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arXiv:2411.12727 · Physical Review A

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

A. Quinn, G. J. Gregory, I. D. Moore, S. Brudney, Jeremy Metzner, E. R. Ritchie, J. O'Reilly, David J. Wineland, D. T. C. Allcock

Published Mar 17, 2026• 1 citation
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Abstract

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.

DOI
10.1103/p3cy-8yjk

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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 ∼94%\sim 94\%∼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.
Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the preexisting toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable D5/2{D}_{5/2}D5/2​ qubit manifold of a single trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion illuminated by 976 nm light that is $\ensuremath{-}44$ THz detuned from the dipole-allowed transition to the P3/2{P}_{3/2}P3/2​ manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities less than ${10}^{\ensuremath{-}4}$ are possible.
Trapped-ion systems are leading candidates for quantum computing, offering long coherence times and high-fidelity gate operations. Scaling them, however, requires advanced capabilities such as mid-circuit measurement, qubit reset, and cooling, which together enable quantum error correction. One approach is the use of mixed qubit types, for example employing different ion species for cooling and computation. Recently, the omg blueprint [1] has gained attention as a method for coherently converting between qubit types within a single ion species, removing the overhead of mixed-species architectures while retaining their flexibility. In this thesis, we realise mixed qubit types in 137Ba+ using optical and metastable qubits. We demonstrate coherent control of both, as well as their coherent interconversion, achieving error rates at the 10−4 level suitable for NISQ applications. To enable selective control in multi-ion chains, we integrate a novel photonic chip for individual addressing of Raman beams [2]. We achieve cross-talk levels at or below 10−3 across all zones, and as low as 10−5 in some cases, establishing the scalability of our approach. Building on this, we present a new protocol for heralded state preparation and measurement (SPAM) [3]. This approach combines high-fidelity measurement with coherent conversion between qubit types to mitigate errors associated with qubit loss, decay, and imperfect SPAM. We demonstrate record-low SPAM error rates across optical, metastable, and ground-state qubits, with a minimum of 5(4)×10−6. This protocol can be integrated with erasure conversion techniques to enable in-sequence qubit loss correction, providing a pathway to scalable error correction even with finite qubit lifetimes. Finally, we introduce two-qubit operations through an implementation of the optical-transition dipole force (OTDF) gate [4]. This is the first implementation of the OTDF gate in 137Ba+, or in any ion with hyperfine structure, and it is directly compatible with our existing 532 nm laser system. Crucially, this gate operates in the σZ basis, avoiding the need for phase coherence between the driving field and the qubit, making it an excellent candidate for use in mixed-qubit-type systems. These results demonstrate the application of mixed-qubit-type architectures within a single ion species and establish a foundation for scaling trapped-ion quantum computers.
Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors.Converting physical noise into erasures can significantly improve the performance of quantum error correction.Here, we apply the idea of performing erasure conversion by encoding qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and Thompson [Nat.Comm.13, 4657 (2022)], to trapped ions.We suggest an erasure-conversion scheme for metastable trapped-ion qubits and develop a detailed model of various types of errors.We then compare the logical performance of ground and metastable qubits on the surface code under various physical constraints and conclude that metastable qubits may outperform ground qubits when the achievable laser power is higher for metastable qubits.
Coherent storage of quantum information is crucial to many quantum technologies. Long coherence times have been demonstrated in trapped-ion qubits, typically using the hyperfine levels within the ground state of a single ion. However, recent research suggests qubits encoded in metastable states could provide architectural benefits for quantum information processing, such as the possibility of effective dual-species operation in a single-species system and erasure-error conversion for fault-tolerant quantum computing. Here we demonstrate long-lived encoding of a quantum state in the metastable states of a trapped ion. By sympathetically cooling with another ion of the same species and constantly monitoring for erasure errors, we demonstrate a coherence time of 136(42) seconds with a qubit encoded in the metastable 5D5/25D_{5/2}5D5/2​ state of a single 137^{137}137Ba+^++ ion. In agreement with a model based on empirical results from dynamical-decoupling-based noise spectroscopy, we find that dephasing of the metastable levels is the dominant source of error once erasure errors are removed.
Dual-type qubits have become a promising way to suppress the crosstalk error of auxiliary operations in large-scale ion trap quantum computation. Here we demonstrate a direct entangling gate between dual-type qubits encoded in the S_{1/2} and D_{5/2} hyperfine manifolds of ^{137}Ba^{+} ions. Our scheme is economic in the hardware, requiring only a single 532 nm laser system to entangle both qubit types by driving their Raman transitions. We achieve a Bell state fidelity of 96.3(4)% for the dual-type Molmer-Sorensen gate between an S-D ion pair, comparable to that for the same-type S-S or D-D gates. This technique can reduce the overhead for back-and-forth conversions between dual-type qubits in the quantum circuit with wide applications in quantum error correction and ion-photon quantum networks.
State-of-the-art two-qubit gates with trapped ions employ open-loop control that rely on simplified models to precompute control sequences. Our aim is to introduce closed-loop control for two-qubit gates to correct disturbances as they occur during the gate implementation. We introduce a spectator ion into the ion chain used for quantum logic processing, where it couples with the other ions through collective motional modes. The spectator ion's position is continuously monitored by driving dipole transitions and detecting the resultant fluorescence. We show that incorporating a spectator ion is feasible for linear Paul trap implementations and is expected to reduce the two-qubit gate Bell-state preparation infidelity by an order of magnitude with the deleterious effects of position monitoring being negligible compared to the thermal effects that exist in the system, even in the absence of the spectator ions. Mathematically, we describe driven ion-trap dynamics, including the spectator ion, by a stochastic quantum master equation involving the amplitude-modulation multimode-motional coupling gate, motional drift, thermal effects, recoil from photon scattering, spontaneous decay, and light shift. Our on-the-fly control method employs reinforcement learning with the reward function based on the actual geometric phase of the spectator ion. A key advantage of our approach is that we introduce a control method that involves `learning' and correcting disturbances happening in the trap on-the-fly, thus achieving high-fidelity gates. Our approach will lead to a significantly higher two-qubit gate fidelity at a reduced calibration overhead owing to the small parameter drift in the control system.