- Open Access
Robust multimode superconducting circuit optimized for quantum information processing
Phys. Rev. Applied 26, 014081 – Published 24 July, 2026
DOI: https://doi.org/10.1103/ksnb-vhsl
Abstract
Multimode superconducting circuits offer a promising platform for engineering robust systems for quantum computation. Previous studies indicate that single-mode devices cannot be engineered to simultaneously exhibit resilience against multiple decoherence sources due to conflicting requirements. In contrast, multimode systems offer increased flexibility and have proven capable of overcoming these fundamental limitations. Here, we present a multimode device optimized for quantum information processing. It features an anharmonicity of a third of the qubit frequency and reduced energy dispersion caused by charge and magnetic flux fluctuations. It exhibits improvements over the fundamental errors limiting transmon and fluxonium coherence and control, achieving ratios between the total coherence time and the gate time one order of magnitude larger than transmon and two times larger than fluxonium for microwave charge drives, assuming equal dielectric and inductive loss quality factors and limited drive strength. Simulations further demonstrate the device’s robustness to circuit parameter deviations, a known limitation of many multimode devices.
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References (63)
- V. Bouchiat, D. Vion, P. Joyez, D. Esteve, and M. H. Devoret, Quantum coherence with a single Cooper pair, Phys. Scr. 1998, 165 (1998).
- Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Coherent control of macroscopic quantum states in a single-Cooper-pair box, Nature (London) 398, 786 (1999).
- J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. V. der Wall, and S. Lloyd, Josephson persistent-current qubit, Science 285, 1036 (1999).
- 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, Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
- H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture, Phys. Rev. Lett. 107, 240501 (2011).
- S. Ganjam, Y. Wang, Y. Lu, A. Banerjee, C. U. Lei, L. Krayzman, K. Kisslinger, C. Zhou, R. Li, Y. Jia, M. Liu, L. Frunzio, and R. J. Schoelkopf, Surpassing millisecond coherence in on chip superconducting quantum memories by optimizing materials and circuit design, Nat. Commun. 15, 3687 (2024).
- A. P. M. Place, L. V. H. Rodgers, P. Mundada, B. M. Smitham, M. Fitzpatrick, Z. Leng, A. Premkumar, J. Bryon, A. Vrajitoarea, S. Sussman, G. Cheng, T. Madhavan, H. K. Babla, X. H. Le, Y. Gang, B. Jäck, A. Gyenis, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck, New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, Nat. Commun. 12, 1779 (2021).
- C. Wang et al., Towards practical quantum computers: Transmon qubits with long coherence time and high fidelity, npj Quantum Inf. 8, 3 (2022).
- V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single Cooper-pair circuit free of charge offsets, Science 326, 113 (2009).
- I. M. Pop, K. Geerlings, G. Catelani, R. J. Schoelkopf, L. I. Glazman, and M. H. Devoret, Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles, Nature (London) 508, 369 (2014).
- L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, High-coherence fluxonium qubit, Phys. Rev. X 9, 041041 (2019).
- H. Zhang, S. Chakram, T. Roy, N. Earnest, Y. Lu, Z. Huang, D. K. Weiss, J. Koch, and D. I. Schuster, Universal fast-flux control of a coherent, low-frequency qubit, Phys. Rev. X 11, 011010 (2021).
- A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. Kuzmin, and V. E. Manucharyan, Millisecond coherence in a fluxonium qubit with minimal dephasing, Phys. Rev. Lett. 130, 267001 (2023).
- A. Gyenis, A. DiPaolo, J. Koch, A. Blais, A. A. Houck, and D. I. Schuster, Moving beyond the transmon: Noise-protected superconducting quantum circuits, PRX Quantum 2, 030101 (2021).
- A. Calzona and M. Carrega, Multi-mode architectures for noise-resilient superconducting qubits, Supercond. Sci. Technol. 36, 023001 (2022).
- L. B. Ioffe, M. V. Feigel’man, A. Ioselevich, D. Ivanov, M. Troyer, and G. Blatter, Topologically protected quantum bits using Josephson junction arrays, Nature (London) 415, 503 (2002).
- S. Gladchenko, D. Olaya, E. Dupont-Ferrier, B. Douçot, L. B. Ioffe, and M. E. Gershenson, Superconducting nanocircuits for topologically protected qubits, Nat. Phys. 5, 48 (2009).
