Skip to main content
Login
Lecture Notes on Quantum Electrical Circuits - cover image
TU Delft OPEN Publishing

Lecture Notes on Quantum Electrical Circuits

2nd Edition

  • Alessandro Ciani(author)
  • David P. DiVincenzo(author)
  • Barbara M. Terhal(author)
  • Export Metadata
  • Metadata
  • Locations
  • Contributors
  • References
Export Metadata
Metadata
TitleLecture Notes on Quantum Electrical Circuits
ContributorBarbara M. Terhal(author)
DOIhttps://doi.org/10.59490/tb.85
Landing pagehttps://books.open.tudelft.nl/home/catalog/book/172
Licensehttps://creativecommons.org/licenses/by/4.0
CopyrightAlessandro Ciani, David P. DiVincenzo, Barbara M. Terhal
PublisherTU Delft OPEN Publishing
Published on2025-07-10
ISBN978-94-6366-815-6 (PDF)
Long abstract During the last 30 years, stimulated by the quest to build superconducting quantum processors, a theory of quantum electrical circuits has emerged, which is called circuit quantum electrodynamics or circuit-QED. The goal of the theory is to provide a quantum description of the most relevant degrees of freedom. The central objects to be derived and studied are the Lagrangian and the Hamiltonian governing these degrees of freedom. Central concepts in classical network theory such as impedance and scattering matrices can be used to obtain the Hamiltonian and Lagrangian description for the lossless (linear) part of the circuits. Methods of analysis, both classical and quantum, can also be developed for nonreciprocal circuits. These lecture notes aim at giving a comprehensive, theoretically oriented, overview of this subject for Master or PhD students in physics and electrical engineering.
LanguageEnglish (Original)
Keywords
  • superconducting electrical circuits
  • circuit-QED
  • quantum computing
  • Josephson junction
  • quantum information
Locations
Landing PageFull text URLPlatform
Paperbackhttps://books.open.tudelft.nl/home/catalog/book/172Landing pagehttps://store.printservice.nl/ustorethemes/HR/150/nl-NL/products/5058/Lecture-Notes-on-Quantum-Electrical-Circuits/Full text URL
PDFhttps://books.open.tudelft.nl/home/catalog/book/172Landing pagehttps://books.open.tudelft.nl/home/catalog/view/172/420/678Full text URL
https://books.open.tudelft.nl/home/catalog/book/172Landing pagehttps://books.open.tudelft.nl/home/catalog/view/172/421/679Full text URL
Contributors

Alessandro Ciani

(author)
https://orcid.org/0000-0002-8707-0532

Alessandro Ciani is a postdoctoral scholar at Forschungszentrum Jülich. He received his PhD in 2019 from RWTH Aachen University. After two years spent at QuTech, TU Delft, he came back to Germany in 2021. His research focuses on superconducting qubits and on fundamental aspects of quantum computing and error correction.

David P. DiVincenzo

(author)
https://orcid.org/0000-0003-4332-645X

David DiVincenzo is a research director at Forschungszentrum Jülich, professor of physics at RWTH Aachen University, and a part-time affiliate of QuTech, TU Delft. He received his PhD from the University of Pennsylvania and came to Germany after 25 years on the staff of the IBM Research Division in New York. He is a fellow of the APS and a member of the National Academy of Sciences of the US. His research interests focus on the physical implementation of high-quality solid-state qubits for quantum computing.

Barbara M. Terhal

(author)
https://orcid.org/0000-0003-0218-6614

Barbara Terhal is a professor in the Department of Applied Mathematics, Faculty EEMCS at TU Delft and an affiliate of QuTech, TU Delft. She received her PhD from the University of Amsterdam (1999) and worked at IBM Research in New York from 2000 till 2010, and as professor of physics at RWTH Aachen from 2010 till 2017. She is a fellow of the APS and a member of the Royal Netherlands Academy of Arts and Sciences. Her research interests are in quantum error correction, in particular for superconducting qubits, and in understanding the computational and conceptual novelty of quantum information.

