Quantum Circuit Compiler for a Shuttling-Based Trapped-Ion Quantum Computer
1Institute of Computer Science, Johannes Gutenberg University, Staudingerweg 9, 55128 Mainz, Germany
2Institute of Physics, Johannes Gutenberg University, Staudingerweg 7, 55128 Mainz, Germany
| Published: | 2023-11-08, volume 7, page 1176 |
| Eprint: | arXiv:2207.01964v4 |
| Doi: | https://doi.org/10.22331/q-2023-11-08-1176 |
| Citation: | Quantum 7, 1176 (2023). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
The increasing capabilities of quantum computing hardware and the challenge of realizing deep quantum circuits require fully automated and efficient tools for compiling quantum circuits. To express arbitrary circuits in a sequence of native gates specific to the quantum computer architecture, it is necessary to make algorithms portable across the landscape of quantum hardware providers. In this work, we present a compiler capable of transforming and optimizing a quantum circuit targeting a shuttling-based trapped-ion quantum processor. It consists of custom algorithms set on top of the quantum circuit framework Pytket. The performance was evaluated for a wide range of quantum circuits and the results show that the gate counts can be reduced by factors up to 5.1 compared to standard Pytket and up to 2.2 compared to standard Qiskit compilation.
Featured image: The graph representation of a quantum circuit used in our paper. The purple boxes are aggregations calculated by our compiler during the compilation process. Aggregations allow the parallelization of certain single-qubit gates contained in them. The blue boxes represent superblocks. Commuting the superblocks, as shown in the image, reduces the number of shuttling operations and requires local corrections on the involved qubits, represented by the orange unitaries.
Popular summary
To run an arbitrary algorithm on such a quantum computer, the quantum circuit describing the gate sequence to be executed must be translated into instructions which the quantum computer understands. This is similar to compiling code of a high-level language into assembler code for classical computers. Just as different processors of classical computers have different instruction sets and components, which a compiler must address during compilation, different quantum computers have different native gates and properties that can be exploited to improve the accuracy of the result.
In our paper, we present a quantum circuit compiler, which transforms a given quantum circuit into the native gate set of a trapped-ion quantum computer and performs optimizations on the code to increase the accuracy of the result. Such optimizations include various ways of reducing the number of gates performed, as well as rearranging them so that the circuit has more favorable properties, such as less ion movement.
► BibTeX data
► References
[1] F. Arute et al. ``Quantum supremacy using a programmable superconducting processor''. Nature 574, 505–510 (2019).
https://doi.org/10.1038/s41586-019-1666-5
[2] L. Postler et al. ``Demonstration of fault-tolerant universal quantum gate operations''. Nature 605, 675–680 (2022). arXiv:2111.12654.
https://doi.org/10.1038/s41586-022-04721-1
arXiv:2111.12654
[3] L. Egan et al. ``Fault-tolerant control of an error-corrected qubit''. Nature 598, 281–286 (2021).
https://doi.org/10.1038/s41586-021-03928-y
[4] J. Preskill. ``Quantum Computing in the NISQ era and beyond''. Quantum 2, 79 (2018). arXiv:1801.00862.
https://doi.org/10.22331/q-2018-08-06-79
arXiv:1801.00862
[5] D. Kielpinski, C. Monroe, and D. J. Wineland. ``Architecture for a large-scale ion-trap quantum computer''. Nature 417, 709 (2002).
https://doi.org/10.1038/nature00784
[6] V. Kaushal et al. ``Shuttling-based trapped-ion quantum information processing''. AVS Quantum Science 2, 014101 (2020). arXiv:1912.04712.
https://doi.org/10.1116/1.5126186
arXiv:1912.04712
[7] J. M. Pino et al. ``Demonstration of the trapped-ion quantum CCD computer architecture''. Nature 592, 209–213 (2021).
https://doi.org/10.1038/s41586-021-03318-4
[8] P. Murali, D. M. Debroy, K. R. Brown, and M. Martonosi. ``Architecting Noisy Intermediate-Scale Trapped Ion Quantum Computers''. In Proceedings of the ACM/IEEE 47th Annual International Symposium on Computer Architecture. Page 529–542. ISCA '20. IEEE Press (2020). arXiv:2004.04706.
https://doi.org/10.1109/ISCA45697.2020.00051
arXiv:2004.04706
[9] J. Hilder et al. ``Fault-Tolerant Parity Readout on a Shuttling-Based Trapped-Ion Quantum Computer''. Phys. Rev. X 12, 011032 (2022). arXiv:2107.06368.
https://doi.org/10.1103/PhysRevX.12.011032
arXiv:2107.06368
[10] J. Wagner. ``Automated generation of shuttling schedules for a scalable trapped-ion quantum processor''. Master's thesis. Johannes Gutenberg University Mainz. (2022).
