{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T06:08:07Z","timestamp":1770962887725,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T00:00:00Z","timestamp":1769817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["24-71-00084"],"award-info":[{"award-number":["24-71-00084"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Priority 2030 program at the NIST ``MISIS''","award":["project K1-2022-027"],"award-info":[{"award-number":["project K1-2022-027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Simulating entangled, many-body quantum systems is notoriously hard, especially in the case of the high-dimensional nature of the underlying physical objects. In this work, we propose an approach for simulating the Potts model based on the Suzuki\u2013Trotter decomposition that we construct for qudit systems. Specifically, we introduce two qudit-native decomposition schemes: (i) the first utilizes the M\u00f8lmer\u2013S\u00f8rensen gate and additional local levels to encode the Potts interactions, while (ii) the second employs a light-shift gate that naturally fits qudit architectures. These decompositions enable a direct and efficient mapping of the Potts model dynamics into hardware-efficient qudit gate sequences for a trapped-ion platform. Furthermore, we demonstrate the use of a Suzuki\u2013Trotter approximation with our evolution-into-gates framework for detecting the dynamical quantum phase transition. Our results establish a pathway toward qudit-based digital quantum simulation of many-body models and provide a new perspective on probing nonanalytic behavior in high-dimensional quantum many-body models.<\/jats:p>","DOI":"10.3390\/e28020160","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T09:48:08Z","timestamp":1770025688000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Qudit-Native Simulation of the Potts Model"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2860-6576","authenticated-orcid":false,"given":"Maksim A.","family":"Gavreev","sequence":"first","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5760-441X","authenticated-orcid":false,"given":"Evgeniy O.","family":"Kiktenko","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4722-3418","authenticated-orcid":false,"given":"Aleksey K.","family":"Fedorov","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8321-7103","authenticated-orcid":false,"given":"Anastasiia S.","family":"Nikolaeva","sequence":"additional","affiliation":[{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology \u201cMISIS\u201d, Moscow 119049, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,31]]},"reference":[{"key":"ref_1","unstructured":"Preskill, J. (2012). Quantum computing and the entanglement frontier. arXiv."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"11032","DOI":"10.1073\/pnas.95.19.11032","article-title":"Quantum computing","volume":"95","author":"Brassard","year":"1998","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1126\/science.1231930","article-title":"Superconducting circuits for quantum information: An outlook","volume":"339","author":"Devoret","year":"2013","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"180509","DOI":"10.1103\/PhysRevLett.119.180509","article-title":"Error Mitigation for short-depth quantum circuits","volume":"119","author":"Temme","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1126\/science.aao4309","article-title":"A blueprint for demonstrating quantum supremacy with superconducting qubits","volume":"360","author":"Neill","year":"2018","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"035004","DOI":"10.1088\/2058-9565\/aabc6b","article-title":"Quantum-secured blockchain","volume":"3","author":"Kiktenko","year":"2018","journal-title":"Quantum Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.aop.2018.03.020","article-title":"SO(3) \u201cnuclear physics\u201d with ultracold gases","volume":"393","author":"Rico","year":"2018","journal-title":"Ann. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"021003","DOI":"10.1103\/RevModPhys.97.021003","article-title":"Colloquium: Qudits for decomposing multiqubit gates and realizing quantum algorithms","volume":"97","author":"Kiktenko","year":"2025","journal-title":"Rev. Mod. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1140\/epjqt\/s40507-024-00250-0","article-title":"Efficient realization of quantum algorithms with qudits","volume":"11","author":"Nikolaeva","year":"2024","journal-title":"EPJ Quantum Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zalivako, I.V., Nikolaeva, A.S., Borisenko, A.S., Korolkov, A.E., Sidorov, P.L., Galstyan, K.P., Semenin, N.V., Smirnov, V.N., Aksenov, M.A., and Makushin, K.M. (2025). Towards multiqudit quantum processor based on a 171Yb+ ion string: Realizing basic quantum algorithms. Quantum Rep., 7.","DOI":"10.3390\/quantum7020019"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1038\/s41567-022-01658-0","article-title":"A universal qudit quantum processor with trapped ions","volume":"18","author":"Ringbauer","year":"2022","journal-title":"Nat. Phys."},{"key":"ref_12","unstructured":"Hill, A.D., Hodson, M.J., Didier, N., and Reagor, M.J. (2021). Realization of arbitrary doubly-controlled quantum phase gates. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"7117","DOI":"10.1038\/s41467-024-51434-2","article-title":"Empowering a qudit-based quantum processor by traversing the dual bosonic ladder","volume":"15","author":"Nguyen","year":"2024","journal-title":"Nat. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1038\/s41467-022-28767-x","article-title":"A programmable qudit-based quantum processor","volume":"13","author":"Chi","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"032619","DOI":"10.1103\/PhysRevA.109.032619","article-title":"Demonstration of a parity-time-symmetry-breaking phase transition using superconducting and trapped-ion qutrits","volume":"109","author":"Kazmina","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1038\/s41567-025-02797-w","article-title":"Simulating two-dimensional lattice gauge theories on a qudit quantum computer","volume":"21","author":"Meth","year":"2025","journal-title":"Nat. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"062602","DOI":"10.1103\/PhysRevA.110.062602","article-title":"Qudit-based quantum simulation of fermionic systems","volume":"110","author":"Chizzini","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1021\/jacs.3c12008","article-title":"Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits","volume":"146","author":"Chicco","year":"2024","journal-title":"J. Am. Chem. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"074512","DOI":"10.1103\/rrmd-fqx6","article-title":"Non-Abelian dynamics on a cube: Improving quantum compilation through qudit-based simulations","volume":"112","author":"Jiang","year":"2025","journal-title":"Phys. Rev. D"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"027001","DOI":"10.1103\/PRXQuantum.4.027001","article-title":"Quantum simulation for high-energy physics","volume":"4","author":"Bauer","year":"2023","journal-title":"PRX Quantum"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.plrev.2017.06.016","article-title":"Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses","volume":"22\u201323","author":"Cheng","year":"2017","journal-title":"Phys. Life Rev."},{"key":"ref_22","first-page":"1","article-title":"Evolutionary potential games on lattices","volume":"624","author":"Borsos","year":"2016","journal-title":"Phys. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.12.003","article-title":"Percolation on complex networks: Theory and application","volume":"907","author":"Li","year":"2021","journal-title":"Phys. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"023614","DOI":"10.1103\/PhysRevA.98.023614","article-title":"Numerical study of the chiral Z3 quantum phase transition in one spatial dimension","volume":"98","author":"Samajdar","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"235104","DOI":"10.1103\/PhysRevB.109.235104","article-title":"Temperature dependence of energy transport in the Z3 chiral clock model","volume":"109","author":"Yoo","year":"2024","journal-title":"Phys. Rev. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"245104","DOI":"10.1103\/PhysRevB.98.245104","article-title":"Exact results for a Z3-clock-type model and some close relatives","volume":"98","author":"Mahyaeh","year":"2018","journal-title":"Phys. Rev. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1038\/nature24622","article-title":"Probing many-body dynamics on a 51-atom quantum simulator","volume":"551","author":"Bernien","year":"2017","journal-title":"Nature"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/s41586-019-1070-1","article-title":"Quantum Kibble\u2013Zurek mechanism and critical dynamics on a programmable Rydberg simulator","volume":"568","author":"Keesling","year":"2019","journal-title":"Nature"},{"key":"ref_29","unstructured":"Liu, F., Whitsitt, S., Bienias, P., Lundgren, R., and Gorshkov, A.V. (2020). Realizing and Probing baryonic excitations in rydberg atom arrays. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Martin, P.P. (1991). Potts Models and Related Problems in Statistical Mechanics, World Scientific.","DOI":"10.1142\/0983"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"144306","DOI":"10.1103\/PhysRevB.105.144306","article-title":"Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model","volume":"105","author":"Lotkov","year":"2022","journal-title":"Phys. Rev. B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/0304-8853(92)90353-P","article-title":"Monte Carlo simulation for the quantum q-state Potts model","volume":"104\u2013107","author":"Pan","year":"1992","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"046102","DOI":"10.1088\/0256-307X\/28\/4\/046102","article-title":"Monte carlo simulation of the potts model on a dodecagonal quasiperiodic structure","volume":"28","author":"Wen","year":"2011","journal-title":"Chin. Phys. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"102257","DOI":"10.1016\/j.softx.2025.102257","article-title":"SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs","volume":"31","author":"Dziubyna","year":"2025","journal-title":"SoftwareX"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2242","DOI":"10.1038\/s41467-023-37375-2","article-title":"Native qudit entanglement in a trapped ion quantum processor","volume":"14","author":"Hrmo","year":"2023","journal-title":"Nat. Commun."},{"key":"ref_36","unstructured":"Joshi, R., Louw, J.C., Meth, M., Osborne, J.J., Mato, K., Su, G.X., Ringbauer, M., and Halimeh, J.C. (2025). Probing hadron scattering in lattice gauge theories on qudit quantum computers. arXiv."},{"key":"ref_37","unstructured":"Low, P.J., Zutt, N.C.F., Tathed, G.A., and Senko, C. (2025). Quantum logic operations and algorithms in a single 25-level atomic qudit. arXiv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"060601","DOI":"10.1103\/p1z9-6w93","article-title":"Scalable improvement of the generalized toffoli gate realization using trapped-ion-based qutrits","volume":"135","author":"Nikolaeva","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1126\/science.273.5278.1073","article-title":"Universal Quantum Simulators","volume":"273","author":"Lloyd","year":"1996","journal-title":"Science"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"022330","DOI":"10.1103\/PhysRevA.96.022330","article-title":"Efficient Z gates for quantum computing","volume":"96","author":"McKay","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Drozhzhin, D.A., Kiktenko, E.O., Fedorov, A.K., and Nikolaeva, A.S. (2026). Transition-aware decomposition of single-qudit gates. Entropy, 28.","DOI":"10.3390\/e28010056"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Sald\u00edvar, J.A., Casta\u00f1os, O., Nahmad-Achar, E., L\u00f3pez-Pe\u00f1a, R., Man\u2019ko, M.A., and Man\u2019ko, V.I. (2018). Geometry and entanglement of two-qubit states in the quantum probabilistic representation. Entropy, 20.","DOI":"10.3390\/e20090630"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1103\/PhysRevLett.71.1291","article-title":"Average entropy of a subsystem","volume":"71","author":"Page","year":"1993","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/160\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T05:14:26Z","timestamp":1770959666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/2\/160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,31]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["e28020160"],"URL":"https:\/\/doi.org\/10.3390\/e28020160","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,31]]}}}