion above an array microtrap. These data are for positions near the center of a $20\times 20$ array. (a) Logarithm of the absolute value of the $x$ (or $y$) component of the force in newtons on an ion produced by an array of microcoils. The lattice spacing is $10\mathrm{\mu }\mathrm{m}$, with a current amplitude of $10\mathrm{mA}$ in each loop of radius $2.5\mathrm{\mu }\mathrm{m}$. The horizontal axis is distance along the unit cell diagonal, and the vertical axis is the ion’s height above the trap-microcoil surface; the relative geometry of a moment in a general location in this plane is shown in the inset diagram. The center of the nearest microcoil is located at 0 on this axis. See Sec. 4 for spin-spin interaction strength attainable with these forces. (b) Force on a moment when its orientation is pinned by an external field. The lower (upper) curve is the logarithm of the $x$ component ($z$ component) of the force on an ion as a function of ion height above the surface of an array with ions centered on loops in the $x$ and $y$ directions and the ion moment pinned in the horizontal $x=y$ (vertical $z$) direction by an external dc magnetic field; the inset diagram shows the relative geometry of a moment in a general position along the axis.

Figure 3

(Color online) Interaction strength $\mid J\mid$ for the same configuration as in Fig. 2 above. (a) Logarithm of the nearest-neighbor interaction strength (in hertz) produced by a $20\times 20$ array of microcoils. The lattice spacing is $10\mathrm{\mu }\mathrm{m}$, with a current amplitude of $10\mathrm{mA}$ in each loop of radius $2.5\mathrm{\mu }\mathrm{m}$. The horizontal axis is distance along the unit cell diagonal, and the vertical axis is the ion’s height above the trap-microcoil surface (see inset diagram). The center of the nearest microcoil is located at 0 on this axis, and an ion of mass of $9\mathrm{amu}$ $\left({}^9\mathrm{Be}^{+}\right)$ is assumed. Interactions in the 1–$100\mathrm{kHz}$ range are attainable at locations 1–$5\mathrm{\mu }\mathrm{m}$ above the coil edge (vertically above $2.5\mathrm{\mu }\mathrm{m}$ on the horizontal axis). (b) The lower (upper) curve is the logarithm of nearest-neighbor interaction strength as a function of ion height above the surface of an array with ions centered on loops in the $x$ and $y$ directions and the ion moment pinned in the $x=y$ direction ($z$ direction) by an external dc magnetic field (see inset diagram).

Figure 4

(Color online) Ring and ladder geometries with periodic boundary conditions. (a) 1D ring: the nearest-neighbor distance is $a$ and the next-nearest neighbors are separated by a distance $s$ dependent on the number of ions in the ring. The NNN interaction strength can be made to closely approach that in a straight-line array for tens of ions. (b) Ladder with periodic boundary conditions: the interaction strength along the exterior leg (length $a_2$) approaches the strength along the inner leg (length $a_1$) within a few percent for a few hundred pairs of ions. The rung length $\mathrm{\Delta }r$ is the difference in the radii of the inner and outer rings, and $n$ is the number of rungs.

Figure 5

Plan view depicting ion surface trap array with one possible electrode configuration and method for array expansion during one-way quantum computing protocol. The ions $(●)$ are in a different plane from the electrode segments $(◻)$. The left panel shows ions in a compressed array, each over a microcoil (not shown), in which configuration a cluster state could be formed as described in the text. The ions would then be repositioned through concerted variation of the potentials on the electrodes to form an expanded array, as in the right panel, suitable for individual qubit rotations via laser or microcoil and readout via resonance fluorescence. The ions would then be returned to the compressed array for the next experiment, or for the next stage in a topological error-correcting protocol [44].