Programmable quantum simulator based on Penning trapped ions

Two-dimensional ion crystals are a proven platform for generating many body spin-spin interactions. We describe recent work constructing a programmable quantum simulator using a few to hundreds of ⁴⁰Ca⁺ ions confined in a compact Penning trap. The motional modes of the ions are cooled near the motional ground state using dark resonance cooling, which is compared to a semi-classical model. We show progress towards simultaneous entanglement of all pairs of atoms through the application of a pair of global optical dipole force beams. Arbitrary Ising interaction graphs can be produced by alternately applying the global entangler with individually addressed one qubit rotations. Using a fast time-tagging camera, the state of each qubit is read out by imaging the planar ion crystal in its rotating frame. Combined, these tools are applied to MaxCut QAOA and could also be used for hybrid digital-analog quantum simulation.