Quantum computing: from qubits to qudits

Autores/as

DOI:

https://doi.org/10.31908/19098367.3279

Palabras clave:

Quantum computing, qudits, high-dimensional quantum systems, Hilbert space

Resumen

Quantum computing has traditionally relied on qubits, which are two-level quantum systems, but the growing demand for scalability and expressivity has driven interest in qudits, their natural generalization to higher-dimensional systems. By expanding the local Hilbert space to ℂd, qudits enable denser information encoding, richer entanglement structures, and more compact representations of multiqubit circuits. This brief review contrasts qubits and qudits, surveys leading physical implementations, and examines representative applications including quantum machine learning, quantum simulation, quantum error correction, quantum communication, and quantum sensing. We highlight algorithmic advantages, and practical achievements. Finally, we discuss the key challenges that currently limit the scalability of qudit platforms and outline future research directions, including hybrid qubit–qudit architectures, AI-assisted control, and advances toward fault-tolerant high-dimensional quantum computing.

 

Descargas

Los datos de descarga aún no están disponibles.

Biografía del autor/a

  • Laura Tenjo-Patiño, Universidad Nacional de Colombia

    Received her B.S. with honors in Engineering Physics from the National University of Colombia, Manizales, Colombia, in 2024. She is currently pursuing an M.Sc. in Physics at the same institution. She has participated in research projects in quantum computing, nanomaterials, and particle physics, contributing to experimental and computational studies across these fields. Her work spans both theoretical and applied aspects of emerging quantum technologies. Her research interests include quantum technologies, machine learning, and photonics.

    ORCID: https://orcid.org/0009-0006-3002-3918.

  • Juan David Hormaza Pantoja, Universidad Nacional de Colombia

    Engineering Physicist and Mathematics student who is currently pursuing a Master’s degree in Physics at the Universidad Nacional de Colombia, Manizales Campus. His main research interests lie in quantum computation, with a particular focus on the quantum simulation of gauge theories in high-energy Physics.

    ORCID: https://orcid.org/0000-0001-8547-5491.

  • Alcides Montoya Cañola, Universidad Nacional de Colombia

    Physicist, M.Sc. in Computer Engineering, and Ph.D. in Systems Engineering from Universidad Nacional de Colombia. Currently Associate Professor at the Physics Department of Universidad Nacional de Colombia, Medellín Campus, and Director of the Center of Excellence in Quantum Computing and Artificial Intelligence. He has published books on quantum computing and artificial intelligence, with several additional titles in editorial process. Creator and host of the educational YouTube channel "Quantum Colombia" with over 3,000 subscribers. He leads multiple nationally and internationally funded research projects and actively participates in formulating public policies on generative AI use in Colombia. He promotes academic collaborations between Latin American and European institutions in quantum technologies. Senior Member of IEEE. His research interests include: quantum computing, machine learning, deep neural networks, quantum algorithms, and education in emerging technologies.

    ORCID: https://orcid.org/0000-0001-9624-6133

Referencias

[1] M. Kjaergaard et al., “Superconducting Qubits: Current State of Play,” Annu. Rev. Condens. Matter Phys., vol. 11, no. Volume 11, 2020, pp. 369–395, Mar. 2020, doi: 10.1146/annurev-conmatphys-031119-050605.

[2] C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, “Trapped-ion quantum computing: Progress and challenges,” Appl. Phys. Rev., vol. 6, no. 2, p. 021314, May 2019, doi: 10.1063/1.5088164.

[3] F. Arute et al., “Quantum supremacy using a programmable superconducting processor,” Nature, vol. 574, no. 7779, pp. 505–510, Oct. 2019, doi: 10.1038/s41586-019-1666-5.

[4] Google Quantum AI, “Suppressing quantum errors by scaling a surface code logical qubit,” Nature, vol. 614, no. 7949, pp. 676–681, Feb. 2023, doi: 10.1038/s41586-022-05434-1.

