Trapped ion quantum computing is a leading approach in the field of quantum information processing. It utilizes ions confined in electromagnetic traps and manipulated using laser beams. A good overview of different types of trapped ion gates is given by [1].
In this text we will go over the gates developed in this group. We will start with the basic MS gate, and slowly build up to gates with more robustness and controllability. The theory background for these gates developed in our group can be found in the following references.
Trapped ion gates can be produced by using lasers. In order to execute the gate, we need to imprint the gate to the laser. We do this via an AOM. We send an rf waveform to the AOM, and the single-frequency that enters teh AOM leaves it with the gate waveform modulating it. Hence, we have imprinted the gate information into the laser.
There are several approaches to engineering this waveform. We can look at it in three ways. We can generate the waveform by modulating the amplitude o frequency of the gate over time, or we can focus on the spectral components of the gate which are static in time. Our group relies on the latter approach.
The Cirac-Zoller gate [2] is one of the earliest proposals for implementing quantum gates with trapped ions. It uses a combination of laser pulses to entangle the internal states of two ions via their collective motion.
The Mølmer-Sørensen gate is a widely used entangling gate in trapped ion systems. It employs bichromatic laser fields to create entanglement between the internal states of ions without requiring precise control over their motion.
We can use a single mode of motion to execute a gate, like teh COM mode in the MS gate, but with additional tones to the bi-chromatic drive which would give the MS gate robustness properties. Such gates are Cardioid gates, Antioid gates, CarNu gates, and the Sapiroid gate.
[1] Cai, Z., Luan, C.Y., Ou, L. et al. “Entangling gates for trapped-ion quantum computation and quantum simulation.” Journal of the Korean Physical Society, vol. 82, pp. 882–900, 2023. https://doi.org/10.1007/s40042-023-00772-3
[2] Cirac, J.I., Zoller, P. “Quantum Computations with Cold Trapped Ions.” Physical Review Letters, vol. 74, no. 20, pp. 4091-4094, 1995. https://doi.org/10.1103/PhysRevLett.74.4091