Comparison of Quantum Entangling Gates for Ions in Penning and RF Paul Traps

Trapped ions have high gate fidelities making them a leading platform for quantum simulation and computation. Entangling gates are typically performed using a Mølmer-Sørensen or light-shift geometric phase gate. In our Penning trap, we have performed quantum simulations on crystals of hundreds of ions using the light-shift gate because of the difficulty of spanning our 124 GHz qubit splitting in ⁹Be⁺ at 4.5 T. One advantage of the Mølmer-Sørensen gate, however, is that it can be configured such that the motion of the ions is less sensitive to the optical phase difference between the driving laser beams. It can therefore be used to improve sensing applications and drive gates in 3-D crystals of up to 10⁵ ions. 

Spontaneous emission has limited our previous work. We show theoretically that in the high-field regime, the two gates perform comparably well. We also examine how detuning the laser beams between the Zeeman levels in the P_3/2 manifold at high fields enables us to improve upon operations with detuning between the P_1/2 and P_3/2 manifolds and explore if this protocol can be extended to lower fields. Finally, we compare the possible fidelity of entangling gates in high and low magnetic fields.