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Qudit gate decomposition for lattice gauge theories on superconducting radio-frequency cavities

Dog̃a Murat Kürkçüog̃lu 1,2,*, Henry Lamm1,2,†, and Andrea Maestri3,‡

  • *Contact author: dogak@fnal.gov
  • †Contact author: hlamm@fnal.gov
  • ‡Contact author: andreamaestrimaestri@gmail.com
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Phys. Rev. A 114, 022460 – Published 27 August, 2026

DOI: https://doi.org/10.1103/bd87-g26f

Abstract

In this work we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: snap and displacement gates, ecd and single-qubit rotations R(θ,ϕ), and optimal pulse control. For all three decompositions, implementing the necessary sequence of rotations concurrently rather than sequentially can reduce the primitive gate run time. The number of blocks required for the faster ecd and Rp(θ) is found to scale as O(d2), while the slower snap and displacement set scales sublinearly with d on the permutation gates relevant for lattice gauge theory. For qudits with d<10, the resulting gate times for the two decompositions are similar, though strongly dependent on experimental design choices. Optimal control can outperform both decompositions for small d by a factor of 2 to 12 at the cost of higher classical resources. Lastly, we find that snap and displacement are slightly more robust to a simplified noise model.

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References (179)

  1. N. Klco, A. Roggero, and M. J. Savage, Standard Model physics and the digital quantum revolution: Thoughts about the interface, Rep. Prog. Phys. 85, 064301 (2022).
  2. M. C. Bañuls et al., Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  3. C. W. Bauer et al., Quantum simulation for high-energy physics, PRX Quantum 4, 027001 (2023).
  4. A. Di Meglio et al., Quantum computing for high-energy physics: State of the art and challenges. Summary of the QC4HEP Working Group, PRX Quantum 5, 037001 (2024).
  5. E. J. Gustafson, Y. Ji, H. Lamm, E. M. Murairi, S. O. Perez, and S. Zhu, Primitive quantum gates for an SU(3) discrete subgroup: Σ(36×3), Phys. Rev. D 110, 034515 (2024).
  6. M. Rhodes, M. Kreshchuk, and S. Pathak, Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques, PRX Quantum 5, 040347 (2024).
  7. E. Gustafson et al., Large scale multi-node simulations of Z2 gauge theory quantum circuits using Google Cloud Platform, arXiv:2110.07482.
  8. E. J. Gustafson, Prospects for simulating a qudit-based model of (1+1)D scalar QED, Phys. Rev. D 103, 114505 (2021).
  9. P. P. Popov, M. Meth, M. Lewestein, P. Hauke, M. Ringbauer, E. Zohar, and V. Kasper, Variational quantum simulation of U(1) lattice gauge theories with qudit systems, Phys. Rev. Res. 6, 013202 (2024).
  10. D. M. Kurkcuoglu, M. S. Alam, J. A. Job, A. C. Y. Li, A. Macridin, G. N. Perdue, and S. Providence, Quantum simulation of ϕ4 theories in qudit systems, arXiv:2108.13357.
  11. G. Calajò, 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 5, 040309 (2024).
  12. 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. 129 160501 (2022).
  13. M. Illa, C. E. P. Robin, and M. J. Savage, Qu8its for quantum simulations of lattice quantum chromodynamics, Phys. Rev. D 110, 014507 (2024).
  14. T. V. Zache, D. González-Cuadra, and P. Zoller, Fermion-qudit quantum processors for simulating lattice gauge theories with matter, Quantum 7, 1140 (2023).
  15. D. Janković, J.-G. Hartmann, M. Ruben, and P.-A. Hervieux, Noisy qudit vs multiple qubits: Conditions on gate efficiency for enhancing fidelity, npj Quantum Inf. 10, 59 (2024).
  16. A. S. Nikolaeva, E. O. Kiktenko, and A. K. Fedorov, Efficient realization of quantum algorithms with qudits, EPJ Quantum Technol. 11, 43 (2024).
  17. M. B. Mansky, S. L. n. Castillo, V. R. Puigvert, and C. Linnhoff-Popien, Near-optimal quantum circuit construction via Cartan decomposition, Phys. Rev. A 108, 052607 (2023).
