Barium-137 Trapped-Ion Qubit

Figure

Description

The barium-137 trapped-ion qubit encodes quantum information in the hyperfine manifold of the $6S_{1/2}$ ground state of ${}^{137}{\mathrm{Ba}}^{+}$. With nuclear spin $I=3/2$, the ground state splits into $F=1$ and $F=2$ hyperfine levels separated by ${\omega }_{\mathrm{hfs}}/2\pi \approx 8.037\mathrm{GHz}$. Both the 2010 single-ion demonstration and Quantinuum’s 2025 Helios processor define the qubit on the magnetically insensitive clock transition $|F=1,m_F=0⟩\leftrightarrow |F=2,m_F=0⟩$, with Helios taking $|0⟩\equiv |F=1,m_F=0⟩$ and $|1⟩\equiv |F=2,m_F=0⟩$.

A major attraction of ${}^{137}{\mathrm{Ba}}^{+}$ is its favorable laser stack for qubit control and readout. Fluorescence detection uses the 493 nm $6S_{1/2}\to 6P_{1/2}$ transition with 650 nm repumping from $5D_{3/2}$, while shelving and protected measurement use the narrow 1762 nm transition to the metastable $5D_{5/2}$ manifold. In Helios, single- and two-qubit gates are driven by pairs of 515 nm Raman beams separated by the qubit splitting. Compared with ultraviolet-gated species, this pushes the core qubit-control optics into a more mature visible/near-IR regime with higher available laser power and reduced UV-induced optics degradation.

Quantinuum’s Helios processor made ${}^{137}{\mathrm{Ba}}^{+}$ the first barium-based species deployed in a large-scale trapped-ion quantum computer. Helios is a 98-qubit QCCD processor with ${}^{137}{\mathrm{Ba}}^{+}$ data qubits and co-trapped ${}^{171}{\mathrm{Yb}}^{+}$ coolant ions for sympathetic recooling. Averaged over its operational zones, Helios reports single-qubit, two-qubit, and SPAM infidelities of $2.5(1)\times 10^{-5}$, $7.9(2)\times 10^{-4}$, and $4.8(6)\times 10^{-4}$ respectively, corresponding to fidelities of 99.9975%, 99.921%, and 99.952%. In 2026, the same Helios hardware was used to demonstrate encoded computations with 48 to 94 logical qubits using high-rate iceberg codes.

Hamiltonian

The relevant internal Hamiltonian is the hyperfine-plus-Zeeman Hamiltonian

$H=A_{\mathrm{hfs}}\mathbf{I}\cdot \mathbf{J}+{\mu }_B(g_J{J}_z+g_I{I}_z)B,$

where $A_{\mathrm{hfs}}$ is the magnetic-dipole hyperfine constant, $\mathbf{I}$ is the nuclear spin, $\mathbf{J}$ is the electronic angular momentum, and $B$ is the applied bias field. For the $6S_{1/2}$ ground state of ${}^{137}{\mathrm{Ba}}^{+}$,

$\Delta E_{\mathrm{hfs}}=h\times 8.037\mathrm{GHz}.$

At zero field, the $m_F=0\leftrightarrow m_F=0$ transition is a true clock transition with no first-order Zeeman shift. Helios operates instead at a finite bias field of about $3.95\mathrm{G}$, where the qubit remains an approximate clock transition with second-order magnetic sensitivity; the paper quotes a second-order coefficient of $488.8Hz/{\mathrm{G}}^2$ at zero field. State preparation and measurement are implemented by coherently mapping the $|F=1,m_F=0⟩$ state into the metastable $5D_{5/2}$ manifold with 1762 nm pulses, followed by fluorescence detection on the 493/650 nm cycling transitions.

Motivation

Barium offers an unusually attractive trapped-ion engineering point: the qubit species itself can be controlled and measured primarily with visible and near-IR light rather than relying on deep-UV qubit lasers. That improves component availability, eases power delivery, and reduces long-term UV damage to fibers and optics. The ${}^{137}{\mathrm{Ba}}^{+}$ hyperfine clock transition also provides the standard trapped-ion virtues of long-lived ground-state storage and magnetic-field robustness.

The species is especially compelling inside a QCCD architecture. In Helios, ${}^{137}{\mathrm{Ba}}^{+}$ serves as the data qubit while ${}^{171}{\mathrm{Yb}}^{+}$ handles sympathetic cooling, separating computation from recooling and helping preserve qubit coherence during long, transport-heavy programs. The tradeoff is that the full dual-species machine still requires additional UV infrastructure for the ytterbium coolant, so the visible-wavelength advantage applies primarily to the qubit species and gate/readout stack rather than the entire system.

