Trapped barium ion qubits and qudits

Short answer: Barium ions are studied as trapped-ion qubits because of a long-lived metastable state and visible and infrared laser wavelengths. A 2010 arXiv paper reports optical and hyperfine qubits in barium-137, a 2017 Physical Review Letters paper reports trapping and spectroscopy of synthetic barium-133, and a 2025 npj Quantum Information paper reports control of a 13-level qudit in barium-137. All of this is laboratory work.

Why barium

The 2010 arXiv paper says barium had never previously been demonstrated as an ionic qubit. It lists several desirable characteristics. The odd isotope barium-137 is about 11% abundant, which the authors say is high enough to trap from a natural source without isotope-selective ionization. Barium has a long-lived metastable 5D5/2 state with a lifetime of 35 seconds, which they say is an order of magnitude longer than that of any other singly ionized alkali earth atom. They note that its decay rate restricts qubit readout fidelity and sets an upper limit on optical qubit coherence times.

The same paper says barium's laser wavelengths are the longest of any ionic qubit candidate, which it describes as favorable for remote photonic coupling through optical fiber, a property it calls important for long-distance entanglement between ionic qubits.

Qubits in barium-137

In that 2010 paper the authors report state preparation, qubit rotation and high-fidelity readout for two separate barium-137 qubit types. One is an optical qubit on the narrow 6S1/2 to 5D5/2 transition at 1.76 micrometres. The other is a ground-state hyperfine qubit on the magnetically insensitive transition at 8 GHz, reached using the readout techniques developed for the optical qubit.

Synthetic barium-133

The 2017 Physical Review Letters paper identifies barium-133 as attractive for quantum information because it combines a spin-1/2 nucleus with visible-wavelength electronic transitions. Using a microgram source of radioactive material, the authors trap and laser cool this synthetic isotope in a radio-frequency ion trap. With a single trapped atom they measure isotope shifts and hyperfine structure on two electronic transitions needed for laser cooling, state preparation and state detection of clock-state hyperfine and optical qubits. They also report an isotope shift for the rare barium-130 and barium-132 nuclides, which they say completes the spectroscopic characterization needed to laser cool all long-lived barium II isotopes.

Qudits

The 2025 npj Quantum Information paper starts from the point that scaling up the computational space is necessary to demonstrate quantum algorithmic advantage, and that using a trapped ion's rich energy-level structure to encode multi-level qudits is a less explored route. The authors report control and single-shot readout of qudits with 13 computational states in barium-137. They say the extra states bring complexities that obscure practical choices of states for encoding, and report tools for predicting practical energy states, validated with good agreement against their experimental data. They also identify the major error sources for qudit control as avenues for improvement. The paper states that state preparation and measurement protocols can be applied with greater than 90% fidelity to the 13-level qudit.

Limits

These are single-ion and small-system laboratory reports. None of the three papers describes a barium-based processor, and the 2025 authors themselves point to error sources that need improving for high-fidelity operations.

FAQ

Can barium-137 be trapped from a natural source?

The 2010 paper says its roughly 11% abundance is high enough to trap it from a natural source without isotope-selective ionization.

What limits optical barium qubit coherence?

According to the 2010 paper, the decay rate of the 35-second metastable 5D5/2 state restricts qubit readout fidelity and sets an upper limit on optical qubit coherence times.

Why are barium's laser wavelengths of interest?

The 2010 authors say they are the longest of any ionic qubit candidate, favorable for coupling to optical fiber and so for long-distance entanglement between ionic qubits.

What was reported for barium-133?

The 2017 paper reports trapping and laser cooling the synthetic isotope with a microgram source of radioactive material, and measuring isotope shifts and hyperfine structure on two transitions.

What was reported for qudits?

The 2025 paper reports control and single-shot readout of 13-state qudits in barium-137, with state preparation and measurement above 90% fidelity.