High-fidelity entanglement of metastable trapped-ion qubits with integrated erasure conversion

Today’s most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of $\sim 94%$ of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73% and a SPAM-corrected Bell state fidelity of 98.61%. When subtracting erasure errors, this fidelity becomes 99.16%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.

💡 Research Summary

This paper addresses two major challenges facing trapped‑ion quantum processors: the experimental overhead associated with dual‑species crystals and the relatively low logical error thresholds that result from generic Pauli‑type errors. The authors demonstrate that qubits encoded in the metastable D5/2 manifold of 40Ca+ (“m‑qubits”) can be operated with high fidelity while simultaneously converting a large fraction of gate errors into erasure errors that are detectable and therefore much easier to correct.

The key idea is “erasure conversion.” Spontaneous Raman scattering (SRS) during stimulated Raman transitions predominantly (≈94 %) returns the ion from the D5/2 manifold to the S1/2 ground state via the P3/2 → S1/2 decay channel. Because the S1/2 ↔ P1/2 cycling transition is used for fluorescence detection, any ion that has undergone such a scattering event can be identified by a simple fluorescence check (FC). Likewise, the natural decay of the D5/2 level (lifetime ≈1.16 s) also leads to a detectable loss of population. Consequently, both SRS‑induced errors and decay‑induced errors become “erasure” errors that can be flagged and either post‑selected or fed into an error‑correcting code that treats them more efficiently than unheralded Pauli errors. The authors report that ≈94 % of SRS errors are thus converted into erasures, and essentially all decay errors are similarly flagged.

To evaluate the performance of m‑qubits, the authors implement a two‑ion geometric phase gate using far‑detuned (‑44 THz) stimulated Raman beams at 976 nm. The Raman system is based on a compact injection‑locked diode laser delivering up to 220 mW per beam, with polarization control that nulls differential light shifts on the qubit states. The gate employs four phase‑space loops with a spin‑echo in the middle (Walsh modulation) and has a total duration of 400 µs. Starting from the product state |↓↓⟩, the ideal output is the Bell state |Φ⁺⟩ = (|↓↓⟩ + |↑↑⟩)/√2. Bell‑state fidelity is extracted from parity‑fringe measurements combined with population readout.

The raw Bell fidelity is 97.73 % (±0.08 %). After correcting for state‑preparation‑and‑measurement (SPAM) errors (≈0.87 × 10⁻³), the fidelity rises to 98.61 %. By discarding the 0.55 % of experimental shots in which an erasure was detected, the post‑selected, SPAM‑corrected fidelity reaches 99.16 %, corresponding to a 39 % reduction in non‑SPAM error due to erasure conversion.

A detailed error budget is presented. Non‑erasure errors total ≈9.75 × 10⁻⁴ and are dominated by motional dephasing (55 × 10⁻⁴) and spin dephasing (26 × 10⁻⁴). Smaller contributions arise from π‑time calibration (6.8 × 10⁻⁴), Raman‑beam intensity drift (4.8 × 10⁻⁴), and mode‑frequency drift (1.9 × 10⁻⁴). Erasure errors amount to ≈5.37 × 10⁻³ and are split among D5/2 lifetime during the gate (11.7 × 10⁻⁴), Raman scattering (13.5 × 10⁻⁴), scattering from the 854 nm light‑shift beam (5.6 × 10⁻⁴), and decay that occurs during the fluorescence checks (≈23.9 × 10⁻⁴). The fluorescence check itself adds overhead: it increases the total error probability by a factor of 1.6 but reduces the unheralded leak‑age probability by a factor of 4.6. The authors argue that with improved photon‑collection efficiency and optimized FC timing (potentially reducing FC duration to ~10 µs), the decay‑related erasure overhead could be lowered to ≈5 × 10⁻⁵.

The paper also outlines concrete pathways to further suppress both erasure and non‑erasure errors. First, encoding the qubit in the |m_J = +5/2⟩ and |m_J = −3/2⟩ sublevels would maximize the difference in Clebsch‑Gordan coefficients, thereby reducing Raman‑induced SRS probability. Second, eliminating Walsh modulation would shorten the gate time, directly reducing exposure to motional and spin dephasing. Third, moving the Raman beams to a counter‑propagating geometry would cut the effective Raman scattering rate by roughly a factor of 17, bringing Raman‑induced errors below 10⁻⁴ as predicted in earlier theoretical work. Fourth, adding a dedicated σ⁻‑polarized Raman beam would remove reliance on the σ⁻ component of the “R‑null” beam, alleviating polarization‑impurity errors. Together with higher laser power or more efficient gate designs, these upgrades could push non‑erasure errors well below the 10⁻⁴ threshold required for fault‑tolerant operation.

In summary, the authors experimentally validate that metastable‑state trapped‑ion qubits can achieve Bell‑state fidelities exceeding 99 % when erasure errors are excluded, and they provide a thorough quantitative analysis of all error channels. By converting the dominant spontaneous‑Raman scattering and natural decay processes into detectable erasures, the work demonstrates a practical route to biasing error channels toward erasures—a regime where quantum error‑correcting codes require fewer physical qubits and have higher fault‑tolerance thresholds. The proposed hardware improvements suggest that trapped‑ion platforms can attain the low‑overhead, high‑fidelity performance needed for scalable, fault‑tolerant quantum computing without resorting to mixed‑species crystals.