Short answer: Calcium-40 ions have long been a workhorse of trapped-ion quantum information, using an optical transition near 729 nm and a spin qubit in the ground state. A 2000 preprint from the Innsbruck group reports cooling one and two ions to the ground state of motion with up to 99.9% probability, a 2009 preprint from Ulm reports a spin qubit in a micro ion trap with 96% rotation fidelity, and a 2013 New Journal of Physics paper describes a small processor that ran the quantum Fourier transform. These are older laboratory results.
2000: cooling and the optical transition
The Innsbruck preprint, posted on arXiv in 2000 and not peer reviewed in that form, says ground state cooling and coherent manipulation of ions in a Paul trap are the prerequisite for quantum information experiments with trapped ions. Using resolved sideband cooling on the optical S1/2 to D5/2 quadrupole transition, the authors cooled one and two calcium-40 ions to the ground state of vibration with up to 99.9% probability. A novel cooling scheme using electromagnetically induced transparency achieved simultaneous ground state cooling of two motional sidebands 1.7 MHz apart. From the motional ground state they demonstrated coherent manipulation on the 729 nm transition, observing up to 30 Rabi oscillations within 1.4 ms in the ground state and in the one-phonon Fock state. In a linear trap with 700 kHz axial frequency, they report a minimum ion spacing above 5 micrometres for up to four ions, and individual addressing of two ions. The abstract was cut off after that point and is not described further.
2009: a spin qubit in a micro trap
The Ulm preprint demonstrates a spin qubit with a single calcium-40 ion in a micro ion trap, encoded in the Zeeman ground-state levels of the S1/2 state. The authors show sideband cooling close to the vibrational ground state and initialization and readout of the qubit levels with 99.5% efficiency. A Raman transition near the S1/2 to P1/2 resonance drives coherent single-qubit rotations, which they report with 96% fidelity and gate times below 5 microseconds. Rabi oscillations on the blue sideband give the phonon number distribution, from which they deduce a trap-induced heating rate of 0.3 phonons per millisecond, with an uncertainty of 0.1.
2013: a small processor and its noise
The New Journal of Physics paper presents a small-scale quantum information processor based on a string of calcium-40 ions in a macroscopic linear Paul trap. The authors review their set of operations, including non-coherent operations that let them realize arbitrary Markovian processes. They say building a larger processor requires lowering error rates, which requires understanding the noise physics, so they identify the dominant noise sources and discuss their effects on different algorithms. They demonstrate the full operation set with the quantum Fourier transform and the quantum order-finding algorithm.
Limits
These are small systems, from one to a few ions, and the results span 2000 to 2013, so they do not describe current calcium-ion hardware. The two preprints are labelled as such, and the heating rate and fidelities come from each group's own traps. The abstracts demonstrate small algorithms, not a large-scale processor.
FAQ
What is the calcium ion optical qubit?
An optical transition at 729 nm between the S1/2 and D5/2 states, used in the Innsbruck experiments.
What is the spin qubit?
Two Zeeman ground-state levels of the S1/2 state, used in the 2009 Ulm work.
How well was the motion cooled?
To the ground state with up to 99.9% probability for one and two ions, per the 2000 preprint.
What algorithms were run?
The quantum Fourier transform and quantum order finding, in the 2013 paper.
Is this current hardware?
No. These are 2000 to 2013 results.
All field notes