  18. 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).
  19. A. S. Nikolaeva et al., Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits, Phys. Rev. Lett. 135 060601 (2025).
  20. P. J. Low, B. White, and C. Senko, Control and readout of a 13-level trapped ion qudit, arXiv:2306.03340.
  21. N. Goss et al., High-fidelity qutrit entangling gates for superconducting circuits, Nat. Commun. 13, 7481 (2022) [Erratum: Nat. Commun. 14, 4256 (2023)].
  22. K. Luo et al., Experimental realization of two qutrits gate with tunable coupling in superconducting circuits, Phys. Rev. Lett. 130, 030603 (2023).
  23. N. Goss, S. Ferracin, A. Hashim, A. Carignan-Dugas, J. M. Kreikebaum, R. K. Naik, D. I. Santiago, and I. Siddiqi, Extending the computational reach of a superconducting qutrit processor, arXiv:2305.16507.
  24. S. Cao, M. Bakr, G. Campanaro, S. D. Fasciati, J. Wills, D. Lall, B. Shteynas, V. Chidambaram, I. Rungger, and P. Leek, Emulating two qubits with a four-level transmon qudit for variational quantum algorithms, Quantum Sci. Technol. 9, 035003 (2024).
  25. L. M. Seifert, Z. Li, T. Roy, D. I. Schuster, F. T. Chong, and J. M. Baker, Exploring ququart computation on a transmon using optimal control, Phys. Rev. A 108, 062609 (2023).
  26. Z. Wang, R. W. Parker, E. Champion, and M. S. Blok, Systematic study of high EJ/EC transmon qudits up to d=12, Phys. Rev. Appl. 23, 034046 (2025).
  27. A. Kruckenhauser, R. van Bijnen, T. V. Zache, M. Di Liberto, and P. Zoller, High-dimensional SO(4)-symmetric Rydberg manifolds for quantum simulation, Quantum Sci. Technol. 8, 015020 (2023).
  28. S. R. Cohen and J. D. Thompson, Quantum computing with circular Rydberg atoms, PRX Quantum 2, 030322 (2021).
  29. Y. Chi et al., A programmable qudit-based quantum processor, Nat. Commun. 13, 1166 (2022).
  30. V. Kasper, D. González-Cuadra, A. Hegde, A. Xia, A. Dauphin, F. Huber, E. Tiemann, M. Lewenstein, F. Jendrzejewski, and P. Hauke, Universal quantum computation and quantum error correction with ultracold atomic mixtures, Quantum Sci. Technol. 7, 015008 (2022).
  31. T. Roy, T. Kim, A. Romanenko, and A. Grassellino, Qudit-based quantum computing with SRF cavities at Fermilab, PoS LATTICE2023, 127 (2024).
  32. R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Cavity state manipulation using photon-number selective phase gates, Phys. Rev. Lett. 115, 137002 (2015).
  33. T. Fösel, S. Krastanov, F. Marquardt, and L. Jiang, Efficient cavity control with snap gates, arXiv:2004.14256.
  34. M. Kudra, M. Kervinen, I. Strandberg, S. Ahmed, M. Scigliuzzo, A. Osman, D. P. Lozano, M. O. Tholén, R. Borgani, D. B. Haviland, et al., Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences, PRX Quantum 3, 030301 (2022).
  35. A. Eickbusch, V. Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Fast universal control of an oscillator with weak dispersive coupling to a qubit, Nat. Phys. 18, 1464 (2022).
  36. G. K. Brennen, S. S. Bullock, and D. P. O'Leary, Efficient circuits for exact-universal computation with qudits, Quant. Inf. Comput. 6, 436 (2006).
  37. M. Howard and J. Vala, Qudit versions of the qubit π/8 gate, Phys. Rev. A 86, 022316 (2012).
  38. A. Bocharov, A note on optimality of quantum circuits over metaplectic basis, Quant. Inf. Comput. 18, 1 (2018).
  39. L. Yeh and J. van de Wetering, Constructing all qutrit controlled Clifford+T gates in Clifford+T, in Reversible Computation (RC 2022), Lecture Notes in Computer Science, Vol. 13354 ( Springer, Cham, 2022), pp. 28–50.