[5] H.-S. Zhong et al., “Quantum computational advantage using photons,” Science, vol. 370, no. 6523, pp. 1460–1463, Dec. 2020, doi: 10.1126/science.abe8770.

[6] H.-L. Liu et al., “Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling,” Aug. 24, 2025, arXiv: arXiv:2508.09092. doi: 10.48550/arXiv.2508.09092.

[7] D. Bluvstein et al., “A fault-tolerant neutral-atom architecture for universal quantum computation,” Nature, Nov. 2025, doi: 10.1038/s41586-025-09848-5.

[8] Y. Wang, Z. Hu, B. C. Sanders, and S. Kais, “Qudits and High-Dimensional Quantum Computing,” Front. Phys., vol. 8, Nov. 2020, doi: 10.3389/fphy.2020.589504.

[9] C. M. Caves and G. J. Milburn, “Qutrit entanglement,” Opt. Commun., vol. 179, no. 1, pp. 439–446, May 2000, doi: 10.1016/S0030-4018(99)00693-8.

[10] D. Kaszlikowski, P. Gnaciński, M. Żukowski, W. Miklaszewski, and A. Zeilinger, “Violations of Local Realism by Two Entangled $mathit{N}$-Dimensional Systems Are Stronger than for Two Qubits,” Phys. Rev. Lett., vol. 85, no. 21, pp. 4418–4421, Nov. 2000, doi: 10.1103/PhysRevLett.85.4418.

[11] D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell Inequalities for Arbitrarily High-Dimensional Systems,” Phys. Rev. Lett., vol. 88, no. 4, p. 040404, Jan. 2002, doi: 10.1103/PhysRevLett.88.040404.

[12] H. Bechmann-Pasquinucci and A. Peres, “Quantum Cryptography with 3-State Systems,” Phys. Rev. Lett., vol. 85, no. 15, pp. 3313–3316, Oct. 2000, doi: 10.1103/PhysRevLett.85.3313.

[13] D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator,” Phys. Rev. A, vol. 64, no. 1, p. 012310, Jun. 2001, doi: 10.1103/PhysRevA.64.012310.

[14] S. S. Bullock, D. P. O’Leary, and G. K. Brennen, “Asymptotically Optimal Quantum Circuits for $d$-Level Systems,” Phys. Rev. Lett., vol. 94, no. 23, p. 230502, Jun. 2005, doi: 10.1103/PhysRevLett.94.230502.

[15] E. O. Kiktenko, A. S. Nikolaeva, and A. K. Fedorov, “Colloquium: Qudits for decomposing multiqubit gates and realizing quantum algorithms,” Rev. Mod. Phys., vol. 97, no. 2, p. 021003, Jun. 2025, doi: 10.1103/RevModPhys.97.021003.

[16] A. Muthukrishnan and C. R. Stroud, “Multivalued logic gates for quantum computation,” Phys. Rev. A, vol. 62, no. 5, p. 052309, Oct. 2000, doi: 10.1103/PhysRevA.62.052309.

[17] X. Shi, J. Sinanan-Singh, T. J. Burke, J. Chiaverini, and I. L. Chuang, “Efficient Implementation of a Quantum Algorithm with a Trapped Ion Qudit,” Jun. 11, 2025, arXiv: arXiv:2506.09371. doi: 10.48550/arXiv.2506.09371.

[18] M. A. Aksenov et al., “Realizing quantum gates with optically addressable $^{171}mathrm{Yb}^{+}$ ion qudits,” Phys. Rev. A, vol. 107, no. 5, p. 052612, May 2023, doi: 10.1103/PhysRevA.107.052612.

[19] A. B. Klimov, R. Guzmán, J. C. Retamal, and C. Saavedra, “Qutrit quantum computer with trapped ions,” Phys. Rev. A, vol. 67, no. 6, p. 062313, Jun. 2003, doi: 10.1103/PhysRevA.67.062313.