[11] J. Durandau. ``Automated Generation of Shuttling Sequences for a Linear Segmented Ion Trap Quantum Computer'' (2022). arXiv:2208.04881.
arXiv:2208.04881
[12] A. A. Saki, R. O. Topaloglu, and S. Ghosh. ``Muzzle the Shuttle: Efficient Compilation for Multi-Trap Trapped-Ion Quantum Computers''. In 2022 Design, Automation & Test in Europe Conference & Exhibition (DATE). Pages 322–327. (2022). arXiv:2111.07961.
https://doi.org/10.23919/DATE54114.2022.9774619
arXiv:2111.07961
[13] T. Schmale et al. ``Backend compiler phases for trapped-ion quantum computers''. In 2022 IEEE International Conference on Quantum Software (QSW). Pages 32–37. Los Alamitos, CA, USA (2022). IEEE Computer Society. arXiv:2206.00544.
https://doi.org/10.1109/QSW55613.2022.00020
arXiv:2206.00544
[14] M. Webber, S. Herbert, S. Weidt, and W. K. Hensinger. ``Efficient Qubit Routing for a Globally Connected Trapped Ion Quantum Computer''. Advanced Quantum Technologies 3, 2000027 (2020). arXiv:2002.12782.
https://doi.org/10.1002/qute.202000027
arXiv:2002.12782
[15] S. Sivarajah et al. ``t$\vert$ket$\rangle$: a retargetable compiler for NISQ devices''. Quantum Science and Technology 6, 014003 (2020). arXiv:2003.10611.
https://doi.org/10.1088/2058-9565/ab8e92
arXiv:2003.10611
[16] V. Bergholm et al. ``PennyLane: Automatic differentiation of hybrid quantum-classical computations'' (2018). arXiv:1811.04968.
arXiv:1811.04968
[17] R. Wille, R. Van Meter, and Y. Naveh. ``IBM’s Qiskit Tool Chain: Working with and Developing for Real Quantum Computers''. In 2019 Design, Automation Test in Europe Conference Exhibition (DATE). Pages 1234–1240. (2019).
https://doi.org/10.23919/DATE.2019.8715261
[18] E. A. Martinez, T. Monz, D. Nigg, P. Schindler, and R. Blatt. ``Compiling quantum algorithms for architectures with multi-qubit gates''. New J. Phys. 18, 063029 (2016). arXiv:1601.06819.
https://doi.org/10.1088/1367-2630/18/6/063029
arXiv:1601.06819
[19] T. Nguyen et al. ``Quantum Circuit Transformations with a Multi-Level Intermediate Representation Compiler'' (2021). arXiv:2112.10677.
arXiv:2112.10677
[20] D. Maslov. ``Basic circuit compilation techniques for an ion-trap quantum machine''. New J. Phys. 19, 023035 (2017). arXiv:1603.07678.
https://doi.org/10.1088/1367-2630/aa5e47
arXiv:1603.07678
[21] B. Coecke and R. Duncan. ``Interacting quantum observables: categorical algebra and diagrammatics''. New J. Phys. 13, 043016 (2011). arXiv:0906.4725.
https://doi.org/10.1088/1367-2630/13/4/043016
arXiv:0906.4725
[22] X. Zhou, S. Li, and Y. Feng. ``Quantum Circuit Transformation Based on Simulated Annealing and Heuristic Search''. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39, 4683–4694 (2020). arXiv:1908.08853.
https://doi.org/10.1109/TCAD.2020.2969647
arXiv:1908.08853
[23] A. Zulehner, A. Paler, and R. Wille. ``An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures''. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 38, 1226–1236 (2019). arXiv:1712.04722.