  40. Y. Nakajima, Y. Kawano, H. Sekigawa, M. Nakanishi, S. Yamashita, and Y. Nakashima, Synthesis of quantum circuits for d-level systems by using cosine-sine, Quant. Inf. Comput. 9, 423 (2009).
  41. S. Prakash, A. R. Kalra, and A. Jain, A normal form for single-qudit Clifford+T operators, Quant. Inf. Proc. 20, 341 (2021).
  42. A. R. Kalra, D. Valluri, and M. Mosca, Synthesis and arithmetic of single qutrit circuits, Quantum 9, 1647 (2023).
  43. R. I. Booth and T. Carette, Complete ZX-calculi for the stabiliser fragment in odd prime dimensions, in 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Leibniz International Proceedings in Informatics (LIPIcs), Vol. 241 (Schloss Dagstuhl Leibniz-Zentrum für Informatik, 2022), pp. 24:1–24:15.
  44. A. N. Glaudell, N. J. Ross, J. van de Wetering, and L. Yeh, Qutrit metaplectic gates are a subset of Clifford+T, in 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022), Leibniz International Proceedings in Informatics (LIPIcs), Vol. 232 (SchlossDagstuhlLeibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany, 2022), pp. 12:1–12:15.
  45. A. N. Glaudell, N. J. Ross, J. van de Wetering, and L. Yeh, Exact synthesis of multiqutrit Clifford-cyclotomic circuits, EPTCS 406, 44 (2024).
  46. S. Prakash, A. Jain, B. Kapur, and S. Seth, Normal form for single-qutrit Clifford +T operators and synthesis of single-qutrit gates, Phys. Rev. A 98, 032304 (2018).
  47. H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), General methods for digital quantum simulation of gauge theories, Phys. Rev. D 100, 034518 (2019).
  48. M. S. Alam, S. Hadfield, H. Lamm, and A. C. Y. Li (SQMS Collaboration), Primitive quantum gates for dihedral gauge theories, Phys. Rev. D 105, 114501 (2022).
  49. E. J. Gustafson, H. Lamm, F. Lovelace, and D. Musk, Primitive quantum gates for an SU(2) discrete subgroup: Binary tetrahedral, Phys. Rev. D 106, 114501 (2022).
  50. T. V. Zache, D. González-Cuadra, and P. Zoller, Quantum and classical spin-network algorithms for q-deformed Kogut-Susskind gauge theories, Phys. Rev. Lett. 131, 171902 (2023).
  51. E. J. Gustafson, H. Lamm, and F. Lovelace, Primitive quantum gates for an SU(2) discrete subgroup: Binary octahedral, Phys. Rev. D 109, 054503 (2024).
  52. H. Lamm, Y.-Y. Li, J. Shu, Y.-L. Wang, and B. Xu, Block encodings of discrete subgroups on quantum computer, arXiv:2405.12890.
  53. E. M. Murairi, M. Sohaib Alam, H. Lamm, S. Hadfield, and E. Gustafson, Highly-efficient quantum Fourier transformations for some nonabelian groups, arXiv:2408.00075.
  54. T. D. Cohen, H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Quantum algorithms for transport coefficients in gauge theories, Phys. Rev. D 104, 094514 (2021).
  55. M. Carena, H. Lamm, Y.-Y. Li, and W. Liu, Improved Hamiltonians for quantum simulations of gauge theories, Phys. Rev. Lett. 129, 051601 (2022).
  56. E. J. Gustafson, Stout smearing on a quantum computer, arXiv:2211.05607.
  57. E. Gustafson and R. Van de Water, Improved fermion Hamiltonians for quantum simulation, PoS LATTICE2023, 215 (2024).
  58. M. Carena, H. Lamm, Y.-Y. Li, and W. Liu, Quantum error thresholds for gauge-redundant digitizations of lattice field theories, arXiv:2402.16780.
  59. E. Zohar, J. I. Cirac, and B. Reznik, Cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory, Phys. Rev. Lett. 110, 125304 (2013).
  60. E. Zohar, J. I. Cirac, and B. Reznik, Simulating compact quantum electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects, Phys. Rev. Lett. 109, 125302 (2012).