[20] A. S. Nikolaeva, “Universal quantum computing with qubits embedded in trapped-ion qudits,” Phys. Rev. A, vol. 109, no. 2, 2024, doi: 10.1103/PhysRevA.109.022615.

[21] M. Ringbauer et al., “A universal qudit quantum processor with trapped ions,” Nat. Phys., vol. 18, no. 9, pp. 1053–1057, Sep. 2022, doi: 10.1038/s41567-022-01658-0.

[22] P. Hrmo et al., “Native qudit entanglement in a trapped ion quantum processor,” Nat. Commun., vol. 14, no. 1, p. 2242, Apr. 2023, doi: 10.1038/s41467-023-37375-2.

[23] G. Puentes, “High-Dimensional Entanglement of Photonic Angular Qudits,” Front. Phys., vol. 10, Apr. 2022, doi: 10.3389/fphy.2022.868522.

[24] A. Suprano et al., “Orbital angular momentum based intra- and interparticle entangled states generated via a quantum dot source,” Adv. Photonics, vol. 5, p. 046008, Jul. 2023, doi: 10.1117/1.AP.5.4.046008.

[25] D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, “High-Dimensional Quantum Communication: Benefits, Progress, and Future Challenges,” Adv. Quantum Technol., vol. 2, no. 12, p. 1900038, 2019, doi: 10.1002/qute.201900038.

[26] M. J. Peterer et al., “Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit,” Phys. Rev. Lett., vol. 114, no. 1, p. 010501, Jan. 2015, doi: 10.1103/PhysRevLett.114.010501.

[27] M. Subramanian and A. Lupascu, “Efficient two-qutrit gates in superconducting circuits using parametric coupling,” Phys. Rev. A, vol. 108, no. 6, p. 062616, Dec. 2023, doi: 10.1103/PhysRevA.108.062616.

[28] N. Goss et al., “Extending the computational reach of a superconducting qutrit processor,” Npj Quantum Inf., vol. 10, no. 1, p. 101, Oct. 2024, doi: 10.1038/s41534-024-00892-z.

[29] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.

[30] A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, “Decomposing the generalized Toffoli gate with qutrits,” Phys. Rev. A, vol. 105, no. 3, p. 032621, Mar. 2022, doi: 10.1103/PhysRevA.105.032621.

[31] A. S. Nikolaeva, E. O. Kiktenko, A. K. Fedorov, A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, “Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits,” Entropy, vol. 25, no. 2, Feb. 2023, doi: 10.3390/e25020387.

[32] S. Wang, X. Li, W. J. B. Lee, S. Deb, E. Lim, and A. Chattopadhyay, “A Comprehensive Study of Quantum Arithmetic Circuits,” Jun. 06, 2024, arXiv: arXiv:2406.03867. doi: 10.48550/arXiv.2406.03867.

[33] A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, “Efficient realization of quantum algorithms with qudits,” EPJ Quantum Technol., vol. 11, no. 1, p. 43, Jun. 2024, doi: 10.1140/epjqt/s40507-024-00250-0.

[34] L. B. Nguyen et al., “Empowering a qudit-based quantum processor by traversing the dual bosonic ladder,” Nat. Commun., vol. 15, no. 1, p. 7117, Aug. 2024, doi: 10.1038/s41467-024-51434-2.

[35] C. Zhu et al., “Quantum Compiler Design for Qubit Mapping and Routing: A Cross-Architectural Survey of Superconducting, Trapped-Ion, and Neutral Atom Systems,” May 23, 2025, arXiv: arXiv:2505.16891. doi: 10.48550/arXiv.2505.16891.

[36] S. Roca-Jerat, J. Román-Roche, and D. Zueco, “Qudit machine learning,” Mach. Learn. Sci. Technol., vol. 5, no. 1, p. 015057, Mar. 2024, doi: 10.1088/2632-2153/ad360d.

