{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:46:44Z","timestamp":1767772004123,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,7]],"date-time":"2022-06-07T00:00:00Z","timestamp":1654560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Over the past two decades, superconducting quantum circuits have become one of the essential platforms for realizing quantum computers. The Hamiltonian of a superconducting quantum circuit system is the key to describing the dynamic evolution of the system. For this reason, various methods for analyzing the Hamiltonian of a superconducting quantum circuit system have been proposed, among which the LOM (Lumped Oscillator Model) and the EPR (Energy Participation Ratio) methods are the most popular ones. To analyze and improve the design methods of superconducting quantum chips, this paper compares the similarities and differences of the LOM and the EPR quantification methods. We verify the applicability of these two theoretical approaches to the design of 2D transmon quantum chips. By comparing the theoretically simulated results and the experimentally measured data at extremely low temperature, the errors between the theoretical calculation and observed measurement values of the two methods were summarized. Results show that the LOM method has more parameter outputs in data diversity and the qubit frequency calculation in LOM is more accurate. The reason is that in LOM more coupling between different systems are taken into consideration. These analyses would have reference significance for the design of superconducting quantum chips.<\/jats:p>","DOI":"10.3390\/e24060792","type":"journal-article","created":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T00:22:39Z","timestamp":1654820559000},"page":"792","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Comparison of Lumped Oscillator Model and Energy Participation Ratio Methods in Designing Two-Dimensional Superconducting Quantum Chips"],"prefix":"10.3390","volume":"24","author":[{"given":"Benzheng","family":"Yuan","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"}]},{"given":"Weilong","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8387-0831","authenticated-orcid":false,"given":"Fudong","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"}]},{"given":"Haoran","family":"He","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"}]},{"given":"Zheng","family":"Shan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"180501","DOI":"10.1103\/PhysRevLett.127.180501","article-title":"Strong Quantum Computational Advantage Using a Superconducting Quantum Processor","volume":"127","author":"Wu","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"250503","DOI":"10.1103\/PhysRevLett.123.250503","article-title":"Boson Sampling with 20 Input Photons and a 60-Mode Interferometer in a 1014-Dimensional Hilbert Space","volume":"123","author":"Wang","year":"2019","journal-title":"Phys. Rev. Lett"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1038\/nphys2252","article-title":"Quantum simulations with trapped ions","volume":"8","author":"Blatt","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1038\/s41586-019-1381-2","article-title":"A two-qubit gate between phosphorus donor electrons in silicon","volume":"571","author":"He","year":"2019","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"041102","DOI":"10.1063\/5.0029735","article-title":"Gate-based superconducting quantum computing","volume":"129","author":"Kwon","year":"2021","journal-title":"J. Appl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1146\/annurev-conmatphys-031119-050605","article-title":"Superconducting Qubits: Current State of Play","volume":"11","author":"Kjaergaard","year":"2020","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"106001","DOI":"10.1088\/1361-6633\/aa7e1a","article-title":"Quantum information processing with superconducting circuits: A review","volume":"80","author":"Wendin","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s43673-021-00028-x","article-title":"Surface atomic-layer superconductors with Rashba\/Zeeman-type spin-orbit coupling","volume":"31","author":"Uchihashi","year":"2021","journal-title":"AAPPS Bull."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e61","DOI":"10.1002\/que2.61","article-title":"Faithful simulation and detection of quantum spin Hall effect on superconducting circuits","volume":"3","author":"Liu","year":"2021","journal-title":"Quantum Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/s43673-022-00043-6","article-title":"Realizing multi-qubit controlled nonadiabatic holonomic gates with connecting systems","volume":"32","author":"Xu","year":"2022","journal-title":"AAPPS Bull."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s43673-022-00038-3","article-title":"Perfect NOT and conjugate transformations","volume":"32","author":"Yan","year":"2022","journal-title":"AAPPS Bull."