References
  1. R. Newcomb, Linear multiport synthesis (McGraw-Hill, New York, 1966)
  2. B. Peikari, Fundamentals of Network Analysis and Synthesis. Solid State Physical Electronics Series (Prentice-Hall, Englewood Cliffs, New Jersey, 1974)
  3. B. Yurke and J. S. Denker, Phys. Rev. A29, 1419 (1984). https://doi.org/10.1103/PhysRevA.29.1419
  4. M. H. Devoret, in Quantum Fluctuations: Lecture Notes of the Les Houches Summer School: Volume 63,July 1995 (Elsevier, 1997) pp. 351-386
  5. G. Burkard, R. Koch, and D. DiVincenzo, Phys. Rev. B69, 064503 (2004). https://doi.org/10.1103/PhysRevB.69.064503
  6. G. Burkard, Phys. Rev. B71, 144511 (2005) https://doi.org/10.1103/PhysRevB.71.144511
  7. S. M. Girvin, in Quantum Machines: Measurement and Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School: Volume 96, July 2011 (Oxford University Press, 2014).
  8. U. Vool and M. Devoret, International Journal of Circuit Theory and Applications45, 897 (2017). https://doi.org/10.1002/cta.2359
  9. Z. K. Minev, Z. Leghtas, S. O. Mundhada, L. Christakis, I. M. Pop, and M. H. Devoret, npj QuantumInformation7(2021). https://doi.org/10.1038/s41534-021-00461-8
  10. A. Blais, A. L. Grimsmo, S. Girvin, and A. Wallraff, Reviews of Modern Physics93(2021). https://doi.org/10.1103/RevModPhys.93.025005
  11. P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, Applied Physics Reviews6, 021318 (2019). https://doi.org/10.1063/1.5089550
  12. P. Groszkowski and J. Koch, Quantum5, 583 (2021). https://doi.org/10.22331/q-2021-11-17-583
  13. S. Rasmussen, K. Christensen, S. Pedersen, L. Kristensen, T. Bækkegaard, N. Loft, and N. Zinner, PRXQuantum2, 040204 (2021). https://doi.org/10.1103/PRXQuantum.2.040204
  14. J. Clarke and A. I. Braginski,The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUIDSystems(Wiley-VCH, 2004) https://doi.org/10.1002/3527603646
  15. M. Tinkham, Introduction to Superconductivity, 2nd ed. (Dover Publications, 2004).
  16. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2004)
  17. N. Muthusubramanianet al., Quantum Science and Technology 9, 025006 (2024).
  18. V. Ambegaokar and A. Baratoff, Phys. Rev. Lett.10, 486 (1963). https://doi.org/10.1103/PhysRevLett.10.486
  19. J. B. Hertzberg et al., npj Quantum Information 7 (2021). https://doi.org/10.1038/s41534-021-00464-5
  20. J. Ulrich and F. Hassler, Phys. Rev. B94, 094505 (2016). https://doi.org/10.1103/PhysRevB.94.094505
  21. A. Osborne, T. Larson, S. Jones, R. W. Simmonds, A. Gyenis, and A. Lucas, Symplectic geometry and circuit quantization. PRX Quantum 5, 020309, 2024 https://doi.org/10.1103/PRXQuantum.5.020309
  22. A. Parra-Rodriguez, I.L. Egusquiza. Geometrical description and Faddeev-Jackiw quantization of electrical networks. Quantum 8, 1466, 2024. https://doi.org/10.22331/q-2024-09-09-1466
  23. S. Bravyi, O. Dial, J. M. Gambetta, D. Gil, and Z. Nazario, Journal of Applied Physics132, 160902 (2022). https://doi.org/10.1063/5.0082975
  24. C. Alexander and M. Sadiku, Fundamentals of Electric Circuits, 4th ed. (McGraw Hill Higher Education, 2008)
  25. D. J. Griffiths, Introduction to electrodynamics, 4th ed. (Pearson, Boston, MA, 2013).
  26. R. Versluis, S. Poletto, N. Khammassi, B. Tarasinski, N. Haider, D. J. Michalak, A. Bruno, K. Bertels, andL. DiCarlo, Phys. Rev. Appl.8, 034021 (2017). https://doi.org/10.1103/PhysRevApplied.8.034021
