- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Three-Qubit Encoding in Ytterbium-171 Atoms for Simulating 1+1D Quantum Chromodynamics

William Huie*, Cianan Conefrey-Shinozaki*, Zhubing Jia, Patrick Draper†, and Jacob P. Covey‡

  • *These authors contributed equally to this work.
  • †Contact author: pdraper@illinois.edu
  • ‡Contact author: jcovey@illinois.edu
PDF

PRX Quantum 7, 010327 – Published 9 February, 2026

DOI: https://doi.org/10.1103/28h7-jl1v

Abstract

Simulating nuclear matter described by quantum chromodynamics using quantum computers is notoriously inefficient because of the assortment of quark degrees of freedom such as matter/antimatter, flavor, color, and spin. Here, we propose to address this resource efficiency challenge by encoding three qubits within individual ytterbium-171 atoms of a neutral atom quantum processor. The three qubits are encoded in three distinct sectors: an electronic “clock” transition, the spin-1/2 nucleus, and the lowest two motional states in one radial direction of the harmonic trapping potential. We develop a family of composite sideband pulses and demonstrate a universal gate set and readout protocol for this three-qubit system. We then apply it to single-flavor quantum chromodynamics in 1+1D axial gauge for which the three qubits directly represent the occupancy of quarks in the three colors. We show that two atoms are sufficient to simulate both vacuum persistence oscillations and a screened hadron-number transition. We consider resource requirements and connections to error detection/correction. Our work is a step toward resource-efficient digital simulation of nuclear matter and opens new opportunities for versatile qubit encoding in neutral atom quantum processors.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

In the era of noisy intermediate-scale quantum devices, resource efficiency is crucial for utilizing quantum hardware in the short term. As many quantum hardware platforms begin to hit scaling barriers, it is increasingly important to optimize the use of resources such as qubit count, connectivity, and coherence time. A paradigmatic example of this need is the digital quantum simulation of nuclear physics phenomena. Simulations of quark matter must contend with several degrees of freedom including flavor, color, matter/antimatter, and spin; and they must also address the underlying fermionic statistics which require the use of notoriously inefficient fermion-to-qubit mapping schemes such as the Jordan-Wigner transformation.

This work presents a resource-efficient three-qubit encoding within neutral ytterbium-171 atoms trapped in optical tweezers. Specifically, this utilizes an electronic qubit based on the optical “clock” transition; a nuclear spin qubit based on the spin-1/2 nucleus; and a motional qubit based on the lowest two harmonic oscillator states of the atom along a radial direction of the tweezer trap. This work presents a qubit-based universal gate set for intraquoct and interquoct operations that include high-fidelity intraquoct CZ, SWAP, and CCZ gates and interquoct CC¯Z gates. The versatility of our three-qubit encoding platform and its utility is demonstrated by developing circuits to simulate single-flavor quantum chromodynamics (QCD) in 1+1D, faithfully simulating vacuum persistence and a screened hadron-number transition with only two atoms.

This multiqubit encoding scheme will contribute to a broad range of applications within quantum computing and digital quantum simulation. Additionally, the use of motional states and the family of composite pulses to isolate the lowest two motional states will aid the development of hybrid digital/continuous variable and bosonic encodings for neutral atoms.

Article Text

References (64)