Experimental Status

First hyperfine-qubit demonstration — Dietrich et al. (2010):

• Demonstrated state preparation, microwave-driven qubit rotation, and shelving-based readout for a single ${}^{137}{\mathrm{Ba}}^{+}$ ion.
• Implemented the ground-state hyperfine qubit on the 8.037 GHz clock transition.
• Used the 1762 nm $6S_{1/2}\leftrightarrow 5D_{5/2}$ transition for selective shelving and readout.

Large-scale processor deployment — Ransford et al. (2025):

• Introduced Helios, a 98-qubit QCCD processor using ${}^{137}{\mathrm{Ba}}^{+}$ hyperfine qubits as data qubits.
• Co-trapped ${}^{171}{\mathrm{Yb}}^{+}$ coolant ions provide sympathetic recooling with 369 nm light.
• Reported average infidelities of $2.5(1)\times 10^{-5}$ (1Q), $7.9(2)\times 10^{-4}$ (2Q), and $4.8(6)\times 10^{-4}$ (SPAM).
• Used a four-way X junction, rotatable storage ring, and 8 parallel operation zones for all-to-all connectivity via transport.

Encoded-computation milestone on Helios — Dasu et al. (2026):

• Demonstrated beyond-break-even encoded computations on the 98-qubit Helios processor using high-rate iceberg codes.
• Realized fault-tolerant and partially fault-tolerant benchmarks with between 48 and 94 logical qubits.
• Shows that the barium-based Helios platform is now supporting logical-layer as well as physical-qubit milestones.

Key Metrics

Metric	Value	Notes	Fidelity reference
Hyperfine splitting	8.037 GHz	$	F=1,m_F=0\rangle \leftrightarrow
1Q gate fidelity	99.9975%	Helios zone-averaged benchmark	Ransford et al. 2025
2Q gate fidelity	99.921%	Native $R_{ZZ}(\pi /2)$ / MS-family entangling benchmark on Helios	Ransford et al. 2025
SPAM fidelity	99.952%	From average infidelity $4.8(6)\times 10^{-4}$	Ransford et al. 2025
1Q/2Q gate wavelength	515 nm	Raman beam pairs separated by the qubit splitting	Ransford et al. 2025
Cooling / detection	493 nm	$6S_{1/2}\to 6P_{1/2}$ fluorescence transition	Dietrich et al. 2010
Repump wavelength	650 nm	Clears population from $5D_{3/2}$ during fluorescence cycle	Dietrich et al. 2010
Shelving wavelength	1762 nm	Coherent mapping to the $5D_{5/2}$ manifold for readout	Dietrich et al. 2010
Bias field (Helios)	3.95 G	Approximate clock-state operation point	Ransford et al. 2025
Logical qubits demonstrated	48–94	High-rate iceberg-code benchmarks on Helios	Dasu et al. 2026

Scaling Considerations

• Visible/near-IR qubit optics: the barium qubit species moves gate, shelving, and fluorescence hardware away from deep-UV qubit lasers, improving component availability and reducing optics degradation.
• Not a fully UV-free computer: Helios still relies on ${}^{171}{\mathrm{Yb}}^{+}$ sympathetic cooling at 369 nm, so the visible-wavelength advantage is species-specific rather than system-wide.
• Dual-species complexity: mixed-species loading, transport, recooling, and calibration add real overhead, even though they decouple cooling from computation.
• QCCD transport overhead: shuttling through junctions and between storage and logic zones trades wiring simplicity for transport scheduling, calibration burden, and clock-speed limits.
• Isotope logistics: ${}^{137}\mathrm{Ba}$ is only about 11% naturally abundant, so isotope-selective loading or enriched sources remain operational considerations.
• Measurement complexity: the high-fidelity readout stack is powerful but nontrivial, involving coherent 1762 nm mapping pulses, fluorescence cycling, and crosstalk-mitigation protocols.

References

Qubit characterization

• M. R. Dietrich, N. Kurz, T. Noel, G. Shu, and B. B. Blinov, “Hyperfine and optical barium ion qubits,” Phys. Rev. A 81, 052328 (2010) | arXiv:1004.1161

Large-scale processor

• A. Ransford et al., “Helios: A 98-qubit trapped-ion quantum computer,” arXiv:2511.05465 (2025)

Logical-layer milestone

• S. Dasu et al., “Computing with many encoded logical qubits beyond break-even,” arXiv:2602.22211 (2026)

Linked Papers

• dietrich-2010-barium-hyperfine-qubit
• ransford-2025-helios-98-qubit
• dasu-2026-many-encoded-logical-qubits

Related Entries

• trapped-ion-qubit — parent platform
• ytterbium-hyperfine-qubit — alternative hyperfine ion species; Yb-171 serves as sympathetic coolant in Helios
• strontium-88-ion-qubit — another visible-wavelength trapped-ion species for comparison
• shuttling-ion-trap-qubit — QCCD architecture used by Helios
• molmer-sorenson-gate — entangling gate family used in Ba+ systems