  27. C. K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G. J. Norris, M. Gabureac, C. Eichler, andA. Wallraff, Nature Physics16, 875 (2020). https://doi.org/10.1038/s41567-020-0920-y
  28. M. H. Devoret, J. M. Martinis, and J. Clarke, Phys. Rev. Lett.55, 1908 (1985). https://doi.org/10.1103/PhysRevLett.55.1908
  29. J. M. Martinis, M. H. Devoret, and J. Clarke, Phys. Rev. Lett.55, 1543 (1985). https://doi.org/10.1103/PhysRevLett.55.1543
  30. X. You, J. A. Sauls, and J. Koch, Phys. Rev. B99, 174512 (2019). https://doi.org/10.1103/PhysRevB.99.174512
  31. J. Bryon, D. Weiss, X. You, S. Sussman, X. Croot, Z. Huang, J. Koch, and A. A. Houck, Phys. Rev. Appl.19, 034031 (2023). https://doi.org/10.1103/PhysRevApplied.19.034031
  32. R.-P. Riwar and D. P. DiVincenzo, npj Quantum Information8(2022). https://doi.org/10.1038/s41534-022-00539-x
  33. S. M. Girvin and K. Yang,Modern Condensed Matter Physics(Cambridge University Press, 2019). https://doi.org/10.1017/9781316480649
  34. C. Timm,Lecture Notes on the Theory of superconductivity(TU Dresden, 2020).
  35. J. E. Mooij and Y. V. Nazarov, Nature Physics2, 169 (2006). https://doi.org/10.1038/nphys234
  36. C. N. Lau, N. Markovic, M. Bockrath, A. Bezryadin, and M. Tinkham, Phys. Rev. Lett.87, 217003 (2001). https://doi.org/10.1103/PhysRevLett.87.217003
  37. A. D. Zaikin, D. S. Golubev, A. van Otterlo, and G. T. Zim ́anyi, Phys. Rev. Lett.78, 1552 (1997). https://doi.org/10.1103/PhysRevLett.78.1552
  38. D. S. Golubev and A. D. Zaikin, Phys. Rev. B78, 144502 (2008). https://doi.org/10.1103/PhysRevB.78.144502
  39. J. R. Kirtley, C. C. Tsuei, and F. Tafuri, Phys. Rev. Lett.90, 257001 (2003). https://doi.org/10.1103/PhysRevLett.90.257001
  40. A. G. Semenov and A. D. Zaikin, Phys. Rev. B94, 014512 (2016). https://doi.org/10.1103/PhysRevB.94.014512
  41. K. A. Matveev, A. I. Larkin, and L. I. Glazman, Phys. Rev. Lett.89, 096802 (2002). https://doi.org/10.1103/PhysRevLett.89.096802
  42. V. E. Manucharyan, Superinductance, Ph.D. thesis, Yale University (2012).
  43. V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Science326, 113 (2009). https://doi.org/10.1126/science.1175552
  44. D. T. Le, A. Grimsmo, C. Müller, and T. M. Stace, Phys. Rev. A100, 062321 (2019).
  45. C. Koliofoti and R.-P. Riwar, npj Quantum Information9, 125 (2023). https://doi.org/10.1038/s41534-023-00790-w
  46. M. Rymarz,The Quantum Electrodynamics of Singular and Nonreciprocal Superconducting Circuits, Master's thesis, RWTH Aachen (2018)
  47. M. Rymarz and D. P. DiVincenzo, Phys. Rev. X13, 021017 (2023). https://doi.org/10.1103/PhysRevX.13.021017
  48. A. M. Zagoskin,Quantum Engineering: Theory and Design of Quantum Coherent Structures(CambridgeUniversity Press, 2011) https://doi.org/10.1017/CBO9780511844157
  49. I. Ozfidanet al., Phys. Rev. Applied13, 034037 (2020) https://doi.org/10.1103/PhysRevApplied.13.034037
  50. A. Ciani and B. M. Terhal, Phys. Rev. A103, 042401 (2021). https://doi.org/10.1103/PhysRevA.103.042401
  51. F. Yanet al., Nature Communications 7, 2041 (2016). https://doi.org/10.1038/ncomms12964
  52. T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo, Phys. Rev.B60, 15398 (1999). https://doi.org/10.1103/PhysRevB.60.15398
  53. R. Harris et al., Phys. Rev. B81, 134510 (2010). https://doi.org/10.1103/PhysRevB.81.134510
  54. J. Q. You, X. Hu, S. Ashhab, and F. Nori, Phys. Rev. B75, 140515 (2007). https://doi.org/10.1103/PhysRevB.75.140515