  61. E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular momentum conservation, Phys. Rev. A 88, 023617 (2013).
  62. E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices, Rep. Prog. Phys. 79, 014401 (2016).
  63. A. Bazavov, Y. Meurice, S.-W. Tsai, J. Unmuth-Yockey, and J. Zhang, Gauge-invariant implementation of the Abelian Higgs model on optical lattices, Phys. Rev. D 92, 076003 (2015).
  64. J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S. W. Tsai, and Y. Meurice, Quantum simulation of the universal features of the Polyakov loop, Phys. Rev. Lett. 121, 223201 (2018).
  65. J. Unmuth-Yockey, J. Zhang, A. Bazavov, Y. Meurice, and S.-W. Tsai, Universal features of the Abelian Polyakov loop in 1+1 dimensions, Phys. Rev. D 98, 094511 (2018).
  66. N. Klco, M. J. Savage, and J. R. Stryker, SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers, Phys. Rev. D 101, 074512 (2020).
  67. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Scalable circuits for preparing ground states on digital quantum computers: The Schwinger model vacuum on 100 qubits, PRX Quantum 5, 020315 (2024).
  68. 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).
  69. A. Ciavarella, N. Klco, and M. J. Savage, A trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis, Phys. Rev. D 103 094501 (2021).
  70. A. Bazavov, S. Catterall, R. G. Jha, and J. Unmuth-Yockey, Tensor renormalization group study of the non-Abelian Higgs model in two dimensions, Phys. Rev. D 99, 114507 (2019).
  71. A. J. Buser, T. Bhattacharya, L. Cincio, and R. Gupta, Quantum simulation of the qubit-regularized O(3)-sigma model, Phys. Rev. D 102 114514 (2020).
  72. T. Bhattacharya, A. J. Buser, S. Chandrasekharan, R. Gupta, and H. Singh, Qubit regularization of asymptotic freedom, Phys. Rev. Lett. 126 172001 (2021).
  73. A. H. Z. Kavaki and R. Lewis, From square plaquettes to triamond lattices for SU(2) gauge theory, Commun. Phys. 7, 208 (2024).
  74. E. M. Murairi, M. J. Cervia, H. Kumar, P. F. Bedaque, and A. Alexandru, How many quantum gates do gauge theories require? Phys. Rev. D 106 094504 (2022).
  75. 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).
  76. I. Raychowdhury and J. R. Stryker, Solving Gauss's law on digital quantum computers with loop-string-hadron digitization, Phys. Rev. Res. 2, 033039 (2020).
  77. S. V. Kadam, Theoretical developments in lattice gauge theory for applications in double-beta decay processes and quantum simulation, Ph.D. thesis, University of Maryland, College Park, 2023.
  78. Z. Davoudi, I. Raychowdhury, and A. Shaw, Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories, Phys. Rev. D 104 074505 (2021).
  79. E. Mathew and I. Raychowdhury, Protecting local and global symmetries in simulating (1+1)D non-Abelian gauge theories, Phys. Rev. D 106, 054510 (2022).
  80. C. W. Bauer and D. M. Grabowska, Efficient representation for simulating U(1) gauge theories on digital quantum computers at all values of the coupling, arXiv:2111.08015.
  81. D. M. Grabowska, C. Kane, B. Nachman, and C. W. Bauer, Overcoming exponential scaling with system size in Trotter-Suzuki implementations of constrained Hamiltonians: 2+1 U(1) lattice gauge theories, arXiv:2208.03333.
  82. D. M. Grabowska, C. F. Kane, and C. W. Bauer, A fully gauge-fixed SU(2) Hamiltonian for quantum simulations, arXiv:2409.10610.
  83. T. Li, Quantum simulations of quantum electrodynamics in Coulomb gauge, arXiv:2406.01204.
  84. P. Fontana, M. M. Riaza, and A. Celi, An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension, Phys. Rev. X 15 031065 (2025.
  85. M. Kreshchuk, W. M. Kirby, G. Goldstein, H. Beauchemin, and P. J. Love, Quantum simulation of quantum field theory in the light-front formulation, Phys. Rev. A 105 032418 (2022).