- B. Douçot and L. B. Ioffe, Physical implementation of protected qubits: A review, Rep. Prog. Phys. 75, 072001 (2012).
- P. Brooks, A. Kitaev, and J. Preskill, Protected gates for superconducting qubits, Phys. Rev. A 87, 052306 (2013).
- W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. Devoret, Superconducting circuit protected by two-Cooper-pair tunneling, npj Quantum Inf. 6, 8 (2020).
- K. Kalashnikov, W. T. Hsieh, W. Zhang, W.-S. Lu, P. Kamenov, A. Di Paolo, A. Blais, M. E. Gershenson, and M. Bell, Bifluxon: Fluxon-parity-protected superconducting qubit, PRX Quantum 1, 010307 (2020).
- E. Hyyppä et al., Unimon qubit, Nat. Commun. 13, 6895 (2022).
- R. A. Mencia, W.-J. Lin, H. Cho, M. G. Vavilov, and V. E. Manucharyan, Integer fluxonium qubit, PRX Quantum 5, 040318 (2024).
- F. A. Cárdenas-López, J. C. Retamal, X. Chen, G. Romero, and M. Sanz, Resilient superconducting-element design with genetic algorithms, Phys. Rev. Appl. 23, 054068 (2025).
- D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Hazard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum 5, 040342 (2024).
- E. J. Weissler, M. Bhat, Z. Liu, and J. Combes, Enumeration of all superconducting circuits up to 5 nodes, arXiv:2410.18497.
- L. B. Nguyen, G. Koolstra, Y. Kim, A. Morvan, T. Chistolini, S. Singh, K. N. Nesterov, C. Jünger, L. Chen, Z. Pedramrazi, B. K. Mitchell, J. M. Kreikebaum, S. Puri, D. I. Santiago, and I. Siddiqi, Blueprint for a high-performance fluxonium quantum processor, PRX Quantum 3, 037001 (2022).
- A. Gyenis, P. S. Mundada, A. D. Paolo, T. M. Hazard, X. You, D. I. Schuster, J. Koch, A. Blais, and A. A. Houck, Experimental realization of a protected superconducting circuit derived from the qubit, PRX Quantum 2, 010339 (2021).
- I. L. Egusquiza, A. Iñiguez, E. Rico, and A. Villarino, Role of anomalous symmetry in qubits, Phys. Rev. B 105, L201104 (2022).
- A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 67, 725 (1987).
- P. Groszkowski, A. D. Paolo, A. L. Grimsmo, A. Blais, D. I. Schuster, A. A. Houck, and J. Koch, Coherence properties of the qubit, New J. Phys. 20, 043053 (2018).
- P. Groszkowski and J. Koch, Scqubits: A python package for superconducting qubits, Quantum 5, 583 (2021).
- D. M. Pozar, Microwave Engineering, 4th ed. (Wiley, New York, 2012).
- G. Ithier, E. Collin, P. Joyez, P. J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, and G. Schön, Decoherence in a superconducting quantum bit circuit, Phys. Rev. B 72, 134519 (2005).
- G. Catelani, R. J. Schoelkopf, M. H. Devoret, and L. I. Glazman, Relaxation and frequency shifts induced by quasiparticles in superconducting qubits, Phys. Rev. B 84, 064517 (2011).
- A. Kou, W. C. Smith, U. Vool, R. T. Brierley, H. Meier, L. Frunzio, S. M. Girvin, L. I. Glazman, and M. H. Devoret, Fluxonium-based artificial molecules with tunable magnetic interaction between two superconducting qubits, Phys. Rev. X 7, 031037 (2017).
- F. Yoshihara, K. Harrabi, A. O. Niskanen, Y. Nakamura, and J. S. Tsai, Decoherence of flux qubits due to 1/f flux noise, Phys. Rev. Lett. 97, 167001 (2006).
- P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).
- L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Phys. Lett. A 367, 47 (2007).
- F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys. Rev. Lett. 103, 110501 (2009).
- Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A G. Fowler, E. Lucero, E. Jeffrey, A. Megrant, J. Mutus, M. Neeley, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, T. C. White, A. N. Korotkov, and J. M. Martinis, Measuring and suppressing quantum state leakage in a superconducting qubit, Phys. Rev. Lett. 116, 020501 (2016).
- F. Motzoi and F. K. Wilhelm, Improving the gate fidelity of encoded qubits by optimal control of decoupling pulses, Phys. Rev. A 88, 062318 (2013).