https://doi.org/10.1109/TCAD.2018.2846658
arXiv:1712.04722
[24] A. Cowtan et al. ``On the Qubit Routing Problem''. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Volume 135 of Leibniz International Proceedings in Informatics (LIPIcs), pages 5:1–5:32. Dagstuhl, Germany (2019). Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. arXiv:1902.08091.
https://doi.org/10.4230/LIPIcs.TQC.2019.5
arXiv:1902.08091
[25] G. Li, Y. Ding, and Y. Xie. ``Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices''. In Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS. Pages 1001–1014. ACM (2019). arXiv:1809.02573.
https://doi.org/10.1145/3297858.3304023
arXiv:1809.02573
[26] F. Zilk et al. ``A compiler for universal photonic quantum computers''. In 2022 IEEE/ACM Third International Workshop on Quantum Computing Software (QCS). Pages 57–67. Los Alamitos, CA, USA (2022). IEEE Computer Society. arXiv:2210.09251.
https://doi.org/10.1109/QCS56647.2022.00012
arXiv:2210.09251
[27] Y. Shi et al. ``Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers''. In Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems. Page 1031–1044. ASPLOS '19New York, NY, USA (2019). Association for Computing Machinery. arXiv:1902.01474.
https://doi.org/10.1145/3297858.3304018
arXiv:1902.01474
[28] J. van de Wetering. ``ZX-calculus for the working quantum computer scientist'' (2020). arXiv:2012.13966.
arXiv:2012.13966
[29] Quantinuum Ltd. ``Extension Modules''. url: https://cqcl.github.io/pytket-extensions/api/index.html. (accessed: 2023-10-25).
https://cqcl.github.io/pytket-extensions/api/index.html
[30] A. Y. Kitaev. ``Quantum computations: algorithms and error correction''. Russian Mathematical Surveys 52, 1191–1249 (1997).
https://doi.org/10.1070/rm1997v052n06abeh002155
[31] C. M. Dawson and M. A. Nielsen. ``The Solovay-Kitaev algorithm''. Quantum Information and Computation 6, 81–95 (2006). arXiv:quant-ph/0505030.
https://doi.org/10.26421/QIC6.1-6
arXiv:quant-ph/0505030
[32] A. Sørensen and K. Mølmer. ``Quantum Computation with Ions in Thermal Motion''. Phys. Rev. Lett. 82, 1971–1974 (1999). arXiv:quant-ph/9810039.
https://doi.org/10.1103/PhysRevLett.82.1971
arXiv:quant-ph/9810039
[33] H. Kaufmann et al. ``Fast ion swapping for quantum-information processing''. Phys. Rev. A 95, 052319 (2017). arXiv:1607.03734.
https://doi.org/10.1103/PhysRevA.95.052319
arXiv:1607.03734
[34] H. Kaufmann, T. Ruster, C. T. Schmiegelow, F. Schmidt-Kaler, and U. G. Poschinger. ``Dynamics and control of fast ion crystal splitting in segmented Paul traps''. New J. Phys. 16, 073012 (2014). arXiv:1403.0097.
https://doi.org/10.1088/1367-2630/16/7/073012
arXiv:1403.0097
[35] M. W. van Mourik et al. ``Coherent rotations of qubits within a surface ion-trap quantum computer''. Phys. Rev. A 102, 022611 (2020). arXiv:2001.02440.
https://doi.org/10.1103/PhysRevA.102.022611
arXiv:2001.02440
[36] Quantinuum Ltd. ``pytket.circuit.OpType — pytket 1.21.0 documentation''. url: https://cqcl.github.io/tket/pytket/api/optype.html. (accessed: 2023-10-25).
https://cqcl.github.io/tket/pytket/api/optype.html
[37] M. A. Nielsen and I. L. Chuang. ``Quantum Computation and Quantum Information: 10th Anniversary Edition''. Pages 216–247. Cambridge University Press. (2010).
https://doi.org/10.1017/CBO9780511976667.009
[38] A. Fagan and R. Duncan. ``Optimising Clifford Circuits with Quantomatic''. Electronic Proceedings in Theoretical Computer Science 287, 85–105 (2019). arXiv:1901.10114.
