{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T07:36:08Z","timestamp":1792740968690,"version":"4.5.0"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","license":[{"start":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T00:00:00Z","timestamp":1792022400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T00:00:00Z","timestamp":1792022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat. Phys."],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Silicon spin qubits offer a promising path to scalable quantum computing due to their compatibility with industrial semiconductor manufacturing. A key requirement for scaling quantum processors is the ability to perform high-fidelity operations in parallel across many qubits. However, simultaneous control remains a major challenge in silicon devices, as fidelities typically degrade under parallel operation. Here we identify microwave-drive-induced a.c.-Stark shifts as the dominant source of this degradation in a five-qubit silicon spin array. We address this by introducing a scalable mitigation protocol based solely on pairwise phase calibrations. Using tailored control pulses on a shared control line, we achieve primitive\n                    <jats:italic>X<\/jats:italic>\n                    and\n                    <jats:italic>Y<\/jats:italic>\n                    gate fidelities well above 99.99% for each qubit individually, with some approaching 99.999%. Furthermore, these fidelities are preserved above 99.99% during simultaneous operation of up to three qubits. During parallel five-qubit operation, fidelities remain above the widely targeted fault-tolerant threshold of 99.9%. By maintaining high-fidelity control during simultaneous operation, shared qubit-control lines can support the development of large-scale semiconductor quantum processors.\n                  <\/jats:p>","DOI":"10.1038\/s41567-026-03466-2","type":"journal-article","created":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T17:49:03Z","timestamp":1792086543000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Simultaneous high-fidelity single-qubit gates in a spin qubit array"],"prefix":"10.1038","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4137-989X","authenticated-orcid":false,"given":"Yi-Hsien","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2278-1915","authenticated-orcid":false,"given":"Leon C.","family":"Camenzind","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3140-4057","authenticated-orcid":false,"given":"Patrick","family":"B\u00fctler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8758-4197","authenticated-orcid":false,"given":"Ik Kyeong","family":"Jin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9145-0303","authenticated-orcid":false,"given":"Akito","family":"Noiri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1240-1103","authenticated-orcid":false,"given":"Kenta","family":"Takeda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6759-6441","authenticated-orcid":false,"given":"Takashi","family":"Nakajima","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2841-8129","authenticated-orcid":false,"given":"Takashi","family":"Kobayashi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2512-0079","authenticated-orcid":false,"given":"Giordano","family":"Scappucci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8117-5846","authenticated-orcid":false,"given":"Hsi-Sheng","family":"Goan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7465-0135","authenticated-orcid":false,"given":"Seigo","family":"Tarucha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,15]]},"reference":[{"key":"3466_CR1","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1103\/PhysRevA.57.120","volume":"57","author":"D