  55. L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, Phys. Rev. X9,041041 (2019). https://doi.org/10.1103/PhysRevX.9.041041
  56. N. Maleeva et al., Nature Communications 9, 2041 (2018).
  57. https://doi.org/10.1038/s41467-018-06386-9
  58. A. D. Paolo, A. L. Grimsmo, P. Groszkowski, J. Koch, and A. Blais, New Journal of Physics21, 043002(2019). https://doi.org/10.1088/1367-2630/ab09b0
  59. W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. Devoret, npj Quantum Information6(2020). https://doi.org/10.1038/s41534-019-0231-2
  60. P. Brooks, A. Kitaev, and J. Preskill, Phys. Rev. A87, 052306 (2013). https://doi.org/10.1103/PhysRevA.87.052306
  61. I. V. Pechenezhskiy, R. A. Mencia, L. B. Nguyen, Y.-H. Lin, and V. E. Manucharyan, Nature585, 368(2020). https://doi.org/10.1038/s41586-020-2687-9
  62. A. Kitaev, "Protected qubit based on a superconducting current mirror," https://doi.org/10.48550/arXiv.cond-mat/0609441
  63. D. K. Weiss, A. C. Y. Li, D. G. Ferguson, and J. Koch, Phys. Rev. B100, 224507 (2019). https://doi.org/10.1103/PhysRevB.100.224507
  64. C. Vuillot, A. Ciani, and B. M. Terhal, "Homological quantum rotor codes: logical qubits from torsion,"(2023) https://doi.org/10.1007/s00220-023-04905-4
  65. M. V. Feigel'man, L. B. Ioffe, V. B. Geshkenbein, P. Dayal, and G. Blatter, Phys. Rev. Lett.92, 098301(2004). https://doi.org/10.1103/PhysRevLett.92.098301
  66. A. Zee, Group Theory in a Nutshell for Physicists (Princeton University Press, Princeton NJ, 2016).
  67. S. Bravyi, M. B. Hastings, and S. Michalakis, Journal of Mathematical Physics51, 093512 (2010). https://doi.org/10.1063/1.3490195
  68. D. Gottesman, Stabilizer Codes and Quantum Error Correction, Ph.D. thesis, CalTech (1997).
  69. M. Hamermesh,Group Theory and its application in physical problems(Addison-Wesley Publishing CompanyInc., Reading, MA, USA, 1989)
  70. S. Asaad et al., npj Quantum Information 2(2016). https://doi.org/10.1038/npjqi.2016.29
  71. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 2nd ed. (Cambridge University Press, 2017). https://doi.org/10.1017/9781108499996
  72. N. W. Ashcroft and N. D. Mermin,Solid State Physics(Holt-Saunders, 1976).
  73. J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M.Girvin, and R. J. Schoelkopf, Phys. Rev. A76, 042319 (2007). https://doi.org/10.1103/PhysRevA.76.042319
  74. D. Thanh Le, J. H. Cole, and T. M. Stace, Phys. Rev. Research2, 013245 (2020). https://doi.org/10.1103/PhysRevResearch.2.013245
  75. C. Gerry and P. Knight, Introductory Quantum Optics(Cambridge University Press, 2005). https://doi.org/10.1017/CBO9780511791239
  76. B. M. Terhal, Rev. Mod. Phys.87, 307 (2015). https://doi.org/10.1103/RevModPhys.87.307
  77. H.-P. Breuer and F. Petruccione,Theory of Open Quantum Systems(Oxford University Press, New York,2002) https://doi.org/10.1007/3-540-44874-8_4
  78. D. Zeuch, F. Hassler, J. J. Slim, and D. P. DiVincenzo, Annals of Physics423, 168327 (2020). https://doi.org/10.1016/j.aop.2020.168327
  79. F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Phys. Rev. Lett.103, 110501 (2009). https://doi.org/10.1103/PhysRevLett.103.110501
  80. H. Paiket al., Phys. Rev. Lett.107, 240501 (2011).
  81. M. Reagor, Superconducting Cavities for Circuit Quantum Electrodynamics, Ph.D. thesis, Yale University(2015).
  82. D. M. Pozar, Microwave engineering, 3rd ed. (Wiley, Hoboken NJ, 2005).
  83. D. Rist'e, S. Poletto, M.-Z. Huang, A. Bruno, V. Vesterinen, O.-P. Saira, and L. DiCarlo, Nat. Commun.6,6983 (2015). https://doi.org/10.1038/ncomms7983
  84. J. Kelly et al., Nature 519, 66 (2015). https://doi.org/10.1038/519S66a
  85. C. W. Gardiner and M. J. Collett, Phys. Rev. A31, 3761 (1985). https://doi.org/10.1103/PhysRevA.31.3761
  86. D. Walls and G. Milburn,Quantum Optics(Springer Berlin, Heidelberg, 2008). https://doi.org/10.1007/978-3-540-28574-8
  87. A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A69, 062320 (2004). https://doi.org/10.1103/PhysRevA.69.062320
  88. F. Mallet, F. R. Ong, A. Palacios-Laloy, F. Nguyen, P. Bertet, D. Vion, and D. Esteve, Nature Physics5,791 (2009). https://doi.org/10.1038/nphys1400
  89. L. DiCarlo et al., Nature460, 240 (2009).
  90. Y. Chen et al., Phys. Rev. Lett.113, 220502 (2014). https://doi.org/10.1103/PhysRevLett.113.216802
  91. J. Stehlik et al., Phys. Rev. Lett.127, 080505 (2021). https://doi.org/10.1103/PhysRevLett.127.080505
  92. B. M. Terhal, J. Conrad, and C. Vuillot, Quantum Science and Technology 5, 043001 (2020). https://doi.org/10.1088/2058-9565/ab98a5
  93. W.-L. Ma, S. Puri, R. J. Schoelkopf, M. H. Devoret, S. Girvin, and L. Jiang, Science Bulletin66, 1789(2021). https://doi.org/10.1016/j.scib.2021.05.024
  94. M. F. Gely, A. Parra-Rodriguez, D. Bothner, Y. M. Blanter, S. J. Bosman, E. Solano, and G. A. Steele,Phys. Rev. B95, 245115 (2017). https://doi.org/10.1103/PhysRevB.95.245115
  95. M. Malekakhlagh, A. Petrescu, and H. E. T ̈ureci, Phys. Rev. Lett.119, 073601 (2017). https://doi.org/10.1103/PhysRevLett.119.073601
  96. A. Parra-Rodriguez, E. Rico, E. Solano, and I. L. Egusquiza, Quantum Science and Technology3, 024012(2018). https://doi.org/10.1088/2058-9565/aab1ba
  97. J. Chow, J. Gambetta, E. Magesan, D. W. Abraham, A. W. Cross, B. R. Johnson, N. A. Masluk, J. A.Smolin, S. J. Srinivasan, and M. Steffen, Nature Communications5, 4015 (2014). https://doi.org/10.1038/ncomms5015
  98. L. Bishop, J. M. Chow, J. Koch, A. Houck, M. Devoret, E. Thuneberg, S. Girvin, and R. Schoelkopf, NaturePhysics5, 105 (2009). https://doi.org/10.1038/nphys1154
  99. D. Braak, Symmetry11, 1259 (2019). https://doi.org/10.3390/sym11101259
  100. N. Langford et al., Nature Communications8, 1715 (2016).
  101. S. Bravyi, D. P. DiVincenzo, and D. Loss, Annals of Physics326, 2793 (2011). https://doi.org/10.1016/j.aop.2011.06.004
  102. L. S. Theis and F. K. Wilhelm, Phys. Rev. A95, 022314 (2017). https://doi.org/10.1103/PhysRevA.95.022314
  103. A. Petrescu, C. Le Calonnec, C. Leroux, A. Di Paolo, P. Mundada, S. Sussman, A. Vrajitoarea, A. A. Houck,and A. Blais, Phys. Rev. Appl.19, 044003 (2023). https://doi.org/10.1103/PhysRevApplied.19.044003
  104. J. Gambetta, inQuantum information processing, Lecture notes of the 44th IFF spring school 2013, editedby D. DiVincenzo (Forschungszentrum, Zentralbibliothek, Jülich, 2013).
  105. S. E. Nigg, H. Paik, B. Vlastakis, G. Kirchmair, S. Shankar, L. Frunzio, M. H. Devoret, R. J. Schoelkopf,and S. M. Girvin, Phys. Rev. Lett.108, 240502 (2012). https://doi.org/10.1103/PhysRevLett.108.240502
  106. M. F. Gely and G. A. Steele, New Journal of Physics22, 013025 (2020). https://doi.org/10.1088/1367-2630/ab60f6
  107. P. Triverio, S. Grivet-Talocia, M. S. Nakhla, F. G. Canavero, and R. Achar, IEEE Transactions on Advanced Packaging30, 795 (2007) https://doi.org/10.1109/TADVP.2007.901567
  108. W. C. Smith, A. Kou, U. Vool, I. M. Pop, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Phys. Rev. B94, 144507 (2016). https://doi.org/10.1103/PhysRevB.94.144507
  109. C. G. Montgomery, R. H. Dicke, and E. M. Purcell, Principles of Microwave Circuits, Electromagnetic Waves (Institution of Engineering and Technology, 1987) https://doi.org/10.1049/PBEW025E
  110. P. Russer,Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering(Artech House, Boston, 2006).
  111. Z. K. Minev, T. G. McConkey, M. Takita, A. D. Corcoles,and J. M. Gambetta, arXiv e-prints ,arXiv:2103.10344 (2021).
  112. J. D. Jackson,Classical electrodynamics(Wiley, New York NY, 1975).
  113. M. A. Rol et al., Phys. Rev. Lett.123, 120502 (2019).
  114. J. M. Martinis et al., Phys. Rev. Lett.95, 210503 (2005).
  115. A. D. O'Connell et al., Applied Physics Letters92, 112903 (2008)
  116. C. Wang, C. Axline, Y. Y. Gao, T. Brecht, Y. Chu, L. Frunzio, M. H. Devoret, and R. J. Schoelkopf,Applied Physics Letters107, 162601 (2015). https://doi.org/10.1063/1.4934486
  117. F. Solgun, D. W. Abraham, and D. P. DiVincenzo, Phys. Rev. B90, 134504 (2014). https://doi.org/10.1103/PhysRevB.90.139904
  118. F. Solgun and D. P. DiVincenzo, Annals of Physics361, 605 (2015). https://doi.org/10.1016/j.aop.2015.07.005
  119. E. A. Guillemin,Synthesis of passive networks: theory and methods appropriate to the realization and approximation problems(Krieger, 1977).
  120. J. M. Martinis and M. R. Geller, Physical Review A90, 022307 (2014). https://doi.org/10.1103/PhysRevA.90.022307
  121. O. Hefti, CPHASEanalysis in the eigenmode approach in presence of ZZ crosstalk, Master's thesis, TU Delft(2020)
  122. B. Abdo, K. Sliwa, L. Frunzio, and M. Devoret, Phys. Rev. X3, 031001 (2013). https://doi.org/10.1103/PhysRevX.3.031001
  123. C. Desoer and E. Kuh,Basic Circuit Theory(McGraw-Hill, 1969) Chap. 16.4, pp. 694-696. https://doi.org/10.1109/TCT.1969.1082904
  124. J. Koch, A. A. Houck, K. L. Hur, and S. M. Girvin, Phys. Rev. A82, 043811 (2010). https://doi.org/10.1103/PhysRevA.82.043811
  125. R. Navarathna, D. T. Le, A. R. Hamann, H. D. Nguyen, T. M. Stace, and A. Fedorov, Phys. Rev. Lett.130, 037001 (2023). https://doi.org/10.1103/PhysRevLett.130.037001
  126. B. Tellegen, "Improvements in or relating to gyrators," (1955), Canadian Patent CA511631.
  127. G. Viola and D. P. DiVincenzo, Phys. Rev. X4, 021019 (2014). https://doi.org/10.1103/PhysRevX.4.039902
  128. B. D. H. Tellegen, Phillips Res. Rept.3, 81 (1948).
  129. C. L. Hogan, The Bell System Technical Journal31, 1 (1952). https://doi.org/10.1002/j.1538-7305.1952.tb01374.x
  130. S. Bosco, D. DiVincenzo, and D. Reilly, Phys. Rev. Applied12, 014030 (2019). https://doi.org/10.1103/PhysRevApplied.12.014030
  131. B. Placke,Admittance of Quantum Hall Effect Gyrators and Circulators, Bachelor thesis, RWTH Aachen(2016)
  132. A. Parra-Rodriguez, I. L. Egusquiza, D. P. DiVincenzo, and E. Solano, Phys. Rev. B99, 014514 (2019). https://doi.org/10.1103/PhysRevB.99.014514
  133. M. Rymarz, S. Bosco, A. Ciani, and D. P. DiVincenzo, Phys. Rev. X11, 011032 (2021). https://doi.org/10.1103/PhysRevX.11.011032
  134. D. T. Le, A. Grimsmo, C. M ̈uller, and T. M. Stace, Phys. Rev. A100, 062321 (2019).
  135. W. Oliver, inQuantum information processing, Lecture notes of the 44th IFF spring school 2013, edited byD. DiVincenzo (Forschungszentrum, Zentralbibliothek, J ̈ulich, 2013).
