Wigner crystals of ions as quantum hard drives

Atomic systems in regular lattices are intriguing systems for implementing ideas in quantum simulation and information processing. Focusing on laser-cooled ions forming Wigner crystals in Penning traps, we find a robust and simple approach to engineering nontrivial two-body interactions sufficient for universal quantum computation. We then consider extensions of our approach to the fast generation of large cluster states and a nonlocal architecture using an asymmetric entanglement generation procedure between a Penning trap system and well-established linear Paul trap designs.

Figure 1

(Color online) Two-qubit gate via intensity modulation of a laser addressing a pair of ions in a crystal rotating at frequency ${\omega }_r$.

Figure 2

(Color online) Phonon spectrum (top) for vertical and lateral phonons for a trap with $N=147$ ions and ${\omega }_z∕{\omega }_{xy}=50$. Bottom left: Fidelity versus temperature for the vertical push gate of Ref. 17 (red-dashed line) and for the modulated carrier gate with $\nu =11{\omega }_{xy}$ between different ion pairs: at the center (upper solid line), as well as two (middle solid line) and four (lower solid line) lattice sites away from the center. Bottom right: Modulated carrier gate’s and vertical push gate’s forces on one of the two ions over the gate time; both gates operate in a time $\tau \sim 1∕{\omega }_{xy}$. Anharmonic corrections to the fidelity are not included here. For this choice of parameters, the vertical push gate [17] requires 20 times the force (and laser power) of our modulated carrier gate to achieve the same final $\pi$ two-body phase.

Figure 3

(Color online) (a) A laser is swept adiabatically from left to right, leading to a weighted graph state with different phases for solid and dashed lines. (b) Laser displacements in the crystal plane needed to obtain a constant sweep velocity at given distances $\xi ∕R=0.2,0.4,0.6,0.8$ (from innermost to outermost) from the center, in the rotating crystal’s frame.

Figure 4

(Color online) (a) Schematic of a quantum processor (such as a linear Paul trap) coupled via a high-finesse cavity to a photodetector system to allow interference with photons from an ion Wigner crystal in Penning trap(s) nearby. Gates between distant ions within the memory are achieved by sequential entanglement between each ion and an ion in the quantum processor, followed by entanglement swapping via Bell measurement of the ions in the quantum processor and teleportation-based gates. (b) Ion-level structure for state-dependent fluorescence (cycling between $E$ and 1) and for single-qubit operations via Raman coupling (1 to 0 rotations with off-resonant beams through the gray intermediate state).