Loss","year":"1998","unstructured":"Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120\u2013126 https:\/\/doi.org\/10.1103\/PhysRevA.57.120 (1998).","journal-title":"Phys. Rev. A"},{"key":"3466_CR2","doi-asserted-by":"publisher","unstructured":"Burkard, G., Ladd, T. D., Pan, A., Nichol, J. M. & Petta, J. R. Semiconductor spin qubits. Rev. Mod. Phys. https:\/\/doi.org\/10.1103\/revmodphys.95.025003 (2023).","DOI":"10.1103\/revmodphys.95.025003"},{"key":"3466_CR3","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1038\/s41586-024-07275-6","volume":"629","author":"S Neyens","year":"2024","unstructured":"Neyens, S. et al. Probing single electrons across 300-mm spin qubit wafers. Nature 629, 80\u201385 https:\/\/doi.org\/10.1038\/s41586-024-07275-6 (2024).","journal-title":"Nature"},{"key":"3466_CR4","doi-asserted-by":"publisher","unstructured":"Elsayed, A. et al. Low charge noise quantum dots with industrial CMOS manufacturing. npj Quantum Inf. https:\/\/doi.org\/10.1038\/s41534-024-00864-3 (2024).","DOI":"10.1038\/s41534-024-00864-3"},{"key":"3466_CR5","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1038\/s41928-022-00727-9","volume":"5","author":"AMJ Zwerver","year":"2022","unstructured":"Zwerver, A. M. J. et al. Qubits made by advanced semiconductor manufacturing. Nat. Electron. 5, 184\u2013190 https:\/\/doi.org\/10.1038\/s41928-022-00727-9 (2022).","journal-title":"Nat. Electron."},{"key":"3466_CR6","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1038\/s41928-022-00722-0","volume":"5","author":"LC Camenzind","year":"2022","unstructured":"Camenzind, L. C. et al. A spin qubit in a fin field-effect transistor. Nat. Electron. 5, 178\u2013183 https:\/\/doi.org\/10.1038\/s41928-022-00722-0 (2022).","journal-title":"Nat. Electron."},{"key":"3466_CR7","doi-asserted-by":"publisher","first-page":"433","DOI":"10.22331\/q-2021-04-15-433","volume":"5","author":"C Gidney","year":"2021","unstructured":"Gidney, C. & Eker\u00e5, M. How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum 5, 433 (2021).","journal-title":"Quantum"},{"key":"3466_CR8","doi-asserted-by":"publisher","first-page":"032324","DOI":"10.1103\/PhysRevA.86.032324","volume":"86","author":"AG Fowler","year":"2012","unstructured":"Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 https:\/\/doi.org\/10.1103\/PhysRevA.86.032324 (2012).","journal-title":"Phys. Rev. A"},{"key":"3466_CR9","doi-asserted-by":"publisher","first-page":"020302","DOI":"10.1103\/PhysRevA.83.020302","volume":"83","author":"DS Wang","year":"2011","unstructured":"Wang, D. S., Fowler, A. G. & Hollenberg, L. C. L. Surface code quantum computing with error rates over 1%. Phys. Rev. A 83, 020302 https:\/\/doi.org\/10.1103\/PhysRevA.83.020302 (2011).","journal-title":"Phys. Rev. A"},{"key":"3466_CR10","unstructured":"Google Quantum AI. Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383\u2013387 (2021)."},{"key":"3466_CR11","doi-asserted-by":"publisher","unstructured":"Xue, X. et al. Benchmarking gate fidelities in a Si\/SiGe two-qubit device. Phys. Rev. X https:\/\/doi.org\/10.1103\/physrevx.9.021011 (2019).","DOI":"10.1103\/physrevx.9.021011"},{"key":"3466_CR12","doi-asserted-by":"publisher","first-page":"eabn5130","DOI":"10.1126\/sciadv.abn5130","volume":"8","author":"AR Mills","year":"2022","unstructured":"Mills, A. R. et al. Two-qubit silicon quantum processor with operation fidelity exceeding 99%. Sci. Adv. 8, eabn5130 https:\/\/doi.org\/10.1126\/sciadv.abn5130 (2022).","journal-title":"Sci. Adv."