Hyperfine Vs Optical Qubits Trapped Ions

Short answer: Trapped-ion qubits come in four types, depending on which pair of ion states stores the quantum information: hyperfine, Zeeman, fine-structure and optical. Hyperfine qubits are separated by about a gigahertz and optical qubits by hundreds of terahertz, and each type has its own advantages and drawbacks. A 2019 arXiv review, a 2011 review and a 2023 conference paper describe these tradeoffs. This post summarises the classification and does not rank the platforms.

The four types

A 2019 arXiv review states that trapped-ion qubits use internal electronic states of the ion for the qubit states. They can generally be grouped into four types. Hyperfine qubits use hyperfine states separated by an energy splitting of order gigahertz. Zeeman qubits use magnetic sublevels split by an applied field, typically with frequencies of tens of megahertz. Fine-structure qubits use fine-structure levels separated by typically tens of terahertz. Optical qubits use states separated by an optical transition, typically hundreds of terahertz. The review adds that each type has benefits and drawbacks. A figure caption gives order-of-magnitude splittings of 1 to 10 MHz for Zeeman, 1 to 10 GHz for hyperfine, 1 to 10 THz for fine-structure and 100 to 1000 THz for optical qubits, and notes all four can be implemented in ions with non-zero nuclear spin if the needed D or F levels are present.

Zeeman and hyperfine qubits

A 2011 review in Contemporary Physics describes the Zeeman qubit, encoded in a pair of S1/2 levels, as having a practically infinite spontaneous decay time. In ions with zero nuclear spin the only states there are the two Zeeman states set by the valence electron spin relative to the magnetic field. The drawbacks it lists: the energy difference depends linearly on the magnetic field, so field noise causes dephasing, and at low fields the separation is smaller than the natural linewidth of the P level, so state-selective fluorescence cannot be used directly for detection.

For odd isotopes, or even isotopes with non-zero nuclear spin, the S1/2 level splits into two hyperfine manifolds, and a qubit can be encoded in any pair of hyperfine states. The 2023 Journal of Physics conference paper says the larger splitting of hyperfine qubits gives advantages in more straightforward state detection as well as long coherence times, and that laser pulses can drive hyperfine operations effectively under certain conditions, including a pulse bandwidth much larger than the qubit splitting and much smaller than the detuning.

Laser-free control

The same 2023 paper notes that laser light is common in trapped-ion systems, but laser intensity and phase noise limit fidelity. Laser-free operations using static magnetic field gradients or microwaves avoid these sources, though the paper says fidelity and speed have been worse in experiments than laser-based interactions. It reports that a newer method using an oscillating near-field radio-frequency magnetic field gradient has reached almost the level of the highest laser-based fidelities, with better speed, in an experiment with two magnesium-25 ions using hyperfine ground-state levels.

What this does not tell you

The splittings quoted are typical orders of magnitude, and each reference presents a general classification. They do not pick a winner. The laser-free result is one experiment.

FAQ

What are the four trapped-ion qubit types?

Hyperfine, Zeeman, fine-structure and optical.

How different are their energy splittings?

From about 1 to 10 MHz for Zeeman up to hundreds of terahertz for optical qubits.

Why use hyperfine qubits?

The 2023 paper cites easier state detection and long coherence times.

What limits Zeeman qubits?

Magnetic field noise causes dephasing, per the 2011 review.

Can control avoid lasers?

Microwave and magnetic gradient methods exist, with fidelity that has lagged laser methods in most experiments.