[37] T. Valtinos, A. Mandilara, and D. Syvridis, “The Gell-Mann feature map of qutrits and its applications in classification tasks,” presented at the Proceedings of SPIE - The International Society for Optical Engineering, 2024. doi: 10.1117/12.3001127.

[38] E. Acar and İ. Yılmaz, “Unlocking the high dimensional’ potential: Comparative analysis of qubits and qutrits in variational quantum neural networks,” Neurocomputing, vol. 623, 2025, doi: 10.1016/j.neucom.2025.129404.

[39] D. Konar, S. Bhattacharyya, B. K. Panigrahi, and E. C. Behrman, “Qutrit-Inspired Fully Self-Supervised Shallow Quantum Learning Network for Brain Tumor Segmentation,” IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 11, pp. 6331–6345, Nov. 2022, doi: 10.1109/TNNLS.2021.3077188.

[40] A. Mandilara, B. Dellen, U. Jaekel, T. Valtinos, and D. Syvridis, “Classification of data with a qudit, a geometric approach,” Quantum Mach. Intell., vol. 6, no. 1, p. 17, Mar. 2024, doi: 10.1007/s42484-024-00146-3.

[41] N. L. Wach, M. S. Rudolph, F. Jendrzejewski, and S. Schmitt, “Data re-uploading with a single qudit,” Quantum Mach. Intell., vol. 5, no. 2, 2023, doi: 10.1007/s42484-023-00125-0.

[42] D. H. Useche, A. Giraldo-Carvajal, H. M. Zuluaga-Bucheli, J. A. Jaramillo-Villegas, and F. A. González, “Quantum measurement classification with qudits,” Quantum Inf. Process., vol. 21, no. 1, 2022, doi: 10.1007/s11128-021-03363-y.

[43] S. Cao et al., “Encoding optimization for quantum machine learning demonstrated on a superconducting transmon qutrit,” Quantum Sci. Technol., vol. 9, no. 4, 2024, doi: 10.1088/2058-9565/ad7315.

[44] L. E. Fischer, D. Miller, F. Tacchino, P. Kl. Barkoutsos, D. J. Egger, and I. Tavernelli, “Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space,” Phys. Rev. Res., vol. 4, no. 3, p. 033027, Jul. 2022, doi: 10.1103/PhysRevResearch.4.033027.

[45] R. Stricker et al., “Experimental Single-Setting Quantum State Tomography,” PRX Quantum, vol. 3, no. 4, p. 040310, Oct. 2022, doi: 10.1103/PRXQuantum.3.040310.

[46] G. Calajó, G. Magnifico, C. Edmunds, M. Ringbauer, S. Montangero, and P. Silvi, “Digital Quantum Simulation of a (1+1)D SU(2) Lattice Gauge Theory with Ion Qudits,” PRX Quantum, vol. 5, no. 4, p. 040309, Oct. 2024, doi: 10.1103/PRXQuantum.5.040309.

[47] D. González-Cuadra, T. V. Zache, J. Carrasco, B. Kraus, and P. Zoller, “Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms,” Phys. Rev. Lett., vol. 129, no. 16, p. 160501, Oct. 2022, doi: 10.1103/PhysRevLett.129.160501.

[48] M. Chizzini, “Qudit-based quantum simulation of fermionic systems,” Phys. Rev. A, vol. 110, no. 6, 2024, doi: 10.1103/PhysRevA.110.062602.

[49] A. Sit et al., “High-dimensional intracity quantum cryptography with structured photons,” Optica, vol. 4, no. 9, pp. 1006–1010, Sep. 2017, doi: 10.1364/OPTICA.4.001006.

[50] M. Ogrodnik et al., “High-dimensional quantum key distribution with resource-efficient detection,” Opt. Quantum, vol. 3, no. 4, pp. 372–380, Aug. 2025, doi: 10.1364/OPTICAQ.560373.

[51] M. Erhard, M. Krenn, and A. Zeilinger, “Advances in high-dimensional quantum entanglement,” Nat. Rev. Phys., vol. 2, no. 7, pp. 365–381, Jul. 2020, doi: 10.1038/s42254-020-0193-5.

