The quartic Blochnium: an anharmonic quasicharge superconducting qubit

Luca Chirolli1, Matteo Carrega2, and Francesco Giazotto1

1NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy
2CNR-Spin, Via Dodecaneso 33, I-16146 Genova

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Abstract

The quasicharge superconducting qubit realizes the dual of the transmon and shows strong robustness to flux and charge fluctuations thanks to a very large inductance closed on a Josephson junction. At the same time, a weak anharmonicity of the spectrum is inherited from the parent transmon, that introduces leakage errors and is prone to frequency crowding in multi-qubit setups. We propose a novel design that employs a quartic superinductor and confers a good degree of anharmonicity to the spectrum. The quartic regime is achieved through a properly designed chain of Josephson junction loops that shows minimal quantum fluctuations without introducing a severe dependence on the external fluxes.

In a quantum chips hosting many qubits it is important to control each qubit independently with high fidelity and qubits that manifest a weakly anharmonic spectrum suffer from leakage errors and are prone to frequency crowding in multi-qubit setups. We propose a novel design that employs a quartic superinductor engineered on purpose through a chain of Josephson junction loops. The system also implements a Hamiltonian $H=p^4-\cos(x)$, that realizes a quantum quartic pendulum.

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[1] Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. Wang, Simon Gustavsson, and William D. Oliver. ``Superconducting qubits: Current state of play''. Annual Review of Condensed Matter Physics 11, 369–395 (2020). Appearances:.
https:/​/​doi.org/​10.1146/​annurev-conmatphys-031119-050605

[2] He-Liang Huang, Dachao Wu, Daojin Fan, and Xiaobo Zhu. ``Superconducting quantum computing: a review''. Science China Information Sciences 63, 180501 (2020). Appearances:.
https:/​/​doi.org/​10.1007/​s11432-020-2881-9

[3] Irfan Siddiqi. ``Engineering high-coherence superconducting qubits''. Nature Reviews Materials 6, 875–891 (2021). Appearances:.
https:/​/​doi.org/​10.1038/​s41578-021-00370-4

[4] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario. ``The future of quantum computing with superconducting qubits''. Journal of Applied Physics 132, 160902 (2022). Appearances:.
https:/​/​doi.org/​10.1063/​5.0082975

[5] Daniel Gottesman. ``Stabilizer codes and quantum error correction''. PhD thesis. California Institute of Technology. (1997). Appearances:.
https:/​/​doi.org/​10.7907/​rzr7-dt72

[6] Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai. ``Coherent control of macroscopic quantum states in a single-cooper-pair box''. Nature 398, 786–788 (1999). Appearances:.
https:/​/​doi.org/​10.1038/​19718

[7] Jay M. Gambetta, Jerry M. Chow, and Matthias Steffen. ``Building logical qubits in a superconducting quantum computing system''. npj Quantum Information 3, 2 (2017). Appearances:.
https:/​/​doi.org/​10.1038/​s41534-016-0004-0

[8] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre 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). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevA.76.042319

[9] Vladimir E. Manucharyan, Jens Koch, Leonid I. Glazman, and Michel H. Devoret. ``Fluxonium: Single cooper-pair circuit free of charge offsets''. Science 326, 113–116 (2009). Appearances:.
https:/​/​doi.org/​10.1126/​science.1175552

[10] Yen-Hsiang Lin, Long B. Nguyen, Nicholas Grabon, Jonathan San Miguel, Natalia Pankratova, and Vladimir E. Manucharyan. ``Demonstration of protection of a superconducting qubit from energy decay''. Phys. Rev. Lett. 120, 150503 (2018). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.150503

[11] Long B. Nguyen, Yen-Hsiang Lin, Aaron Somoroff, Raymond Mencia, Nicholas Grabon, and Vladimir E. Manucharyan. ``High-coherence fluxonium qubit''. Phys. Rev. X 9, 041041 (2019). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevX.9.041041

[12] Aaron Somoroff, Quentin Ficheux, Raymond A. Mencia, Haonan Xiong, Roman Kuzmin, and Vladimir E. Manucharyan. ``Millisecond coherence in a superconducting qubit''. Phys. Rev. Lett. 130, 267001 (2023). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.130.267001

[13] Helin Zhang, Srivatsan Chakram, Tanay Roy, Nathan Earnest, Yao Lu, Ziwen Huang, D. K. Weiss, Jens Koch, and David I. Schuster. ``Universal fast-flux control of a coherent, low-frequency qubit''. Phys. Rev. X 11, 011010 (2021). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevX.11.011010