https://doi.org/10.4204/eptcs.287.5
arXiv:1901.10114
[39] R. R. Tucci. ``An Introduction to Cartan's KAK Decomposition for QC Programmers'' (2005). arXiv:QUANT-PH/0507171.
arXiv:QUANT-PH/0507171
[40] Quantinuum Ltd. ``Pytket User Manual – Compilation''. url: https://cqcl.github.io/pytket/manual/manual_compiler.html#predefined-sequences. (accessed: 2023-10-25).
https://cqcl.github.io/pytket/manual/manual_compiler.html#predefined-sequences
[41] D. C. McKay, C. J. Wood, S. Sheldon, J. M. Chow, and J. M. Gambetta. ``Efficient $Z$ gates for quantum computing''. Phys. Rev. A 96, 022330 (2017). arXiv:1612.00858.
https://doi.org/10.1103/PhysRevA.96.022330
arXiv:1612.00858
[42] J. Biamonte et al. ``Quantum machine learning''. Nature 549, 195–202 (2017). arXiv:1611.09347.
https://doi.org/10.1038/nature23474
arXiv:1611.09347
[43] M. Cerezo et al. ``Variational quantum algorithms''. Nature Reviews Physics 3, 625–644 (2021). arXiv:2012.09265.
https://doi.org/10.1038/s42254-021-00348-9
arXiv:2012.09265
[44] A. Edgington et al. (2021). code: CQCL/pytket commit:8867249.
https://github.com/CQCL/pytket/blob/main/examples/ansatz_sequence_example.ipynb
[45] A. Anand et al. ``A quantum computing view on unitary coupled cluster theory''. Chem. Soc. Rev. 51, 1659–1684 (2022). arXiv:2109.15176.
https://doi.org/10.1039/D1CS00932J
arXiv:2109.15176
[46] J. Tilly et al. ``The Variational Quantum Eigensolver: A review of methods and best practices''. Physics Reports 986, 1–128 (2022). arXiv:2111.05176.
https://doi.org/10.1016/j.physrep.2022.08.003
arXiv:2111.05176
[47] Z. Xiangzhen (2019). code: BensonZhou1991/circuittransform commit:8e6e5b1.
https://github.com/BensonZhou1991/circuittransform/tree/master/inputs/QASM%20example
[48] N. Moll et al. ``Quantum optimization using variational algorithms on near-term quantum devices''. Quantum Science and Technology 3, 030503 (2018). arXiv:1710.01022.
https://doi.org/10.1088/2058-9565/aab822
arXiv:1710.01022
[49] S. Boixo et al. ``Characterizing quantum supremacy in near-term devices''. Nature Phys 14, 595–600 (2018). arXiv:1608.00263.
https://doi.org/10.1038/s41567-018-0124-x
arXiv:1608.00263
[50] S. Boixo (2019). code: sboixo/GRCS commit:f4981a7.
https://github.com/sboixo/GRCS
[51] A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta. ``Validating quantum computers using randomized model circuits''. Phys. Rev. A 100, 032328 (2019). arXiv:1811.12926.
https://doi.org/10.1103/PhysRevA.100.032328
arXiv:1811.12926
[52] T. Tomesh and G. Contreras (2021). code: teaguetomesh/quantum_circuit_generator commit:0225dc5.
https://github.com/teaguetomesh/quantum_circuit_generator
[53] I. Pogorelov et al. ``Compact Ion-Trap Quantum Computing Demonstrator''. PRX Quantum 2, 020343 (2021). arXiv:2101.11390.
https://doi.org/10.1103/PRXQuantum.2.020343
arXiv:2101.11390
[54] Y. Shapira et al. ``Theory of robust multiqubit nonadiabatic gates for trapped ions''. Phys. Rev. A 101, 032330 (2020). arXiv:1911.03073.
https://doi.org/10.1103/PhysRevA.101.032330
arXiv:1911.03073
Cited by
[1] Satwik Kundu and Swaroop Ghosh, Proceedings of the Great Lakes Symposium on VLSI 2025 273 (2025) ISBN:9798400714962.
[2] Hanrui Wang, Pengyu Liu, Daniel Bochen Tan, Yilian Liu, Jiaqi Gu, David Z. Pan, Jason Cong, Umut A. Acar, and Song Han, 2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA) 293 (2024) ISBN:979-8-3503-2658-1.
