Mid-circuit ground-state cooling and ancilla readout in the $\textit{omg}$ architecture

Abstract: The trapped-ion optical-metastable-ground ($\textit{omg}$) architecture for quantum processors promises the full functionality of two-species experiments, including sympathetic cooling and non-destructive ancilla readout, without the corresponding hardware overhead. We confirm that we can cool a global motional mode of a mixed metastable-ground state Coulomb crystal to the motional ground state via dissipative operations on the ground ($\textit{g}$) qubit without disturbing coherence of the metastable ($\textit{m}$) qubit. This enables quantum logic spectroscopy to non-destructively readout the state of the $\textit{m}$ qubit using fluorescence detection of the $\textit{g}$ qubit. Extensions of these demonstrations to larger system sizes should enable the mitigation of motional heating after ion shuttling and syndrome extraction for quantum error correction, both crucial primitives for future fault-tolerant quantum computers based on trapped ions.

• The paper demonstrates sympathetic mid-circuit cooling of a shared motional mode to n̄=0.02(1) while preserving metastable-qubit lifetime, Ramsey coherence, and protected-subspace stability.
• The paper introduces measurement-based erasure-conversion cooling with 79(5)% efficiency and shows that quantum-logic-spectroscopy ancilla readout achieves up to 97.4(5)% fidelity with minimal data-qubit disturbance.
• The paper establishes key fault-tolerant primitives for the single-species omg architecture, while identifying 729 nm laser servo noise, magnetic-field noise, and motional coherence as priorities for improvement.

Overview

This paper reports the first demonstration of non-destructive, sympathetic ground-state cooling and ancilla readout compatible with mid-circuit operation in a single-species mixed-manifold ("omg") trapped-ion system (2608.13181). Using two $^{40}$Ca$^+$ ions in a linear RF Paul trap—one encoding an m-qubit in the D$_{5/2}$ metastable manifold and one serving as a g-qubit ancilla in S$_{1/2}$—the authors show that dissipative operations on the ground-state ion can recool a shared motional mode to $\bar{n}=0.02(1)$ without measurably degrading the coherence or lifetime of the metastable qubit. This cooling then enables quantum-logic-spectroscopy (QLS) readout of the m-qubit via fluorescence detection of the identical-species ancilla, providing the two primitives—mid-circuit recooling after measurement-induced heating or shuttling, and syndrome-style ancilla readout—that underpin fault-tolerant operation of the omg architecture [omgBlueprint].

The central motivation is that dual-type (mixed-manifold) operation promises the functionality of two-species experiments—sympathetic cooling and non-destructive readout—without the hardware overhead of a second isotope or element. Prior work had demonstrated sympathetic Doppler and EIT cooling of metastable ions [Yang2022, feng_realization_2024] and near-ground-state sympathetic cooling in multi-species systems [NISTneargroundstatecooling], but a single-species, mixed-manifold demonstration reaching the motional ground state was outstanding. The paper closes that gap.

Mid-circuit recooling

The authors first characterize two realistic sources of motional excitation on the 1.86 MHz center-of-mass radial mode (idle heating rate 1.7(4) quanta/s). Fluorescence checks (FCs) used for state detection heat the crystal to $\bar{n}=17^{+6}_{-3}$ during a standard 1 ms FC; a resonant RF pulse mimicking shuttling-induced displacement produces $|\alpha|=1.12(3)$, comparable to values reported in recent transport experiments [clark2023characterization, lancellotti2024low]. Both are recoverable: 1 ms of Doppler cooling brings the crystal near the Doppler limit ($\bar{n}=5.6(9)$), and a subsequent 1 ms of EIT cooling approaches the calculated limit of $\bar{n}=0.15^{+0.11}_{-0.08}$. For the displaced state, EIT cooling alone for 400 μs yields $\bar{n}=0.080(6)$.

Crucially, these dissipative operations do not disturb the m-qubit. The D$^+$0 lifetime measured under all beam configurations exceeds the natural lifetime of 1.168(9) s (biased upward by residual 393 nm repumping), spin-echo Ramsey $^+$1 remains at 4.0(1) ms regardless of which laser set is active, and the protected-subspace parity decay constant stays within uncertainty of the no-laser baseline across all cases. The implication is that mid-circuit measurement and recooling can be interleaved with coherent storage in metastable-encoded data qubits—but the paper notes that Doppler plus EIT cooling alone does not reach the ground state required for high-fidelity entangling gates, motivating the next section.

Measurement-based cooling

Conventional sideband cooling routes are incompatible with mid-circuit operation here: quench light at 854 nm induces excessive scattering out of the m-qubit and Stark-shift-induced decoherence even when detuned by −20 GHz with >99% pure σ$^+$2 polarization. The authors therefore implement measurement-based (erasure-conversion) cooling [eschner1995nulldetectcool, lee2023heraldmotionalground, shaw2025erasure]: the g-qubit is shelved to $^+$3, phonon-subtracting 729 nm sideband pulses deshelve any population with $^+$4, optical pumping resets S$^+$5 population to $^+$6 between pulses, and a final FC heralds success. A key operational distinction is that this constitutes pre-selection rather than post-selection: failed heralds abort the experiment before it runs, reducing wasted shots.