},{"key":"3466_CR13","doi-asserted-by":"publisher","unstructured":"Lawrie, W. I. L. et al. Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold. Nat. Commun. https:\/\/doi.org\/10.1038\/s41467-023-39334-3 (2023).","DOI":"10.1038\/s41467-023-39334-3"},{"key":"3466_CR14","doi-asserted-by":"publisher","unstructured":"Gambetta, J. M. et al. Characterization of addressability by simultaneous randomized benchmarking. Phys. Rev. Lett. https:\/\/doi.org\/10.1103\/physrevlett.109.240504 (2012).","DOI":"10.1103\/physrevlett.109.240504"},{"key":"3466_CR15","doi-asserted-by":"publisher","unstructured":"McKay, D. C., Sheldon, S., Smolin, J. A., Chow, J. M. & Gambetta, J. M. Three-qubit randomized benchmarking. Phys. Rev. Lett. https:\/\/doi.org\/10.1103\/physrevlett.122.200502 (2019).","DOI":"10.1103\/physrevlett.122.200502"},{"key":"3466_CR16","doi-asserted-by":"publisher","unstructured":"Mundada, P., Zhang, G., Hazard, T. & Houck, A. Suppression of qubit crosstalk in a tunable coupling superconducting circuit. Phys. Rev. Appl. https:\/\/doi.org\/10.1103\/physrevapplied.12.054023 (2019).","DOI":"10.1103\/physrevapplied.12.054023"},{"key":"3466_CR17","doi-asserted-by":"publisher","unstructured":"Zhao, P. et al. Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits. PRX Quantum https:\/\/doi.org\/10.1103\/prxquantum.3.020301 (2022).","DOI":"10.1103\/prxquantum.3.020301"},{"key":"3466_CR18","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1038\/s41586-022-05117-x","volume":"609","author":"SGJ Philips","year":"2022","unstructured":"Philips, S. G. J. et al. Universal control of a six-qubit quantum processor in silicon. Nature 609, 919\u2013924 https:\/\/doi.org\/10.1038\/s41586-022-05117-x (2022).","journal-title":"Nature"},{"key":"3466_CR19","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1038\/nnano.2014.153","volume":"9","author":"E Kawakami","year":"2014","unstructured":"Kawakami, E. et al. Electrical control of a long-lived spin qubit in a Si\/SiGe quantum dot. Nat. Nanotechnol. 9, 666\u2013670 https:\/\/doi.org\/10.1038\/nnano.2014.153 (2014).","journal-title":"Nat. Nanotechnol."},{"key":"3466_CR20","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1038\/s41565-017-0014-x","volume":"13","author":"J Yoneda","year":"2018","unstructured":"Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102\u2013106 https:\/\/doi.org\/10.1038\/s41565-017-0014-x (2018).","journal-title":"Nat. Nanotechnol."},{"key":"3466_CR21","doi-asserted-by":"publisher","first-page":"165319","DOI":"10.1103\/PhysRevB.74.165319","volume":"74","author":"VN Golovach","year":"2006","unstructured":"Golovach, V. N., Borhani, M. & Loss, D. Electric-dipole-induced spin resonance in quantum dots. Phys. Rev. B 74, 165319 (2006).","journal-title":"Phys. Rev. B"},{"key":"3466_CR22","doi-asserted-by":"publisher","first-page":"047202","DOI":"10.1103\/PhysRevLett.96.047202","volume":"96","author":"Y Tokura","year":"2006","unstructured":"Tokura, Y., van der Wiel, W. G., Obata, T. & Tarucha, S. Coherent single electron spin control in a slanting Zeeman field. Phys. Rev. Lett. 96, 047202 (2006).","journal-title":"Phys. Rev. Lett."},{"key":"3466_CR23","doi-asserted-by":"publisher","first-page":"776","DOI":"10.1038\/nphys1053","volume":"4","author":"M Pioro-Ladri\u00e8re","year":"2008","unstructured":"Pioro-Ladri\u00e8re, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776\u2013779 https:\/\/doi.org\/10.1038\/nphys1053 (2008).","journal-title":"Nat. Phys."