[3] Jonathan Durandau, Janis Wagner, Frédéric Mailhot, Charles-Antoine Brunet, Ferdinand Schmidt-Kaler, Ulrich Poschinger, and Yves Bérubé-Lauzière, "Automated Generation of Shuttling Sequences for a Linear Segmented Ion Trap Quantum Computer", Quantum 7, 1175 (2023).
[4] Ludwig Schmid, Korbinian Staudacher, and Robert Wille, 2026 Design, Automation & Test in Europe Conference (DATE) 1 (2026) ISBN:978-3-9826741-1-7.
[5] Yannick Stade, Ludwig Schmid, Lukas Burgholzer, and Robert Wille, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 784 (2024) ISBN:979-8-3315-4137-8.
[6] Ludwig Schmid, David F Locher, Manuel Rispler, Sebastian Blatt, Johannes Zeiher, Markus Müller, and Robert Wille, "Computational capabilities and compiler development for neutral atom quantum processors—connecting tool developers and hardware experts", Quantum Science and Technology 9 3, 033001 (2024).
[7] Daniel Schoenberger, Janine Hilder, Ferdinand Schmidt-Kaler, and Robert Wille, 2025 IEEE International Conference on Quantum Software (QSW) 123 (2025) ISBN:979-8-3315-6720-0.
[8] Matthew Steinberg, Medina Bandić, Sacha Szkudlarek, Carmen G. Almudever, Aritra Sarkar, and Sebastian Feld, "Lightcone bounds for quantum circuit mapping via uncomplexity", npj Quantum Information 10 1, 113 (2024).
[9] Daniel Schoenberger, Stefan Hillmich, Matthias Brandl, and Robert Wille, "Shuttling for Scalable Trapped-Ion Quantum Computers", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 44 6, 2144 (2025).
[10] Daniel Schoenberger and Robert Wille, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 1069 (2025) ISBN:979-8-3315-5736-2.
[11] Thomas Noll, Christina Gehnen, and Roy Hermanns, Lecture Notes in Computer Science 15260, 201 (2025) ISBN:978-3-031-75782-2.
[12] Francesco Preti, Michael Schilling, Sofiene Jerbi, Lea M. Trenkwalder, Hendrik Poulsen Nautrup, Felix Motzoi, and Hans J. Briegel, "Hybrid discrete-continuous compilation of trapped-ion quantum circuits with deep reinforcement learning", Quantum 8, 1343 (2024).
[13] Daniel Schoenberger, Stefan Hillmich, Matthias Brand, and Robert Wille, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1102 (2024) ISBN:979-8-3315-4137-8.
[14] Ludwig Schmid, Daniel Schoenberger, Yannick Stade, Lukas Burgholzer, and Robert Wille, Design Automation for Quantum Computing 119 (2026) ISBN:978-3-032-09302-8.
[15] Bao Bach, Ilya Safro, and Ed Younis, "Efficient Compilation for Shuttling Trapped-Ion Machines via the Position Graph Architectural Abstraction", ACM Transactions on Quantum Computing 3831246 (2026).
[16] Paul V. Klimov, Andreas Bengtsson, Chris Quintana, Alexandre Bourassa, Sabrina Hong, Andrew Dunsworth, Kevin J. Satzinger, William P. Livingston, Volodymyr Sivak, Murphy Yuezhen Niu, Trond I. Andersen, Yaxing Zhang, Desmond Chik, Zijun Chen, Charles Neill, Catherine Erickson, Alejandro Grajales Dau, Anthony Megrant, Pedram Roushan, Alexander N. Korotkov, Julian Kelly, Vadim Smelyanskiy, Yu Chen, and Hartmut Neven, "Optimizing quantum gates towards the scale of logical qubits", Nature Communications 15 1, 2442 (2024).
[17] Xian Wu, Chenghong Zhu, Jingbo Wang, and Xin Wang, Proceedings of the 58th IEEE/ACM International Symposium on Microarchitecture 749 (2025) ISBN:9798400715730.