  1. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  2. M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  3. D. Paulson, L. Dellantonio, J. F. Haase, A. Celi, A. Kan, A. Jena, C. Kokail, R. van Bijnen, K. Jansen, P. Zoller, and C. A. Muschik, Simulating 2D effects in lattice gauge theories on a quantum computer, PRX Quantum 2, 030334 (2021).
  4. R. C. Farrell, I. A. Chernyshev, S. J. M. Powell, N. A. Zemlevskiy, M. Illa, and M. J. Savage, Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge, Phys. Rev. D 107, 054512 (2023).
  5. R. C. Farrell, I. A. Chernyshev, S. J. M. Powell, N. A. Zemlevskiy, M. Illa, and M. J. Savage, Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. II. Single-baryon β-decay in real time, Phys. Rev. D 107, 054513 (2023).
  6. P. Jordan and E. Wigner, Uber das Paulische Aquivalenzverbot, Z. Phys. 47, 631 (1928).
  7. S. B. Bravyi and A. Y. Kitaev, Fermionic quantum computation, Ann. Phys. 298, 210 (2002).
  8. D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, J. Ye, and P. Zoller, Fermionic quantum processing with programmable neutral atom arrays, Proc. Natl. Acad. Sci. U.S.A. 120, e2304294120 (2023).
  9. E. Crane, K. C. Smith, T. Tomesh, A. Eickbusch, J. M. Martyn, S. Kühn, L. Funcke, M. A. DeMarco, I. L. Chuang, N. Wiebe, A. Schuckert, and S. M. Girvin, Hybrid oscillator-qubit quantum processors: Simulating fermions, bosons, and gauge fields, arXiv:2409.03747.
  10. B. M. Terhal, J. Conrad, and C. Vuillot, Towards scalable bosonic quantum error correction, Quantum Sci. Technol. 5, 043001 (2020).
  11. W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, Bosonic quantum error correction codes in superconducting quantum circuits, Fundam. Res. 1, 50 (2021).
  12. L. E. Fischer, A. Chiesa, F. Tacchino, D. J. Egger, S. Carretta, and I. Tavernelli, Universal qudit gate synthesis for transmons, PRX Quantum 4, 030327 (2023).
  13. Z. Wang, R. W. Parker, E. Champion, and M. S. Blok, High- EJ/EC transmon qudits with up to 12 levels, Phys. Rev. Appl. 23, 034046 (2025).
  14. P. J. Low, B. M. White, A. A. Cox, M. L. Day, and C. Senko, Practical trapped-ion protocols for universal qudit-based quantum computing, Phys. Rev. Res. 2, 033128 (2020).
  15. S. Omanakuttan, A. Mitra, M. J. Martin, and I. H. Deutsch, Quantum optimal control of ten-level nuclear spin qudits in 87Sr, Phys. Rev. A 104, L060401 (2021).
  16. M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nat. Phys. 18, 1053 (2022).
  17. P. Hrmo, B. Wilhelm, L. Gerster, M. W. van Mourik, M. Huber, R. Blatt, P. Schindler, T. Monz, and M. Ringbauer, Native qudit entanglement in a trapped ion quantum processor, Nat. Commun. 14, 2242 (2023).
  18. S. Omanakuttan, A. Mitra, E. J. Meier, M. J. Martin, and I. H. Deutsch, Qudit entanglers using quantum optimal control, PRX Quantum 4, 040333 (2023).
  19. P. J. Low, B. White, and C. Senko, Control and readout of a 13-level trapped ion qudit, Npj Quantum Inf. 11, 85 (2025).
  20. S. Omanakuttan, V. Buchemmavari, J. A. Gross, I. H. Deutsch, and M. Marvian, Fault-tolerant quantum computation using large spin cat-codes, PRX Quantum 5, 020355 (2024).
  21. I. V. Zalivako, A. S. Nikolaeva, A. S. Borisenko, A. E. Korolkov, P. L. Sidorov, K. P. Galstyan, N. V. Semenin, V. N. Smirnov, M. A. Aksenov, K. M. Makushin, E. O. Kiktenko, A. K. Fedorov, I. A. Semerikov, K. Y. Khabarova, and N. N. Kolachevsky, Towards multiqudit quantum processor based on a 171Yb+ ion string: Realizing basic quantum algorithms, Quantum Rep. 7, 19 (2025).