[14] Long B. Nguyen, Gerwin Koolstra, Yosep Kim, Alexis Morvan, Trevor Chistolini, Shraddha Singh, Konstantin N. Nesterov, Christian Jünger, Larry Chen, Zahra Pedramrazi, Bradley K. Mitchell, John Mark Kreikebaum, Shruti Puri, David I. Santiago, and Irfan Siddiqi. ``Blueprint for a high-performance fluxonium quantum processor''. PRX Quantum 3, 037001 (2022). Appearances:.
https:/​/​doi.org/​10.1103/​PRXQuantum.3.037001

[15] T. P. Orlando, J. E. Mooij, Lin Tian, Caspar H. van der Wal, L. S. Levitov, Seth Lloyd, and J. J. Mazo. ``Superconducting persistent-current qubit''. Phys. Rev. B 60, 15398–15413 (1999). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.60.15398

[16] V. E. Manucharyan. ``Superinductance''. PhD thesis. Yale University. (2012). Appearances:.

[17] Seth Lloyd and Samuel L. Braunstein. ``Quantum computation over continuous variables''. Phys. Rev. Lett. 82, 1784–1787 (1999). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1784

[18] Daniel Gottesman, Alexei Kitaev, and John Preskill. ``Encoding a qubit in an oscillator''. Phys. Rev. A 64, 012310 (2001). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevA.64.012310

[19] Nissim Ofek, Andrei Petrenko, Reinier Heeres, Philip Reinhold, Zaki Leghtas, Brian Vlastakis, Yehan Liu, Luigi Frunzio, S. M. Girvin, L. Jiang, Mazyar Mirrahimi, M. H. Devoret, and R. J. Schoelkopf. ``Extending the lifetime of a quantum bit with error correction in superconducting circuits''. Nature 536, 441–445 (2016). Appearances:.
https:/​/​doi.org/​10.1038/​nature18949

[20] L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C. L. Zou, S. M. Girvin, L-M. Duan, and L. Sun. ``Quantum error correction and universal gate set operation on a binomial bosonic logical qubit''. Nature Physics 15, 503–508 (2019). Appearances:.
https:/​/​doi.org/​10.1038/​s41567-018-0414-3

[21] P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf, L. Frunzio, M. Mirrahimi, and M. H. Devoret. ``Quantum error correction of a qubit encoded in grid states of an oscillator''. Nature 584, 368–372 (2020). Appearances:.
https:/​/​doi.org/​10.1038/​s41586-020-2603-3

[22] Gianni Blatter, Vadim B. Geshkenbein, and Lev B. Ioffe. ``Design aspects of superconducting-phase quantum bits''. Phys. Rev. B 63, 174511 (2001). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.63.174511

[23] Ivan V. Protopopov and Mikhail V. Feigel'man. ``Anomalous periodicity of supercurrent in long frustrated josephson-junction rhombi chains''. Phys. Rev. B 70, 184519 (2004). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.70.184519

[24] Alexei Kitaev. ``Protected qubit based on a superconducting current mirror'' (2006). arXiv:cond-mat/​0609441. Appearances:.
https:/​/​doi.org/​10.48550/​arXiv.cond-mat/​0609441
arXiv:cond-mat/0609441

[25] Sergey Gladchenko, David Olaya, Eva Dupont-Ferrier, Benoit Douçot, Lev B. Ioffe, and Michael E. Gershenson. ``Superconducting nanocircuits for topologically protected qubits''. Nature Physics 5, 48–53 (2009). Appearances:.
https:/​/​doi.org/​10.1038/​nphys1151

[26] W. C. Smith, A. Kou, X. Xiao, U. Vool, and M. H. Devoret. ``Superconducting circuit protected by two-cooper-pair tunneling''. npj Quantum Information 6, 8 (2020). Appearances:.
https:/​/​doi.org/​10.1038/​s41534-019-0231-2

[27] András Gyenis, Pranav S. Mundada, Agustin Di Paolo, Thomas M. Hazard, Xinyuan You, David I. Schuster, Jens Koch, Alexandre Blais, and Andrew A. Houck. ``Experimental realization of a protected superconducting circuit derived from the $0$–${\pi}$ qubit''. PRX Quantum 2, 010339 (2021). Appearances:.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010339

[28] Luca Chirolli and Joel E. Moore. ``Enhanced coherence in superconducting circuits via band engineering''. Phys. Rev. Lett. 126, 187701 (2021). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.126.187701