  86. M. Kreshchuk, S. Jia, W. M. Kirby, G. Goldstein, J. P. Vary, and P. J. Love, Simulating hadronic physics on NISQ devices using basis light-front quantization, Phys. Rev. A 103 062601 (2021).
  87. M. Kreshchuk, S. Jia, W. M. Kirby, G. Goldstein, J. P. Vary, and P. J. Love, Light-front field theory on current quantum computers, Entropy 23 597 (2020).
  88. J. Liu and Y. Xin, Quantum simulation of quantum field theories as quantum chemistry, J. High Energ. Phys. 12 (2020) 011.
  89. M. Fromm, O. Philipsen, W. Unger, and C. Winterowd, Quantum gate sets for lattice QCD in the strong coupling limit: Nf=1, EPJ Quantum Technol. 11, 24 (2024).
  90. A. N. Ciavarella and C. W. Bauer, Quantum simulation of SU(3) lattice Yang Mills theory at leading order in large N, arXiv:2402.10265.
  91. A. Alexandru, P. F. Bedaque, A. Carosso, M. J. Cervia, E. M. Murairi, and A. Sheng, Fuzzy gauge theory for quantum computers, Phys. Rev. D 109, 094502 (2024).
  92. R. Brower, S. Chandrasekharan, and U. J. Wiese, QCD as a quantum link model, Phys. Rev. D 60, 094502 (1999).
  93. H. Singh, Qubit O(N) nonlinear sigma models, arXiv:1911.12353.
  94. H. Singh and S. Chandrasekharan, Qubit regularization of the O(3) sigma model, Phys. Rev. D 100, 054505 (2019).
  95. U.-J. Wiese, Towards quantum simulating QCD, Nucl. Phys. A 931, 246 (2014).
  96. R. C. Brower, D. Berenstein, and H. Kawai, Lattice gauge theory for a quantum computer, PoS LATTICE2019, 112 (2019).
  97. S. V. Mathis, G. Mazzola, and I. Tavernelli, Toward scalable simulations of lattice gauge theories on quantum computers, Phys. Rev. D 102, 094501 (2020).
  98. J. C. Halimeh, R. Ott, I. P. McCulloch, B. Yang, and P. Hauke, Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories, Phys. Rev. Res. 2, 033361 (2020).
  99. T. Budde, M. K. Marinković, and J. C. P. Barros, Quantum many-body scars for arbitrary integer spin in 2+1D Abelian gauge theories, arXiv:2403.08892.
  100. J. Osborne, I. P. McCulloch, and J. C. Halimeh, Quantum many-body scarring in 2+1D gauge theories with dynamical matter, arXiv:2403.08858.
  101. J. Osborne, B. Yang, I. P. McCulloch, P. Hauke, and J. C. Halimeh, Spin-SU(1) quantum link models with dynamical matter on a quantum simulator, arXiv:2305.06368.
  102. D. Luo, J. Shen, M. Highman, B. K. Clark, B. DeMarco, A. X. El-Khadra, and B. Gadway, A framework for simulating gauge theories with dipolar spin systems, Phys. Rev. A 102 032617 (2020).
  103. E. Zohar and M. Burrello, Formulation of lattice gauge theories for quantum simulations, Phys. Rev. D 91, 054506 (2015).
  104. E. Zohar, A. Farace, B. Reznik, and J. I. Cirac, Digital lattice gauge theories, Phys. Rev. A 95, 023604 (2017).
  105. J. Bender, E. Zohar, A. Farace, and J. I. Cirac, Digital quantum simulation of lattice gauge theories in three spatial dimensions, New J. Phys. 20, 093001 (2018).
  106. D. C. Hackett, K. Howe, C. Hughes, W. Jay, E. T. Neil, and J. N. Simone, Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers, Phys. Rev. A 99, 062341 (2019).
  107. A. Alexandru, P. F. Bedaque, S. Harmalkar, H. Lamm, S. Lawrence, and N. C. Warrington (NuQS Collaboration), Gluon field digitization for quantum computers, Phys. Rev. D 100, 114501 (2019).
  108. A. Yamamoto, Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits, Prog. Theor. Exp. Phys. 2021, 013B06 (2021).
  109. Y. Ji, H. Lamm, and S. Zhu (NuQS Collaboration), Gluon field digitization via group space decimation for quantum computers, Phys. Rev. D 102, 114513 (2020).