},{"key":"3466_CR24","doi-asserted-by":"publisher","unstructured":"Kobayashi, T. et al. Feedback-based active reset of a spin qubit in silicon. npj Quantum Inf. https:\/\/doi.org\/10.1038\/s41534-023-00719-3 (2023).","DOI":"10.1038\/s41534-023-00719-3"},{"key":"3466_CR25","doi-asserted-by":"publisher","unstructured":"Yoneda, J. et al. Quantum non-demolition readout of an electron spin in silicon. Nat. Commun. https:\/\/doi.org\/10.1038\/s41467-020-14818-8 (2020).","DOI":"10.1038\/s41467-020-14818-8"},{"key":"3466_CR26","doi-asserted-by":"publisher","first-page":"045025","DOI":"10.1088\/2058-9565\/acf786","volume":"8","author":"M Rimbach-Russ","year":"2023","unstructured":"Rimbach-Russ, M., Philips, S. G. J., Xue, X. & Vandersypen, L. M. K. Simple framework for systematic high-fidelity gate operations. Quantum Sci. Technol. 8, 045025 https:\/\/doi.org\/10.1088\/2058-9565\/acf786 (2023).","journal-title":"Quantum Sci. Technol."},{"key":"3466_CR27","doi-asserted-by":"publisher","unstructured":"Noiri, A. et al. A shuttling-based two-qubit logic gate for linking distant silicon quantum processors. Nat. Commun. https:\/\/doi.org\/10.1038\/s41467-022-33453-z (2022).","DOI":"10.1038\/s41467-022-33453-z"},{"key":"3466_CR28","doi-asserted-by":"publisher","first-page":"080505","DOI":"10.1103\/PhysRevLett.109.080505","volume":"109","author":"E Magesan","year":"2012","unstructured":"Magesan, E. et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett. 109, 080505 https:\/\/doi.org\/10.1103\/PhysRevLett.109.080505 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"3466_CR29","doi-asserted-by":"publisher","unstructured":"Rojas-Arias, J. et al. Spatial noise correlations beyond nearest neighbors in si-28-ge spin qubits. Phys. Rev. Appl. https:\/\/doi.org\/10.1103\/physrevapplied.20.054024 (2023).","DOI":"10.1103\/physrevapplied.20.054024"},{"key":"3466_CR30","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1038\/s41586-021-04182-y","volume":"601","author":"A Noiri","year":"2022","unstructured":"Noiri, A. et al. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature 601, 338\u2013342 https:\/\/doi.org\/10.1038\/s41586-021-04182-y (2022).","journal-title":"Nature"},{"key":"3466_CR31","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1038\/s41567-023-02238-6","volume":"19","author":"J Yoneda","year":"2023","unstructured":"Yoneda, J. et al. Noise-correlation spectrum for a pair of spin qubits in silicon. Nat. Phys. 19, 1793\u20131798 https:\/\/doi.org\/10.1038\/s41567-023-02238-6 (2023).","journal-title":"Nat. Phys."},{"key":"3466_CR32","doi-asserted-by":"publisher","unstructured":"Nakajima, T. et al. Coherence of a driven electron spin qubit actively decoupled from quasistatic noise. Phys. Rev. X https:\/\/doi.org\/10.1103\/physrevx.10.011060 (2020).","DOI":"10.1103\/physrevx.10.011060"},{"key":"3466_CR33","doi-asserted-by":"publisher","first-page":"e1600694","DOI":"10.1126\/sciadv.1600694","volume":"2","author":"K Takeda","year":"2016","unstructured":"Takeda, K. et al. A fault-tolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 https:\/\/doi.org\/10.1126\/sciadv.1600694 (2016).","journal-title":"Sci. Adv."},{"key":"3466_CR34","doi-asserted-by":"publisher","unstructured":"Vallabhapurapu, H. H. et al. Fast coherent control of a nitrogen-vacancy-center spin ensemble using a KTaO3 dielectric resonator at cryogenic temperatures. Phys. Rev. Appl. https:\/\/doi.org\/10.1103\/physrevapplied.16.044051 (2021).","DOI":"10.1103\/physrevapplied.16.044051"},{"key":"3466_CR35","doi-asserted-by":"publisher","unstructured":"Malkoc, O., Stano, P. & Loss, D. Optimal geometry of lateral GaAs and Si\/SiGe quantum dots for electrical control of spin qubits. Phys. Rev. B