With three optimized 170(13) μs sideband pulses, the protocol achieves $^+$7 with per-cycle efficiency $^+$8, limited fundamentally by the post-EIT ground-state population of $^+$9. The efficiency far exceeds the earlier trapped-ion demonstration ($_{5/2}$0) [lee2023heraldmotionalground] and matches the best neutral-atom tweezer result ($_{5/2}$1) [shaw2025erasure]. A Lindbladian model attributes the residual temperature to off-resonant carrier couplings from servo bumps in the 729 nm laser spectrum—with relative strengths 0.166(4) and 0.019(1)—and predicts that suppressing them would yield $_{5/2}$2, competitive with Raman sideband cooling. One full cooling cycle takes ~3.3 ms, much shorter than metastable clock-qubit coherence times [Shi2025].

As with the recooling experiments, the m-qubit is preserved: neither lifetime nor Ramsey coherence is affected, and the protected-subspace decay constant of 0.22(3) s exceeds the total 729 nm pulse duration by three orders of magnitude.

Non-destructive ancilla readout

Quantum logic spectroscopy

In the first readout scheme, the m-qubit state is mapped onto the COM mode via carrier and phonon-adding π-pulses, and a phonon-subtracting pulse transfers $_{5/2}$3 population from the shelved ancilla to $_{5/2}$4 for fluorescence detection. At $_{5/2}$5, achieved with five sideband pulses, the method yields fidelities of 92.2(8)% and 97.4(5)% for $_{5/2}$6 and $_{5/2}$7 respectively, with efficiencies of 94.3(7)% and 97.3(5)%. Spectroscopy and Rabi flopping of the m-qubit RF transition show excellent overlap between direct and ancilla-based readouts (center frequencies 2.6335(2) vs. 2.6336(3) MHz; Rabi frequencies 250.9(6) vs. 250.5(7) kHz). Post-sequence direct readout shows bit-flip probabilities of only 0.7(1)% and 0.4(1)%, confirming non-destructiveness within the qubit subspace—though leakage out of D$_{5/2}$8 scales with residual motional excitation.

Spin-dependent force readout

The second scheme uses a state-dependent optical dipole force from interfering 976 nm beams to write the m-qubit state onto motion, avoiding the leakage inherent to sideband-based mapping. Because geometry restricts the available polarization, the sequence applies the force, swaps m-qubit populations with a Raman pulse, and reapplies the force with a π phase shift. Measured displacement rates are $_{5/2}$9 ms$_{1/2}$0 and $_{1/2}$1 ms$_{1/2}$2. Single-shot detection gives bright-ancilla probability 51(2)% for $_{1/2}$3 and dark probability 88(1)% for $_{1/2}$4; repeating the full non-destructive sequence raises the $_{1/2}$5 figure to 75(1)% but degrades $_{1/2}$6 to 80(1)%—an explicit fidelity tradeoff that adaptive sequences only partially break. The paper states plainly that efficient high-fidelity operation requires either better motional coherence ($_{1/2}$7 ms currently) or selection rules allowing only one state to be driven, in which case $_{1/2}$8 would give single-shot fidelity above 0.99.

Limitations and open questions

The dominant technical limitations are servo bumps in the 729 nm spectrum, which drive unintended carrier transitions and cap the cooling efficiency, and magnetic-field noise, which limits both sideband contrast and motional coherence. The proposed remedies—laser feedforward [li2022active], cavity filtering [levine2018high], faster sidebands via higher 729 nm power, and magnetic shielding—are identified but not demonstrated here. Several questions remain open: whether the predicted $_{1/2}$9 can be realized in practice; whether the spin-dependent-force readout tradeoff can be broken via polarization geometry changes or adaptive protocols; and how these two-ion demonstrations scale to larger crystals where motional-mode crowding and crosstalk will matter. The suggestion of true motional erasure conversion—checking for motional excitation immediately after a gate—is raised as a possibility but not tested.

Conclusion

This work establishes that a single species of trapped ion, with qubits encoded in spectrally isolated ground and metastable manifolds, can support the full suite of mid-circuit primitives previously requiring dual-species hardware: sympathetic recooling to the motional ground state ($\bar{n}=0.02(1)$0), preservation of metastable-qubit coherence throughout all dissipative operations, and non-destructive ancilla readout via QLS with fidelities approaching 97%. The results position the omg architecture as a lower-overhead alternative for fault-tolerant trapped-ion quantum computing, contingent on suppressing the identified laser-noise and magnetic-field limitations.