[52] E. T. Campbell, “Enhanced Fault-Tolerant Quantum Computing in $d$-Level Systems,” Phys. Rev. Lett., vol. 113, no. 23, p. 230501, Dec. 2014, doi: 10.1103/PhysRevLett.113.230501.

[53] J. Keppens, Q. Eggerickx, V. Levajac, G. Simion, and B. Sorée, “Qudit vs. qubit: Simulated performance of error-correction codes in higher dimensions,” Phys. Rev. A, vol. 112, no. 3, p. 032435, Sep. 2025, doi: 10.1103/2w52-qd2j.

[54] R. F. Uy and D. A. Gangloff, “Qudit-based quantum error-correcting codes from irreducible representations of SU($d$),” Phys. Rev. A, vol. 112, no. 4, p. 042402, Oct. 2025, doi: 10.1103/6z3t-96t9.

[55] B. L. Brock et al., “Quantum error correction of qudits beyond break-even,” Nature, vol. 641, no. 8063, pp. 612–618, May 2025, doi: 10.1038/s41586-025-08899-y.

[56] B. Ilikj and N. V. Vitanov, “Ramsey Interferometry with Qudits,” Sep. 08, 2025, arXiv: arXiv:2509.06290. doi: 10.48550/arXiv.2509.06290.

[57] A. R. Shlyakhov et al., “Quantum metrology with a transmon qutrit,” Phys. Rev. A, vol. 97, no. 2, p. 022115, Feb. 2018, doi: 10.1103/PhysRevA.97.022115.

[58] X. Ma, V. Takhistov, N. Mizuochi, and E. D. Herbschleb, “Beyond Qubits: Multilevel Quantum Sensing for Dark Matter,” Oct. 22, 2025, arXiv: arXiv:2510.19918. doi: 10.48550/arXiv.2510.19918.

[59] D. Venturelli, E. Gustafson, D. Kurkcuoglu, and S. Zorzetti, “Near-Term Application Engineering Challenges in Emerging Superconducting Qudit Processors,” in 2025 55th Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshops (DSN-W), Jun. 2025, pp. 196–199. doi: 10.1109/DSN-W65791.2025.00061.

[60] T. de S. Farias, L. Friedrich, and J. Maziero, “A short review on qudit quantum machine learning,” May 08, 2025, arXiv: arXiv:2505.05158. doi: 10.48550/arXiv.2505.05158.

[61] L. Lysaght, T. Goubault, P. Sinnott, S. Mansfield, and P.-E. Emeriau, “Quantum circuit compression using qubit logic on qudits,” Nov. 06, 2024, arXiv: arXiv:2411.03878. doi: 10.48550/arXiv.2411.03878.

[62] J. Preskill, “Quantum Computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, Aug. 2018, doi: 10.22331/q-2018-08-06-79.

[63] K. Mato, M. Ringbauer, L. Burgholzer, and R. Wille, “MQT Qudits: A Software Framework for Mixed-Dimensional Quantum Computing,” Oct. 03, 2024, arXiv: arXiv:2410.02854. doi: 10.48550/arXiv.2410.02854.

Descargas

Publicado

2026-07-05

Número

Vol. 19 Núm. 38 (2025)

Sección

Artículos

Licencia

Derechos de autor 2025 Laura Tenjo-Patiño, Juan David Hormaza Pantoja, Alcides Montoya Cañola

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.

Cómo citar

[1]
L. Tenjo-Patiño, J. D. . Hormaza Pantoja, and A. . Montoya Cañola, “Quantum computing: from qubits to qudits”, Entre cienc. ing., vol. 19, no. 38, pp. 29–36, Jul. 2026, doi: 10.31908/19098367.3279.
Crossref
Scopus
Google Scholar
Europe PMC

Artículos similares

21-30 de 400

También puede Iniciar una búsqueda de similitud avanzada para este artículo.