  22. J. D. Jost, J. P. Home, J. M. Amini, D. Hanneke, R. Ozeri, C. Langer, J. J. Bollinger, D. Leibfried, and D. J. Wineland, Entangled mechanical oscillators, Nature 459, 683 (2009).
  23. C. Flühmann, T. L. Nguyen, M. Marinelli, V. Negnevitsky, K. Mehta, and J. P. Home, Encoding a qubit in a trapped-ion mechanical oscillator, Nature 566, 513 (2019).
  24. A. L. Shaw, P. Scholl, R. Finkelstein, R. B.-S. Tsai, J. Choi, and M. Endres, Erasure cooling, control, and hyperentanglement of motion in optical tweezers, Science 388, 845 (2025).
  25. P. T. Grochowski, H. Pichler, C. A. Regal, and O. Romero-Isart, Quantum control of continuous systems via nonharmonic potential modulation, Quantum 9, 1824 (2025).
  26. Y. Liu, S. Singh, K. C. Smith, E. Crane, J. M. Martyn, A. Eickbusch, A. Schuckert, R. D. Li, J. Sinanan-Singh, M. B. Soley, T. Tsunoda, I. L. Chuang, N. Wiebe, and S. M. Girvin, Hybrid oscillator-qubit quantum processors: Instruction set architectures, abstract machine models, and applications, arXiv:2407.10381.
  27. Y. Liu, J. M. Martyn, J. Sinanan-Singh, K. C. Smith, S. M. Girvin, and I. L. Chuang, Toward mixed analog-digital quantum signal processing: Quantum AD/DA conversion and the Fourier transform, IEEE Trans. Signal Process. 73, 3641 (2025).
  28. L. H. Bohnmann, D. F. Locher, J. Zeiher, and M. Müller, Bosonic quantum error correction with neutral atoms in optical dipole traps, Phys. Rev. A 111, 022432 (2025).
  29. M. Meth, J. Zhang, J. F. Haase, C. Edmunds, L. Postler, A. J. Jena, A. Steiner, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. Muschik, and M. Ringbauer, Simulating two-dimensional lattice gauge theories on a qudit quantum computer, Nat. Phys. 21, 570 (2025).
  30. Z. Jia, W. Huie, L. Li, W. K. C. Sun, X. Hu, Aakash, H. Kogan, A. Karve, J. Y. Lee, and J. P. Covey, An architecture for two-qubit encoding in neutral ytterbium-171 atoms, npj Quantum Inf. 10, 106 (2024).
  31. W. C. Campbell and E. R. Hudson, Polyqubit quantum processing, arXiv:2210.15484.
  32. A. M. Kaufman, B. J. Lester, and C. A. Regal, Cooling a single atom in an optical tweezer to its quantum ground state, Phys. Rev. X 2, 041014 (2012).
  33. J. D. Thompson, T. G. Tiecke, A. S. Zibrov, V. Vuletić, and M. D. Lukin, Coherence and Raman sideband cooling of a single atom in an optical tweezer, Phys. Rev. Lett. 110, 133001 (2013).
  34. A. Jenkins, J. W. Lis, A. Senoo, W. F. McGrew, and A. M. Kaufman, Ytterbium nuclear-spin qubits in an optical tweezer array, Phys. Rev. X 12, 021027 (2022).
  35. H. K. Cummins, G. Llewellyn, and J. A. Jones, Tackling systematic errors in quantum logic gates with composite rotations, Phys. Rev. A 67, 042308 (2003).
  36. J. W. Lis, A. Senoo, W. F. McGrew, F. Rönchen, A. Jenkins, and A. M. Kaufman, Midcircuit operations using the omg architecture in neutral atom arrays, Phys. Rev. X 13, 041035 (2023).
  37. L. Li, X. Hu, Z. Jia, W. Huie, W. K. C. Sun, Aakash, Y. Dong, N. Hiri-O-Tuppa, and J. P. Covey, Parallelized telecom quantum networking with a ytterbium-171 atom array, Nat. Phys. 21, 1826 (2025).
  38. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, Demonstration of a neutral atom controlled-NOT quantum gate, Phys. Rev. Lett. 104, 010503 (2010).
  39. M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010).
  40. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, Entanglement of two individual neutral atoms using Rydberg blockade, Phys. Rev. Lett. 104, 010502 (2010).
