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Chinese Physics Letters 42, 110601 (2025)High-Fidelity Two-Qubit Quantum Logic Gates in a Trapped-Ion ChainUsing Axial Motional ModesXingyu Zhao 1,2† , Ji Bian 1† , Yi Li 1,2,3 , Yue Li 1 , Mengxiang Zhang 4 , and Yiheng Lin 1,5,2*1 Laboratory of Spin Magnetic Resonance, School of Physical Sciences, Anhui Province Key Laboratory of Scientif i cInstrument Development and Application, University of Science and Technology of China, Hefei 230026, China2 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China3 National Advanced Talent Cultivation Center for Physics, University of Science and Technology of China,Hefei 230026, China4 Anhui Province Engineering Research Center for Quantum Precision Measurement,University of Science and Technology of China, Hefei 230088, China5 Hefei National Research Center for Physical Sciences at the Microscale,University of Science and Technology of China, Hefei 230026, China(Received 25 June 2025; accepted manuscript online 11 September 2025)Trapped-ion systems are one of the leading platforms for quantum information processing, where a keychallenge is to scale up system size while maintaining high-f i delity two-qubit operations. A promising approach isto build high-performance modules interconnected via strong coupling. In particular, axial motional modes of f era practical mechanism to couple the ions in a chain, enabling the preparation of Greenberger–Horne–Zeilingerstates with up to 24 ions using global operations, as well as high-f i delity two-qubit gates (96.6%–98.0%) in fullyconnected f i ve-ion chains. Here, we demonstrate two-qubit quantum logic gates in a 5-ion40 Ca +chain using axialmodes, achieving f i delities exceeding 99% for adjacent pairs and over 98% for arbitrary pairs by carefully tacklingdominant error sources. Our results are benef i cial to the development of scalable ion-trap quantum processors,quantum simulation and quantum-enhanced metrology.DOI: 10.1088/0256-307X/42/11/110601 CSTR: 32039.14.0256-307X.42.11.1106011. Introduction. Trapped-ion systems are among themost promising platforms for quantum computing, owingto their exceptional gate f i delities, long coherence times,and potential for scalability. [1–3] For single-ion or ion-pairsystems, both single- and two-qubit gate f i delities havesurpassed the 99.9% fault-tolerance threshold. [4–6] Con-siderable progress has been made toward direct scalingvia long linear ion chains, [7–11] including demonstrationsof all-to-all two-qubit operations based on radial modeswith average f i delities of 99.5% across 30 ions. [12] In par-allel, axial motional modes have enabled global all-to-allentangling operations that prepare Greenberger–Horne–Zeilinger (GHZ) states [13] in increasingly long chains, un-derscoring the scalability of axial-mode coupling. No-tably, reference [14] reported GHZ states with f i delitiesof 98.6(2)% (2 ions), 94.4(5)% (5 ions), and 50.8(9)% (14ions), while reference [15] extended this to 24 ions, achiev-ing 99.83(1)% (2 ions) and 54.4(7)% (24 ions). However,direct evidence of high-f i delity arbitrary two-qubit gatesbetween selected ions remains elusive in these demonstra-tions utilizing axial modes.Alternatively, two-dimensional (2D) ion crystals of f eranother path to scaling, [16,17] enabling entangling gatesbetween arbitrary pairs in a 4-ion array with f i delitiesranging from 96.0% to 98.6%. [18] However, as system sizeincreases, maintaining high-f i delity two-qubit gates be-comes increasingly challenging due to control complexityand noise accumulation. This imposes a fundamental bot-tleneck on direct scaling approaches. A natural solutionis to adopt a modular architecture, dividing complexityinto intra-module and inter-module operations, which canbe optimized independently. [19] Notable modular strate-gies for trapped ions include quantum charge-coupleddevices (QCCDs) based on ion shuttling, [20–22] anddistributed processors using ion-photon networks. [23–27]QCCD architectures scale by transporting ions and havedemonstrated high-f i delity (>99.8%) two-qubit gates ina 56-qubit processor. [28] Its practical implementationsneed to overcome several challenges, such as complex oper-ations including ion separation, shuttling, recombination,and re-cooling; resulting in a duty cycle below 2% for quan-tum gate operations. [22]An alternative inter-module connection involves di-rect Coulomb coupling between ions in separate potentialwells. [29–31] Each well contains multiple ions and formsa module. This method has enabled entanglement be-tween two ions in adjacent wells with 82% f i delity. [32]Crucially, axial motional modes provide stronger inter-module coupling than radial modes under typical trappingconditions, [32,33] with the coupling strength scaling nearlyquadratically with ion number. [34] For example, in 5-ionchains, axial-mode coupling can be an order of magnitude† These authors contributed equally to this work.* Corresponding author. Email: yiheng@ustc.edu.cn©2025 Chinese Physical Society and IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similartechnologies, are reserved.110601-1