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"133102","DOI":"10.1063\/1.2904700","article-title":"Generation of squeezed states of nanomechanical resonator using three-wave mixing","volume":"92","author":"Huo","year":"2008","journal-title":"Appl. Phys. Lett."},{"doi-asserted-by":"crossref","unstructured":"Haroche, S., and Raimond, J.M. (2006). Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press. [1st ed.].","key":"ref_13","DOI":"10.1093\/acprof:oso\/9780198509141.001.0001"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1238\/Physica.Topical.076a00127","article-title":"Strong interactions of single atoms and photons in cavity QED","volume":"76","author":"Kimble","year":"1998","journal-title":"Phys. Scr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1038\/s41567-020-0806-z","article-title":"Quantum information processing and quantum optics with circuit quantum electrodynamics","volume":"16","author":"Blais","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"040202","DOI":"10.1103\/PRXQuantum.2.040202","article-title":"Practical Guide for Building Superconducting Quantum Devices","volume":"2","author":"Gao","year":"2021","journal-title":"PRX Quantum."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"021318","DOI":"10.1063\/1.5089550","article-title":"A quantum engineer\u2019s guide to superconducting qubits","volume":"6","author":"Krantz","year":"2019","journal-title":"Appl. Phys. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"040204","DOI":"10.1103\/PRXQuantum.2.040204","article-title":"The superconducting circuit companion\u2014An introduction with worked examples","volume":"2","author":"Rasmussen","year":"2021","journal-title":"PRX Quantum."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"062320","DOI":"10.1103\/PhysRevA.69.062320","article-title":"Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation","volume":"69","author":"Blais","year":"2004","journal-title":"Phys. Rev. A."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"025005","DOI":"10.1103\/RevModPhys.93.025005","article-title":"Circuit quantum electrodynamics","volume":"93","author":"Blais","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s11128-009-0101-5","article-title":"Josephson charge qubits: A brief review","volume":"8","author":"Pashkin","year":"2009","journal-title":"Quantum Inf. Process."},{"unstructured":"Schuster, D.I. (2007). Circuit Quantum Electrodynamic, Yale University.","key":"ref_22"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"042319","DOI":"10.1103\/PhysRevA.76.042319","article-title":"Charge-insensitive qubit design derived from the Cooper pair box","volume":"76","author":"Koch","year":"2007","journal-title":"Phys. Rev. A."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"080502","DOI":"10.1103\/PhysRevLett.111.080502","article-title":"Coherent josephson qubit suitable for scalable quantum integrated circuits","volume":"111","author":"Barends","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1038\/s41467-021-22030-5","article-title":"New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds","volume":"12","author":"Place","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1038\/s41534-021-00510-2","article-title":"Towards practical quantum computers: Transmon qubit with a lifetime approaching 0.5 milliseconds","volume":"8","author":"Wang","year":"2022","journal-title":"NPJ Quantum Inf."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"074002","DOI":"10.1063\/5.0078785","article-title":"Environmental radiation impact on lifetimes and quasiparticle tunneling rates of fixed-frequency transmon qubits","volume":"120","author":"Gordon","year":"2022","journal-title":"Appl. Phys. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/s41534-021-00461-8","article-title":"Energy-participation quantization of Josephson circuits","volume":"131","author":"Minev","year":"2021","journal-title":"NPJ Quantum Inf."},{"unstructured":"Minev, Z.K., Mcconkey, T.G., Takita, M., Corcoles, A.D., and Gambetta, J.M. (2021). Circuit quantum electrodynamics (cQED) with modular quasi-lumped models. arXiv.","key":"ref_29"},{"key":"ref_30","first-page":"6510","article-title":"Blackbox quantization of superconducting circuits using exact impedance synthesis","volume":"90","author":"Solgun","year":"2014","journal-title":"Phys. Rev. B."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"064503","DOI":"10.1103\/PhysRevB.69.064503","article-title":"Multilevel quantum description of decoherence in superconducting qubits","volume":"69","author":"Burkard","year":"2004","journal-title":"Phys. Rev. B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/792\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:25:18Z","timestamp":1760138718000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/792"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,7]]},"references-count":31,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["e24060792"],"URL":"https:\/\/doi.org\/10.3390\/e24060792","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,6,7]]}}}