  110. J. F. Haase, L. Dellantonio, A. Celi, D. Paulson, A. Kan, K. Jansen, and C. A. Muschik, A resource efficient approach for quantum and classical simulations of gauge theories in particle physics, Quantum 5, 393 (2021).
  111. M. Carena, H. Lamm, Y.-Y. Li, and W. Liu, Lattice renormalization of quantum simulations, Phys. Rev. D 104 094519 (2021).
  112. T. Armon, S. Ashkenazi, G. García-Moreno, A. González-Tudela, and E. Zohar, Photon-mediated stroboscopic quantum simulation of a Z2 lattice gauge theory, Phys. Rev. Lett. 127, 250501 (2021).
  113. C. Charles, E. J. Gustafson, E. Hardt, F. Herren, N. Hogan, H. Lamm, S. Starecheski, R. S. Van de Water, and M. L. Wagman, Simulating Z2 lattice gauge theory on a quantum computer, arXiv:2305.02361.
  114. R. Irmejs, M. C. Banuls, and J. I. Cirac, Quantum simulation of Z2 lattice gauge theory with minimal resources, Phys. Rev. D 108, 074503 (2023).
  115. E. J. Gustafson and H. Lamm, Toward quantum simulations of Z2 gauge theory without state preparation, Phys. Rev. D 103, 054507 (2021).
  116. T. Hartung, T. Jakobs, K. Jansen, J. Ostmeyer, and C. Urbach, Digitising SU(2) gauge fields and the freezing transition, Eur. Phys. J. C 82, 237 (2022).
  117. M. Creutz, L. Jacobs, and C. Rebbi, Monte Carlo study of Abelian lattice gauge theories, Phys. Rev. D 20, 1915 (1979).
  118. M. Creutz and M. Okawa, Generalized actions in Z(p) lattice gauge theory, Nucl. Phys. B 220, 149 (1983).
  119. G. Bhanot and C. Rebbi, Monte Carlo simulations of lattice models with finite subgroups of SU(3) as gauge groups, Phys. Rev. D 24, 3319 (1981).
  120. D. Petcher and D. H. Weingarten, Monte Carlo calculations and a model of the phase structure for gauge theories on discrete subgroups of SU(2), Phys. Rev. D 22, 2465 (1980).
  121. G. Bhanot, SU(3) lattice gauge theory in four-dimensions with a modified Wilson action, Phys. Lett. B 108, 337 (1982).
  122. D. H. Weingarten and D. N. Petcher, Monte Carlo integration for lattice gauge theories with fermions, Phys. Lett. B 99, 333 (1981).
  123. D. Weingarten, Monte Carlo evaluation of hadron masses in lattice gauge theories with fermions, Phys. Lett. B 109, 57 (1982).
  124. Y. Ji, H. Lamm, and S. Zhu, Gluon digitization via character expansion for quantum computers, Phys. Rev. D 107 114503 (2023).
  125. A. Alexandru, P. F. Bedaque, R. Brett, and H. Lamm, Spectrum of digitized QCD: Glueballs in a S(1080) gauge theory, Phys. Rev. D 105, 114508 (2022).
  126. M. Carena, E. J. Gustafson, H. Lamm, Y.-Y. Li, and W. Liu, Gauge theory couplings on anisotropic lattices, Phys. Rev. D 106, 114504 (2022).
  127. J. B. Kogut, 1/n expansions and the phase diagram of discrete lattice gauge theories with matter fields, Phys. Rev. D 21, 2316 (1980).
  128. J. Romers, Discrete gauge theories in two spatial dimensions, Ph.D. thesis, Master's thesis, Universiteit van Amsterdam, 2007.
  129. E. H. Fradkin and S. H. Shenker, Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D 19, 3682 (1979).
  130. D. Harlow and H. Ooguri, Symmetries in quantum field theory and quantum gravity, arXiv:1810.05338.
  131. D. Horn, M. Weinstein, and S. Yankielowicz, Hamiltonian approach to Z(N) lattice gauge theories, Phys. Rev. D 19, 3715 (1979).