[18] Jian-Wei Yin, Zi-Rong Chen, Shun Peng, Hao-Chen Luo, Chen-Ning Tao, Si-Wei Tan, and Li-Qiang Lu, "A Review of Quantum Computing Systems and Software", Journal of Computer Science and Technology 41 1, 147 (2026).
[19] Jeonghoon Lee, Hyeongjun Jeon, and Taehyun Kim, "Ion-trap chip architecture optimized for the implementation of quantum error-correcting codes", Physical Review A 113 3, 032432 (2026).
[20] Yannick Stade, Wan-Hsuan Lin, Jason Cong, and Robert Wille, 2025 IEEE/ACM International Conference On Computer Aided Design (ICCAD) 1 (2025) ISBN:979-8-3315-1560-7.
[21] Min Ye and Nicolas Delfosse, "Quantum error correction for long chains of trapped ions", Quantum 9, 1920 (2025).
[22] Jion Tamamoto, Yuto Matuda, Daniel Schoenberger, Shigeru Yamashita, and Robert Wille, 2026 IEEE 56th International Symposium on Multiple-Valued Logic (ISMVL) 7 (2026) ISBN:979-8-3315-5956-4.
[23] Remmy Zen, Jan Olle, Luis Colmenarez, Matteo Puviani, Markus Müller, and Florian Marquardt, "Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning", Physical Review X 15 4, 041012 (2025).
[24] Patrick Hopf, Erick Ochoa, Yannick Stade, Damian Rovara, Nils Quetschlich, Ioan Albert Florea, Josh Izaac, Robert Wille, and Lukas Burgholzer, Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region 42 (2026) ISBN:9798400720673.
[25] Fabian Kreppel, Christian Melzer, Janis Wagner, Janine Hilder, Ulrich Poschinger, Ferdinand Schmidt-Kaler, and André Brinkmann, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1065 (2024) ISBN:979-8-3315-4137-8.
[26] Sascha Heußen and Janine Hilder, "Efficient fault-tolerant code switching via one-way transversal CNOT gates", Quantum 9, 1846 (2025).
[27] Chenghong Zhu, Xian Wu, Zhaohui Yang, Jingbo Wang, Anbang Wu, Shenggen Zheng, and Xin Wang, "Quantum Compiler Design for Qubit Mapping and Routing: A Cross-Architectural Survey of Superconducting, Trapped-Ion, and Neutral Atom Systems", arXiv:2505.16891, (2025).
[28] Thomas Strohm, Karen Wintersperger, Florian Dommert, Daniel Basilewitsch, Georg Reuber, Andrey Hoursanov, Thomas Ehmer, Davide Vodola, and Sebastian Luber, "Ion-Based Quantum Computing Hardware: Performance and End-User Perspective", arXiv:2405.11450, (2024).
[29] Fabian Kreppel, Reza Salkhordeh, Ferdinand Schmidt-Kaler, and André Brinkmann, "Shuttling Compiler for Trapped-Ion Quantum Computers Based on Large Language Models", arXiv:2512.18021, (2025).
[30] Hanrui Wang, Daniel Bochen Tan, Pengyu Liu, Yilian Liu, Jiaqi Gu, Jason Cong, and Song Han, "Q-Pilot: Field Programmable Qubit Array Compilation with Flying Ancillas", arXiv:2311.16190, (2023).
[31] Francisco Romão, Daniel Vonk, Emmanuil Giortamis, Dennis Sprokholt, and Pramod Bhatotia, "MultiQ: Multi-Programming Neutral Atom Quantum Architectures", arXiv:2601.08504, (2026).
[32] Patrick Hopf, Erick Ochoa Lopez, Yannick Stade, Damian Rovara, Nils Quetschlich, Ioan Albert Florea, Josh Izaac, Robert Wille, and Lukas Burgholzer, "Integrating Quantum Software Tools with(in) MLIR", arXiv:2601.02062, (2026).
The above citations are from Crossref's cited-by service (last updated successfully 2026-07-17 04:12:37) and SAO/NASA ADS (last updated successfully 2026-07-16 15:12:18). The list may be incomplete as not all publishers provide suitable and complete citation data.
Could not fetch ADS cited-by data during last attempt 2026-07-17 04:12:37: Cannot retrieve data from ADS due to rate limitations.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.