- P. van Mulbregt et al. (SciPy 1.0 Contributors), Scipy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
- A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004).
- F. Pfeiffer et al., Efficient decoupling of a non-linear qubit mode from its environment, Phys. Rev. X 14, 041007 (2024).
- R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, C. Lang, L. Steffen, M. Boissonneault, A. Blais, and A. Wallraff, Control and tomography of a three level superconducting artificial atom, Phys. Rev. Lett. 105, 223601 (2010).
- E. A. Sete, J. M. Martinis, and A. N. Korotkov, Quantum theory of a bandpass Purcell filter for qubit readout, Phys. Rev. A 92, 012325 (2015).
- R. Shillito, A. Petrescu, J. Cohen, J. Beall, M. Hauru, M. Ganahl, A. G. M. Lewis, G. Vidal, and A. Blais, Ionization of a Josephson junction artificial atom, Phys. Rev. Appl. 18, 034031 (2022).
- M. Boissonneault, J. M. Gambetta, and A. Blais, Dispersive regime of circuit QED: Photon-dependent qubit dephasing and relaxation rates, Phys. Rev. A 77, 060305(R) (2008).
- F. Motzoi, L. Buchmann, and C. Dickel, Simple, smooth and fast pulses for dispersive measurements in cavities and quantum networks, arXiv:1809.04116.
- M. Jerger, F. Motzoi, Y. Gao, C. Dickel, L. Buchmann, A. Bengtsson, G. Tancredi, C. Warren, J. Bylander, D. DiVincenzo et al., Dispersive qubit readout with intrinsic resonator reset, arXiv:2406.04891.
- J. Gambetta, A. Blais, D. I. Schuster, A. Wallraff, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting, Phys. Rev. A 74, 042318 (2006).
- 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, Controlling the spontaneous emission of a superconducting transmon qubit, Phys. Rev. Lett. 101, 080502 (2008).
- J. Cohen, A. Petrescu, R. Shillito, and A. Blais, Reminiscence of classical chaos in driven transmons, PRX Quantum 4, 020312 (2023).
- L. Ateshian, M. Hays, D. A. Rower, H. Zhang, K. Azar, R. Assouly, L. Ding, M. Gingras, H. Stickler, B. M. Niedzielski, M. E. Schwartz, T. P. Orlando, J. I. j. Wang, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, Temperature and magnetic-field dependence of energy relaxation in a fluxonium qubit, arXiv:2507.01175.
- M. F. Dumas, B. Groleau-Paré, A. McDonald, M. H. Muñoz Arias, C. Lledó, B. D’Anjou, and A. Blais, Measurement-induced transmon ionization, Phys. Rev. X 14, 041023 (2024).
- E. Dogan, D. Rosenstock, L. Le Guevel, H. Xiong, R. A. Mencia, A. Somoroff, K. N. Nesterov, M. G. Vavilov, V. E. Manucharyan, and C. Wang, Two-fluxonium cross-resonance gate, Phys. Rev. Appl. 20, 024011 (2023).
- E. Hyyppä, A. Vepsäläinen, M. Papič, C. F. Chan, S. Inel, A. Landra, W. Liu, J. Luus, F. Marxer, C. Ockeloen-Korppi, S. Orbell, B. Tarasinski, and J. Heinsoo, Reducing leakage of single-qubit gates for superconducting quantum processors using analytical control pulse envelopes, PRX Quantum 5, 030353 (2024).
- J. Koch, V. Manucharyan, M. H. Devoret, and L. I. Glazman, Charging effects in the inductively shunted Josephson junction: Model of the fluxonium qubit, Phys. Rev. Lett. 103, 217004 (2009).
- K. Nabors and J. White, FastCap: A multipole accelerated 3-D capacitance extraction program, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 10, 1447 (1991).
- K. Nabors and J. White, Fastcap: A multipole accelerated 3-D capacitance extraction program, IEEE Trans. Comput.Aided Des. Integr. Circuits Syst. 10, 1447 (1991).
- S. P. Chitta, T. Zhao, Z. Huang, I. Mondragon-Shem, and J. Koch, Computer-aided quantization and numerical analysis of superconducting circuits, New J. Phys. 24, 103020 (2022).
- G. Wedin, Quantum information processing with superconducting circuits: A review, Rep. Prog. Phys. 80, 106001 (2017).