SPAM error characterization protocol in trapped ions

Answer

The standard SPAM (state preparation and measurement) characterization protocol for trapped-ion qubits is a repeated-cycle procedure: prepare the qubit in each computational basis state, read it out by state-dependent fluorescence detection, and report the probability of misclassifying the result, averaged over both preparation states. This is described identically by two independent sources — Wright et al. 2019 602ed535 and a 2024 Physics-Uspekhi review 77c5f91d — as combining fast optical-pumping initialization with fluorescence-based readout. The lowest combined SPAM error reported for a single dedicated qubit under this protocol is 9.0(1.3)x10^-5 (0.009%), for a 137Ba+ hyperfine qubit using a stroboscopic strong/weak-transition preparation scheme d057acd7, independently cited by the 2024 review as the field's best combined-SPAM figure 77c5f91d. Among multi-qubit processors reporting an average combined SPAM error across an operating register, the current record in this corpus is 3.3(5)×10^(-4), from Quantinuum's 98-qubit Helios system (137Ba+ hyperfine qubits, 2026) 71d3db20, improving on 0.7% for an 11-qubit 171Yb+ system (2019) 602ed535.

Summary

Two distinct "state of the art" figures coexist and answer different questions, and readers should not conflate them. The best combined SPAM error for one carefully tuned, individually addressed qubit is 9.0x10^-5. The best combined SPAM error averaged across an entire multi-qubit operating processor is roughly four times worse, 3.3(5)×10^(-4) — the gap reflects the added difficulty of maintaining uniform low error across many ions simultaneously rather than in a single-qubit demonstration. Several other corpus values are readout-only or detection-only component benchmarks, not full combined SPAM, and citing them as SPAM figures would overstate performance: 40Ca+ readout fidelity 99.991% 02c444f9, 171Yb+ APD detection error 1.8(2)x10^-3 5ccb9b5f, and a four-qubit 138Ba+ camera-based detection error of 17 ppm b954f40f. At the opposite end, an 8-ion 171Yb+ qudit (four-level) processor reports a much higher per-ion SPAM error of ~3.6% 9c1ce6fa, illustrating that encoding scheme (qubit vs. qudit) and register size drive SPAM performance as much as ion species does. Across the full corpus the span from the best single-qubit figure (9.0x10^-5) to the worst reported figure (~3.6%, the qudit processor) is a factor of roughly 400 — about two and a half orders of magnitude, not the "four orders of magnitude" an earlier version of this report claimed before the underlying arithmetic was rechecked.

Evidence

• Quantinuum 98-qubit Helios, 137Ba+, 2026 71d3db20 — average SPAM error 3.3(5)×10^(-4) across all operational zones, current best multi-qubit-register figure in this corpus.
• 2024 Physics-Uspekhi review of trapped-ion computing 77c5f91d — defines the optical-pumping + fluorescence-readout SPAM protocol; cites 137Ba+ SPAM error 9.0(1.3)x10^-5 as best-in-field and 133Ba+ SPAM error ~2.9x10^-4 as a second data point.
• 8-ion 171Yb+ qudit (ququart) processor, 2025 9c1ce6fa — mean per-ion SPAM fidelity 96.4(2)%, i.e. SPAM error ~3.6% per ion; two-qudit gate fidelity 92.7(7)% including SPAM.
• 11-qubit 171Yb+ system, 2019 (Wright et al., Nat. Commun.) 602ed535 — repeated prep/measure protocol; SPAM error ~0.7%; single-qubit gate fidelity 99.5%, two-qubit gate fidelity 97.5%.
• Single 43Ca+ hyperfine qubit, 2014 (Harty et al., PRL) 55352904 — combined state-preparation and single-shot-readout fidelity 99.93%, i.e. 0.07% combined SPAM error, directly measured on one qubit.
• Single 40Ca+ optical qubit, 2008 (Myerson et al., PRL) 02c444f9 — readout-only benchmark (not full SPAM): 99.991(1)% single-shot readout fidelity over 1,000,000 trials.
• 171Yb+ electron-shelving readout, PRA 5ccb9b5f — readout-only benchmark: APD detection error 1.8(2)x10^-3 in 100us; long-lived-state limit 6(7)x10^-6 in 1ms.
• Four-qubit 138Ba+ camera readout, 2021 (Zhukas et al., PRA) b954f40f — readout-only benchmark: single-qubit detection error 4.2 ppm, four-qubit combined detection error 17 ppm; does not include a state-preparation component.
• 137Ba+ I=3/2 hyperfine qubit, 2022 (An et al., PRL) d057acd7 — primary source for the corpus's lowest full combined-SPAM figure: stroboscopic strong/weak-transition preparation plus fluorescence detection reaches 9.0(1.3)x10^-5 SPAM infidelity.
• 9Be+/25Mg+ indirect readout, 2021 (Erickson et al., PRL) c0ce8ac1 — combined readout-and-back-action error (not a full SPAM figure with independent state-prep term) of 1.2x10^-4 for one subspace and consistent with zero (upper bound ~1.9x10^-5) for the other, at 68% confidence; technique also protects spectator qubits from readout-induced disturbance.

Methodology

Submissions were first separated by what they actually measure: full combined SPAM error (state-preparation plus measurement, reported as one number) versus readout/detection-only component error, since several submissions explicitly flag this distinction themselves. Only full combined-SPAM figures were used to answer the "state-of-the-art" half of the question; readout-only figures were kept in the evidence list but excluded from the SOTA comparison, since citing them as SPAM numbers would be citing a smaller, easier-to-achieve quantity as if it were the harder combined one. Full-SPAM figures were then separated again by scope — single dedicated qubit versus an entire multi-qubit register averaged together — because these answer different practical questions. No values were pooled or averaged across submissions; each figure is reported as its source states it, in the source's own units, with only unit-name normalization (e.g., dimensionless probability vs. percent) where the source itself provided an explicit conversion. A prior version of this report additionally cited a 2023 Quantinuum H2 (32-qubit) result as an intermediate multi-qubit data point; that submission has since been sent back for revision and is not in this task's currently verified corpus, so it is omitted here rather than cited from memory.

Limitations

• No submission in this corpus provides a numeric error-budget table that separates the state-preparation contribution from the measurement contribution within a combined SPAM figure; the standard protocol reports the two together.
• The corpus's lowest full-SPAM figure (9.0x10^-5) and its best multi-qubit-register figure (3.3(5)×10^(-4)) come from different ion species handling (137Ba+ single-qubit tuning vs. a 98-qubit operating processor) and different years; whether the single-qubit record has since been reproduced at register scale is not established here.
• The 8-ion qudit result (~3.6% per-ion SPAM) is the only qudit (non-binary) encoding in the corpus, so it is not possible to say whether the higher error reflects the qudit encoding specifically, the smaller research-stage system, or both.
• A previously verified 2023 Quantinuum H2 (32-qubit, 1.6(1)x10^-3 combined SPAM) result that placed a data point between the single-qubit and Helios register figures is currently under revision (NEEDS_REVISION) and is not part of this corpus snapshot; if it is re-verified unchanged, it would sit between the two figures discussed above without changing either endpoint of the range.