  41. Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydberg-dressed spin-flip blockade, Nat. Phys. 12, 71 (2016).
  42. T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, Rydberg-mediated entanglement in a two-dimensional neutral atom qubit array, Phys. Rev. Lett. 123, 230501 (2019).
  43. H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019).
  44. W. Huie, L. Li, N. Chen, X. Hu, Z. Jia, W. K. C. Sun, and J. P. Covey, Repetitive readout and real-time control of nuclear spin qubits in 171Yb atoms, PRX Quantum 4, 030337 (2023).
  45. M. A. Norcia et al., Midcircuit qubit measurement and rearrangement in a Yb-171 atomic array, Phys. Rev. X 13, 041034 (2023).
  46. J. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  47. P. Sala, T. Shi, S. Kühn, M. C. Bañuls, E. Demler, and J. I. Cirac, Variational study of U(1) and SU(2) lattice gauge theories with gaussian states in 1+1 dimensions, Phys. Rev. D 98, 034505 (2018).
  48. M. Illa, C. E. P. Robin, and M. J. Savage, Qu8its for quantum simulations of lattice quantum chromodynamics, Phys. Rev. D 110, 014507 (2024).
  49. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).
  50. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits, Phys. Rev. D 109, 114510 (2024).
  51. S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum algorithms for quantum field theories, Science 336, 1130 (2012).
  52. Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer, Quantum 8, 1520 (2024).
  53. D. Gottesman, A. Kitaev, and J. Preskill, Encoding a qubit in an oscillator, Phys. Rev. A 64, 012310 (2001).
  54. V. V. Albert, J. P. Covey, and J. Preskill, Robust encoding of a qubit in a molecule, Phys. Rev. X 10, 031050 (2020).
  55. S. P. Jain, E. R. Hudson, W. C. Campbell, and V. V. Albert, Absorption-emission codes for atomic and molecular quantum information platforms, Phys. Rev. Lett. 133, 260601 (2024).
  56. P. Balaji, C. Conefrey-Shinozaki, P. Draper, J. K. Elhaderi, D. Gupta, L. Hidalgo, A. Lytle, and E. Rinaldi, Quantum circuits for SU(3) lattice gauge theory, Phys. Rev. D 112, 054511 (2025).
  57. A. Ciavarella, N. Klco, and M. J. Savage, Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis, Phys. Rev. D 103, 094501 (2021).
  58. D. S. Barker, N. C. Pisenti, B. J. Reschovsky, and G. K. Campbell, Three-photon process for producing a degenerate gas of metastable alkaline-earth-metal atoms, Phys. Rev. A 93, 053417 (2016).
  59. G. Panelli, S. C. Burd, E. J. Porter, and M. Kasevich, Doppler-free three-photon spectroscopy on narrow-line optical transitions, Phys. Rev. A 111, 033112 (2025).
  60. S. Jandura and G. Pupillo, Time-optimal two- and three-qubit gates for Rydberg atoms, Quantum 6, 712 (2022).
  61. Y. Liu, J. Sinanan-Singh, M. T. Kearney, G. Mintzer, and I. L. Chuang, Constructing qudits from infinite-dimensional oscillators by coupling to qubits, Phys. Rev. A 104, 032605 (2021).
  62. If we chose |br⟩ instead of |rb⟩, for example, there would be no minus phase in c~r but two in c~g and c~b.
  63. M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University, Cambridge, England, 2014).
  64. S. Weinberg, The Quantum Theory of Fields (Cambridge University, Cambridge, England, 1996).

Outline

Information

PRX Quantum 7, 010327– Published 9 February, 2026
  • Received 27 July 2025
  • Accepted 22 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation