Simulation of the three-qubit repetition code on the chain of superconducting qubits with couplers
Berezkin N. G.
1,2,3, Simakov I. A.
1,2, Mazhorin G. S.
1,21National University of Science and Technology MISiS, Moscow, Russia
2Russian Quantum Center, Moscow, Russia
3Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
Email: berezkin.ng@phystech.edu, simakovilyaspb@gmail.com, mag.grigoriy@yandex.ru
In superconducting quantum circuits, a promising method for implementing high-fidelity two-qubit gates is the microwave drive of a coupler. This paper presents the simulation of the three-qubit repetition code, taking into account the physical mechanism of two-qubit operation implementation: the effect of parasitic population of the excited state of the coupler is investigated, and the successful correction of this error using quantum error correction codes is demonstrated. Keywords: superconducting qubits, coupler, microwave gates, repetition code, leakages from computational subspace.
- A.D. Corcoles, E. Magesan, S.J. Srinivasan, A.W Cross, M. Steffen, J.M. Gambetta, J.M. Chow, Nat. Commun., 6, 6979 (2015). DOI: 10.1038/ncomms7979
- S.J. Devitt, W.J. Munro, K. Nemoto, Rep. Prog. Phys., 76 (7), 076001 (2013). DOI: 10.1088/0034-4885/76/7/076001
- A.G. Fowler, M. Mariantoni, J.M. Martinis, A.N. Cleland, Phys. Rev. A, 86 (3), 032324 (2012). DOI: 10.1103/PhysRevA.86.032324
- J. Kelly, R. Barends, A.G. Fowler, A. Megrant, E. Jeffrey, T.C. White, D. Sank, J.Y. Mutus, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P.J.J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, A.N. Cleland, J.M. Martinis, Nature, 519, 66 (2015). DOI: 10.1038/nature14270
- C.K. Andersen, A. Remm, S. Lazar, S. Krinner, N. Lacroix, G.J. Norris, M. Gabureac, C. Eichler, A. Wallraff, Nat. Phys., 16, 875 (2020). DOI: 10.1038/s41567-020-0920-y
- Google Quantum AI and Collaborators, Nature, 614, 676 (2023). DOI: doi.org/10.1038/s41586-022-05434-1
- Google Quantum AI and Collaborators, Nature, 638, 920 (2025). DOI: 10.1038/s41586-024-08449-y
- N.P. Breuckmann, J.N. Eberhardt, PRX Quantum, 2, 040101 (2021). DOI: 10.1103/PRXQuantum.2.040101
- K. Wang, Z. Lu, C. Zhang, G. Liu, J. Chen, Y. Wang, Y. Wu, S. Xu, X. Zhu, F. Jin, Y. Gao, Z. Tan, Z. Cui, N. Wang, Y. Zou, A. Zhang, T. Li, F. Shen, J. Zhong, Z. Bao, Z. Zhu, Y. Han, Y. He, J. Shen, H. Wang, J.-N. Yang, Z. Song, J. Deng, H. Dong, Z.-Z. Sun, W. Li, Q. Ye, S. Jiang, Y. Ma, P.-X. Shen, P. Zhang, H. Li, Q. Guo, Z. Wang, C. Song, H. Wang, D.-L. Deng, arXiv:2505.09684 [quant-ph] (2025). DOI: 10.48550/arXiv.2505.09684
- B.W. Reichardt, D. Aasen, R. Chao, A. Chernoguzov, W. van Dam, J.P. Gaebler, D. Gresh, D. Lucchetti, M. Mills, S.A. Moses, B. Neyenhuis, A. Paetznick, A. Paz, P.E. Siegfried, M.P. da Silva, K.M. Svore, Z. Wang, M. Zanner, arXiv:2409.04628 [quant-ph] (2024). DOI: 10.48550/arXiv.2409.04628
- B.W. Reichardt, A. Paetznick, D. Aasen, I. Basov, J.M. Bello-Rivas, P. Bonderson, R. Chao, W. van Dam, M.B. Hastings, R.V. Mishmash, A. Paz, M.P. da Silva, A. Sundaram, K.M. Svore, A. Vaschillo, Z. Wang, M. Zanner, W.B. Cairncross, C.-A. Chen, D. Crow, H. Kim, J.M. Kindem, J. King, M. McDonald, M.A. Norcia, A. Ryou, M. Stone, L. Wadleigh, K. Barnes, P. Battaglino, T.C. Bohdanowicz, G. Booth, A. Brown, M.O. Brown, K. Cassella, R. Coxe, J.M. Epstein, M. Feldkamp, C. Griger, E. Halperin, A. Heinz, F. Hummel, M. Jaffe, A.M.W. Jones, E. Kapit, K. Kotru, J. Lauigan, M. Li, J. Marjanovic, E. Megidish, M. Meredith, R. Morshead, J.A. Muniz, S. Narayanaswami, C. Nishiguchi, T. Paule, K.A. Pawlak, K.L. Pudenz, D. Rodri guez Perez, J. Simon, A. Smull, D. Stack, M. Urbanek, R.J.M. van de Veerdonk, Z. Vendeiro, R.T. Weverka, T. Wilkason, T.-Y. Wu, X. Xie, E. Zalys-Geller, X. Zhang, B.J. Bloom, arXiv:2411.11822 [quant-ph] (2024). DOI: 10.48550/arXiv.2411.11822
- Z. Chen, K. Satzinger, J. Atalaya, A. Dunsworth, D. Sank, C. Quintana, M. McEwen, R. Barends, P. Klimov, S. Hong, C. Jones, A. Petukhov, D. Kafri, S. Demura, B. Burkett, C. Gidney, A. Fowler, A. Paler, J. Kelly, Nature, 595, 383 (2021). DOI: 10.1038/s41586-021-03588-y
- B. Varbanov, F. Battistel, B. Tarasinski, V. Ostroukh, T. O'Brien, L. DiCarlo, B. Terhal, npj Quantum Inf., 6, 102 (2020). DOI: 10.1038/s41534-020-00330-w
- Q. Ficheux, L.B. Nguyen, A. Somoroff, H. Xiong, K.N. Nesterov, M.G. Vavilov, V.E. Manucharyan, Phys. Rev. X, 11, 021026 (2021). DOI: 10.1103/PhysRevX.11.021026
- I.A. Simakov, G.S. Mazhorin, I.N. Moskalenko, N.N. Abramov, A.A. Grigorev, D.O. Moskalev, A.A. Pishchimova, N.S. Smirnov, E.V. Zikiy, I.A. Rodionov, I.S. Besedin, PRX Quantum, 4, 040321 (2023). DOI: 10.1103/PRXQuantum.4.040321
- L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A.H. Karamlou, T.M. Hazard, K. Azar, D.K. Kim, B.M. Niedzielski, A. Melville, M.E. Schwartz, J.L. Yoder, T.P. Orlando, S. Gustavsson, J.A. Grover, K. Serniak, W.D. Oliver, Phys. Rev. X, 13, 031035 (2023). DOI: 10.1103/PhysRevX.13.031035
- I.N. Moskalenko, I.A. Simakov, N.N. Abramov, A.A. Grigorev, D.O. Moskalev, A.A. Pishchimova, N.S. Smirnov, E.V. Zikiy, I.A. Rodionov, I.S. Besedin, npj Quantum Inf., 8, 130 (2022). DOI: 10.1038/s41534-022-00644-x
- M. Nielsen, I. Chuang, Kvantovye vychisleniya i kvantovaya informatsiya (Mir, M., 2006), pp. 471-480 (in Russian)
- A. Javadi-Abhari, M. Treinish, K. Krsulich, C.J. Wood, J. Lishman, J. Gacon, S. Martiel, P.D. Nation, L.S. Bishop, A.W. Cross, B.R. Johnson, J.M. Gambetta, arXiv:2405.08810 [quant-ph] (2024). DOI: 10.48550/arXiv.2405.08810
- S.T. Spitz, B. Tarasinski, C.W.J. Beenakker, T.E. O'Brien, Adv. Quantum Technol., 1 (1), 1800012 (2018). DOI: 10.1002/qute.201870015