  136. M. Spiecker, A. I. Pavlov, A. Shnirman, and I. M. Pop, "Solomon equations for qubit and two-level systems,"(2023), arXiv:2307.06900 [quant-ph] .
  137. J. Burnett, A. Bengtsson, M. Scigliuzzo, D. Niepce, M. Kudra, P. Delsing, and J. Bylander, npj QuantumInformation5(2019). https://doi.org/10.1038/s41534-019-0168-5
  138. T. Thorbeck, A. Eddins, I. Lauer, D. T. McClure, and M. Carroll, PRX Quantum4, 020356 (2023). https://doi.org/10.1103/PRXQuantum.4.020356
  139. P. Fischer and G. Catelani, Physical Review Applied19, 054087 (2023). https://doi.org/10.1103/PhysRevApplied.19.054087
  140. D. Riste, C. C. Bultink, K. W. Lehnert, and L. DiCarlo, Phys. Rev. Lett.109, 240502 (2012). https://doi.org/10.1103/PhysRevLett.109.240502
  141. A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett.46, 211 (1981). https://doi.org/10.1103/PhysRevLett.46.211
  142. A. Parra-Rodriguez and I. L. Egusquiza, Phys. Rev. B106, 054504 (2022). https://doi.org/10.1103/PhysRevB.106.054504
  143. R. Schoelkopf, A. Clerk, S. Girvin, K. Lehnert, and M. Devoret, Quantum noise in mesoscopic physics , 175(2003). https://doi.org/10.1007/978-94-010-0089-5_9
  144. A. A. Houck, J. A. Schreier, B. R. Johnson, J. M. Chow, J. Koch, J. M. Gambetta, D. I. Schuster, L. Frunzio,M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. Lett.101, 080502 (2008). https://doi.org/10.1103/PhysRevLett.101.080502
  145. M. Cattaneo and G. S. Paraoanu, Advanced Quantum Technologies4, 2100054 (2021). https://doi.org/10.1002/qute.202100054
  146. M. G ̈oppl, A. Fragner, M. Baur, R. Bianchetti, S. Filipp, J. M. Fink, P. J. Leek, G. Puebla, L. Steffen, andA. Wallraff, Journal of Applied Physics104, 113904 (2008). https://doi.org/10.1063/1.3010859
  147. A. Gyenis, A. Di Paolo, J. Koch, A. Blais, A. A. Houck, and D. I. Schuster, PRX Quantum2(2021). https://doi.org/10.1103/PRXQuantum.2.030101
  148. D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A64, 012310 (2001). https://doi.org/10.1103/PhysRevA.64.012310
  149. P. Campagne-Ibarcqet al., Nature584, 368 (2020).
  150. A. Roy and M. Devoret, Comptes Rendus Physique17, 740 (2016). https://doi.org/10.1016/j.crhy.2016.07.012
  151. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Rev. Mod. Phys.82, 1155(2010). https://doi.org/10.1103/RevModPhys.82.1155
  152. H. Goldstein, C. P. Poole, and J. L. Safko,Classical Mechanics (3rd Edition), 3rd ed. (Addison-Wesley,2001). https://doi.org/10.1119/1.1484149
  153. R. A. Horn and C. R. Johnson,Matrix Analysis, 2nd ed. (Cambridge University Press, 2012). https://doi.org/10.1017/CBO9781139020411
  154. M. Born and R. Oppenheimer, Annalen der Physik389, 457 (1927). https://doi.org/10.1002/andp.19273892002
  155. D. P. DiVincenzo, F. Brito, and R. H. Koch, Phys. Rev. B74, 014514 (2006). https://doi.org/10.1103/PhysRevB.74.014514
  156. R. M. Foster, Bell System Technical Journal3, 259-267 (1924). https://doi.org/10.1002/j.1538-7305.1924.tb01358.x
  157. L. Egusquiza and A. Parra-Rodriguez, Phys. Rev. B106, 024510 (2022). https://doi.org/10.1103/PhysRevB.106.054504

UK registered social enterprise and Community Interest Company (CIC).

Company registration 14549556

Metadata

  • By book
  • By publisher
  • GraphQL API
  • Export API

Resources

  • Downloads
  • Videos
  • Merch
  • Presentations
  • Service status

Contact

  • Email
  • Bluesky
  • Mastodon
  • Github

Copyright © 2026 Thoth Open Metadata. Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution 4.0 International license.