  132. B. Assi and H. Lamm, Digitization and subduction of SU(N) gauge theories, Phys. Rev. D 110, 074511 (2024).
  133. T. Kim et al., Ultracoherent superconducting cavity-based multiqudit platform with error-resilient control, arXiv:2506.03286.
  134. T. Tilma and E. C. G. Sudarshan, Generalized Euler angle parametrization for SU(N), J. Phys. A: Math. Gen. 35, 10467 (2002).
  135. S. Bertini, S. L. Cacciatori, and B. L. Cerchiai, On the Euler angles for SU(N), J. Math. Phys. 47, 043510 (2006).
  136. T. Tilma and E. C. G. Sudarshan, Generalized Euler angle parameterization for U(N) with applications to SU(N) coset volume measures, J. Geom. Phys. 52, 263 (2004).
  137. F. S. Khan and M. Perkowski, Synthesis of multi-qudit hybrid and d-valued quantum logic circuits by decomposition, Theor. Comput. Sci. 367, 336 (2006).
  138. J. R. Stryker, Oracles for Gauss's law on digital quantum computers, Phys. Rev. A 99, 042301 (2019).
  139. S. Harmalkar, H. Lamm, and S. Lawrence (NuQS Collaboration), Quantum simulation of field theories without state preparation, arXiv:2001.11490 [hep-lat].
  140. J. Saroni, H. Lamm, P. P. Orth, and T. Iadecola, Reconstructing thermal quantum quench dynamics from pure states, Phys. Rev. B 108, 134301 (2023).
  141. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  142. M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A 79, 013819 (2009).
  143. S. Krastanov, V. V. Albert, C. Shen, C.-L. Zou, R. W. Heeres, B. Vlastakis, R. J. Schoelkopf, and L. Jiang, Universal control of an oscillator with dispersive coupling to a qubit, Phys. Rev. A 92, 040303(R) (2015).
  144. F. W. Strauch, All-resonant control of superconducting resonators, Phys. Rev. Lett. 109, 210501 (2012).
  145. C. K. Law and J. H. Eberly, Arbitrary control of a quantum electromagnetic field, Phys. Rev. Lett. 76, 1055 (1996).
  146. T. F. Roque, A. A. Clerk, and H. Ribeiro, Engineering fast high-fidelity quantum operations with constrained interactions, arXiv:2003.12096.
  147. X. Fei, L. T. Brady, J. Larson, S. Leyffer, and S. Shen, Binary control pulse optimization for quantum systems, Quantum 7, 892 (2023).
  148. L. M. Seifert, J. Chadwick, A. Litteken, F. T. Chong, and J. M. Baker, Time-efficient qudit gates through incremental pulse re-seeding, in 2022 IEEE International Conference on Quantum Computing and Engineering (IEEE, Piscataway, NJ, 2022), pp. 304–313.
  149. P. Luchi, F. Turro, V. Amitrano, F. Pederiva, X. Wu, K. Wendt, J. L. Dubois, and S. Quaglioni, Control optimization for parametric Hamiltonians by pulse reconstruction, Eur. Phys. J. A 59, 196 (2023).
  150. A. Reineri, S. Zorzetti, T. Roy, and X. You, Exploration of superconducting multi-mode cavity architectures for quantum computing, arXiv:2308.11740.
  151. X. You et al., Crosstalk-robust quantum control in multimode bosonic systems, Phys. Rev. Appl. 22, 044072 (2024).
  152. J. Job, Efficient, direct compilation of SU(N) operations into snap & displacement gates, arXiv:2307.11900.
  153. O. Ogunkoya, J. Kim, B. Peng, A. B. Özgüler, and Y. Alexeev, Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation, Phys. Rev. A 109, 012426 (2024).
  154. P. Roy, J. van de Wetering, and L. Yeh, The qudit ZH-calculus: Generalised Toffoli+Hadamard and universality, EPTCS 384, 142 (2023).
  155. K. Mato, M. Ringbauer, S. Hillmich, and R. Wille, Compilation of entangling gates for high-dimensional quantum systems, in Proceedings of the 28th Asia and South Pacific Design Automation Conference, ASPDAC'23 (ACM Press, New York, NY, 2023), pp. 202–208.
  156. O. Ogunkoya, K. Morris, and D. M. Kürkçüoglu, Investigating parameter trainability in the SNAP-displacement protocol of a qudit system, arXiv:2309.14942.
  157. B. Şahinoğlu and R. D. Somma, Hamiltonian simulation in the low energy subspace, npj Quantum Inf 7, 119 (2020).
  158. T. Hatomura, State-dependent error bound for digital quantum simulation of driven systems, Phys. Rev. A 105, L050601 (2022).
  159. D. Burgarth, N. Galke, A. Hahn, and L. van Luijk, State-dependent Trotter limits and their approximations, Phys. Rev. A 107, L040201 (2023).
  160. K. Kormann, S. Holmgren, and H. Karlsson, A Fourier-coefficient based solution of an optimal control problem in quantum chemistry, J. Optim Theory Appl. 147, 491 (2010).
  161. A. Pagano, M. M. Müller, T. Calarco, S. Montangero, and P. Rembold, The role of bases in quantum optimal control, Phys. Rev. A 110 062608 (2024).
  162. N. Karjanto, Properties of Chebyshev polynomials, arXiv:2002.01342.
  163. C. Gerry and P. Knight, Introductory Quantum Optics (Cambridge University Press, Cambridge, 2004).
  164. M. S. Alam et al., Quantum computing hardware for HEP algorithms and sensing, arXiv:2204.08605.
  165. J. Y. Araz, S. Bhowmick, M. Grau, T. J. McEntire, and F. Ringer, State preparation of lattice field theories using quantum optimal control, Phys. Rev. D 111, 034506 (2025).
  166. C. J. Axline, L. D. Burkhart, W. Pfaff, M. Zhang, K. Chou, P. Campagne-Ibarcq, P. Reinhold, L. Frunzio, S. Girvin, L. Jiang, et al., On-demand quantum state transfer and entanglement between remote microwave cavity memories, Nat. Phys. 14, 705 (2018).
  167. T. Fösel, S. Krastanov, F. Marquardt, and L. Jiang, Efficient cavity control with snap gates, arXiv:2004.14256.
  168. J. J. Vartiainen, M. Möttönen, and M. M. Salomaa, Efficient decomposition of quantum gates, Phys. Rev. Lett. 92, 177902 (2004).
  169. N. P. D. Sawaya, T. Menke, T. H. Kyaw, S. Johri, A. Aspuru-Guzik, and G. G. Guerreschi, Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians, npj Quantum Inf. 6, 49 (2020).
  170. O. Di Matteo, A. McCoy, P. Gysbers, T. Miyagi, R. M. Woloshyn, and P. Navrátil, Improving Hamiltonian encodings with the Gray code, Phys. Rev. A 103, 042405 (2021).
  171. C. C. Chang, K. S. McElvain, E. Rrapaj, and Y. Wu, Improving Schrödinger equation implementations with Gray code for adiabatic quantum computers, PRX Quantum 3, 020356 (2022).
  172. M. G. Kendall, A new measure of rank correlation, Biometrika 30, 81 (1938).
  173. F. J. Damerau, A technique for computer detection and correction of spelling errors, Commun. ACM 7, 171 (1964).
  174. V. Levenshtein, Binary codes capable of correcting deletions, insertions, and reversals, in Proceedings of the Soviet physics doklady (1966).
  175. V. V. Shende, I. L. Markov, and S. S. Bullock, Minimal universal two-qubit controlled-not-based circuits, Phys. Rev. A 69, 062321 (2004).
  176. D. C. McKay, I. Hincks, E. J. Pritchett, M. Carroll, L. C. G. Govia, and S. T. Merkel, Benchmarking quantum processor performance at scale, arXiv:2311.05933.
  177. D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program. 45, 503 (1989).
  178. https://github.com/AndreaMaestri18/Opt3DQalgs.
  179. M. J. Cervia, H. Lamm, D. Liu, E. M. Murairi, and S. Zhu, Magic state distillation using asymptotically good codes on qudits, arXiv:2512.21874.

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Phys. Rev. A 114, 022460– Published 27 August, 2026
  • Received 16 March 2025
  • Accepted 15 July 2026
Article part of CHORUS
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