https:\/\/doi.org\/10.1103\/physrevb.93.235413 (2016).","DOI":"10.1103\/physrevb.93.235413"},{"key":"3466_CR36","doi-asserted-by":"publisher","unstructured":"Undseth, B. et al. Hotter is easier: Unexpected temperature dependence of spin qubit frequencies. Phys. Rev. X https:\/\/doi.org\/10.1103\/physrevx.13.041015 (2023).","DOI":"10.1103\/physrevx.13.041015"},{"key":"3466_CR37","doi-asserted-by":"publisher","first-page":"1037","DOI":"10.1103\/revmodphys.76.1037","volume":"76","author":"LMK Vandersypen","year":"2005","unstructured":"Vandersypen, L. M. K. & Chuang, I. L. Nmr techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037\u20131069 https:\/\/doi.org\/10.1103\/revmodphys.76.1037 (2005).","journal-title":"Rev. Mod. Phys."},{"key":"3466_CR38","doi-asserted-by":"publisher","unstructured":"Wu, Y.-H. et al. Hamiltonian phase error in resonantly driven CNOT gate above the fault-tolerant threshold. npj Quantum Inf. https:\/\/doi.org\/10.1038\/s41534-023-00802-9 (2024).","DOI":"10.1038\/s41534-023-00802-9"},{"key":"3466_CR39","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1038\/s41586-021-04273-w","volume":"601","author":"X Xue","year":"2022","unstructured":"Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343\u2013347 https:\/\/doi.org\/10.1038\/s41586-021-04273-w (2022).","journal-title":"Nature"},{"key":"3466_CR40","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-021-98212-4","volume":"11","author":"M Tadokoro","year":"2021","unstructured":"Tadokoro, M. et al. Designs for a two-dimensional Si quantum dot array with spin qubit addressability. Sci. Rep. 11, 19406 (2021).","journal-title":"Sci. Rep."},{"key":"3466_CR41","doi-asserted-by":"publisher","first-page":"1838","DOI":"10.1021\/acs.nanolett.4c05037","volume":"25","author":"M Aldeghi","year":"2025","unstructured":"Aldeghi, M. et al. Simulation and measurement of stray fields for the manipulation of spin qubits in one- and two-dimensional arrays. Nano Lett. 25, 1838\u20131844 https:\/\/doi.org\/10.1021\/acs.nanolett.4c05037 (2025).","journal-title":"Nano Lett."},{"key":"3466_CR42","doi-asserted-by":"publisher","unstructured":"Li, R. et al. A trilinear quantum dot architecture for semiconductor spin qubits. Preprint at https:\/\/doi.org\/10.48550\/arXiv.2501.17814 (2025).","DOI":"10.48550\/arXiv.2501.17814"},{"key":"3466_CR43","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-01905-6","volume":"8","author":"M Veldhorst","year":"2017","unstructured":"Veldhorst, M., Eenink, H. G. J., Yang, C. H. & Dzurak, A. S. Silicon CMOS architecture for a spin-based quantum computer. Nat. Commun. 8, 1766 https:\/\/doi.org\/10.1038\/s41467-017-01905-6 (2017).","journal-title":"Nat. Commun."},{"key":"3466_CR44","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1021\/acs.nanolett.4c05205","volume":"25","author":"HC George","year":"2025","unstructured":"George, H. C. et al. 12-spin-qubit arrays fabricated on a 300 mm semiconductor manufacturing line. Nano Lett. 25, 793\u2013799 (2025).","journal-title":"Nano Lett."},{"key":"3466_CR45","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1038\/s41586-023-05777-3","volume":"615","author":"AJ Weinstein","year":"2023","unstructured":"Weinstein, A. J. et al. Universal logic with encoded spin qubits in silicon. Nature 615, 817\u2013822 https:\/\/doi.org\/10.1038\/s41586-023-05777-3 (2023).","journal-title":"Nature"},{"key":"3466_CR46","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","author":"P Virtanen","year":"2020","unstructured":"Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261\u2013272 https:\/\/doi.org\/10.1038\/s41592-019-0686-2 (2020).","journal-title":"Nat. Methods"},{"key":"3466_CR47","doi-asserted-by":"publisher","first-page":"084401","DOI":"10.7567\/apex.8.084401","volume":"8","author":"J Yoneda","year":"2015","unstructured":"Yoneda, J. et al. Robust micromagnet design for fast electrical manipulations of single spins in quantum dots. Appl. Phys. Express 8, 084401 https:\/\/doi.org\/10.7567\/apex.8.084401 (2015).","journal-title":"Appl. Phys. Express"},{"key":"3466_CR48","doi-asserted-by":"publisher","first-page":"154205","DOI":"10.1088\/0953-8984\/27\/15\/154205","volume":"27","author":"JT Muhonen","year":"2015","unstructured":"Muhonen, J. T. et al. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking. J. Phys. Condens. Matter 27, 154205 https:\/\/doi.org\/10.1088\/0953-8984\/27\/15\/154205 (2015).","journal-title":"J. Phys. Condens. Matter"},{"key":"3466_CR49","doi-asserted-by":"publisher","unstructured":"Harper, R., Hincks, I., Ferrie, C., Flammia, S. T. & Wallman, J. J. Statistical analysis of randomized benchmarking. Phys. Rev. A https:\/\/doi.org\/10.1103\/physreva.99.052350 (2019).","DOI":"10.1103\/physreva.99.052350"},{"key":"3466_CR50","doi-asserted-by":"publisher","unstructured":"Epstein, J. M., Cross, A. W., Magesan, E. & Gambetta, J. M. Investigating the limits of randomized benchmarking protocols. Phys. Rev. A https:\/\/doi.org\/10.1103\/physreva.89.062321 (2014).","DOI":"10.1103\/physreva.89.062321"},{"key":"3466_CR51","doi-asserted-by":"publisher","first-page":"11738","DOI":"10.1073\/pnas.1603251113","volume":"113","author":"E Kawakami","year":"2016","unstructured":"Kawakami, E. et al. Gate fidelity and coherence of an electron spin in an Si\/SiGe quantum dot with micromagnet. Proc. Natl Acad. Sci. USA 113, 11738\u201311743 (2016).","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"3466_CR52","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1103\/RevModPhys.86.361","volume":"86","author":"E Paladino","year":"2014","unstructured":"Paladino, E., Galperin, Y. M., Falci, G. & Altshuler, B. L. 1\/fnoise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361\u2013418 (2014).","journal-title":"Rev. Mod. Phys."},{"key":"3466_CR53","doi-asserted-by":"publisher","first-page":"095004","DOI":"10.1088\/1367-2630\/15\/9\/095004","volume":"15","author":"TJ Green","year":"2013","unstructured":"Green, T. J., Sastrawan, J., Uys, H. & Biercuk, M. J. Arbitrary quantum control of qubits in the presence of universal noise. New J. Phys. 15, 095004 (2013).","journal-title":"New J. Phys."},{"key":"3466_CR54","doi-asserted-by":"publisher","unstructured":"Wu, Y.-H. et al. Supporting material for \u201csimultaneous high- fidelity single-qubit gates in a spin qubit array\u201d. Zenodo https:\/\/doi.org\/10.5281\/zenodo.21507661 (2026).","DOI":"10.5281\/zenodo.21507661"}],"container-title":["Nature Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41567-026-03466-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41567-026-03466-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41567-026-03466-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T17:49:05Z","timestamp":1792086545000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41567-026-03466-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,15]]},"references-count":54,"alternative-id":["3466"],"URL":"https:\/\/doi.org\/10.1038\/s41567-026-03466-2","relation":{},"ISSN":["1745-2473","1745-2481"],"issn-type":[{"value":"1745-2473","type":"print"},{"value":"1745-2481","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,15]]},"assertion":[{"value":"4 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Ethics"}}]}}