[29] Luca Chirolli, Norman Y. Yao, and Joel E. Moore. ``Swap gate between a majorana qubit and a parity-protected superconducting qubit''. Phys. Rev. Lett. 129, 177701 (2022). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.129.177701

[30] W. C. Smith, M. Villiers, A. Marquet, J. Palomo, M. R. Delbecq, T. Kontos, P. Campagne-Ibarcq, B. Douçot, and Z. Leghtas. ``Magnifying quantum phase fluctuations with cooper-pair pairing''. Phys. Rev. X 12, 021002 (2022). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevX.12.021002

[31] Alessio Calzona and Matteo Carrega. ``Multi-mode architectures for noise-resilient superconducting qubits''. Superconductor Science and Technology 36, 023001 (2022). Appearances:.
https:/​/​doi.org/​10.1088/​1361-6668/​acaa64

[32] Alessio Calzona, Matteo Carrega, and Luca Chirolli. ``Anomalous periodicity and parafermion hybridization in superconducting qubits''. Phys. Rev. B 107, 045105 (2023). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.107.045105

[33] Konstantin Kalashnikov, Wen Ting Hsieh, Wenyuan Zhang, Wen-Sen Lu, Plamen Kamenov, Agustin Di Paolo, Alexandre Blais, Michael E. Gershenson, and Matthew Bell. ``Bifluxon: Fluxon-parity-protected superconducting qubit''. PRX Quantum 1, 010307 (2020). Appearances:.
https:/​/​doi.org/​10.1103/​PRXQuantum.1.010307

[34] M. T. Bell, I. A. Sadovskyy, L. B. Ioffe, A. Yu. Kitaev, and M. E. Gershenson. ``Quantum superinductor with tunable nonlinearity''. Phys. Rev. Lett. 109, 137003 (2012). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.137003

[35] Matthew T. Bell, Benoı̂t Douçot, Michael E. Gershenson, Lev B. Ioffe, and Aleksandra Petković. ``Josephson ladders as a model system for 1d quantum phase transitions''. Comptes Rendus Physique 19, 484–497 (2018). Appearances:.
https:/​/​doi.org/​10.1016/​j.crhy.2018.09.002

[36] M. Peruzzo, A. Trioni, F. Hassani, M. Zemlicka, and J. M. Fink. ``Surpassing the resistance quantum with a geometric superinductor''. Phys. Rev. Appl. 14, 044055 (2020). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevApplied.14.044055

[37] Feng-Ming Liu, Ming-Cheng Chen, Can Wang, Shao-Wei Li, Zhong-Xia Shang, Chong Ying, Jian-Wen Wang, Cheng-Zhi Peng, Xiaobo Zhu, Chao-Yang Lu, and Jian-Wei Pan. ``Quantum design for advanced qubits: plasmonium'' (2021). arXiv:2109.00994. Appearances:.
https:/​/​doi.org/​10.48550/​arXiv.2109.00994
arXiv:2109.00994

[38] Matilda Peruzzo, Farid Hassani, Gregory Szep, Andrea Trioni, Elena Redchenko, Martin Žemlička, and Johannes M. Fink. ``Geometric superinductance qubits: Controlling phase delocalization across a single josephson junction''. PRX Quantum 2, 040341 (2021). Appearances:.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040341

[39] Arpit Ranadive, Martina Esposito, Luca Planat, Edgar Bonet, Cécile Naud, Olivier Buisson, Wiebke Guichard, and Nicolas Roch. ``Kerr reversal in josephson meta-material and traveling wave parametric amplification''. Nature Communications 13, 1737 (2022). Appearances:.
https:/​/​doi.org/​10.1038/​s41467-022-29375-5

[40] Jens Koch, V. Manucharyan, M. H. Devoret, and L. I. Glazman. ``Charging effects in the inductively shunted josephson junction''. Phys. Rev. Lett. 103, 217004 (2009). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.103.217004

[41] Ivan V. Pechenezhskiy, Raymond A. Mencia, Long B. Nguyen, Yen-Hsiang Lin, and Vladimir E. Manucharyan. ``The superconducting quasicharge qubit''. Nature 585, 368–371 (2020). Appearances:.
https:/​/​doi.org/​10.1038/​s41586-020-2687-9

[42] David A. Herrera-Martí, Ahsan Nazir, and Sean D. Barrett. ``Tradeoff between leakage and dephasing errors in the fluxonium qubit''. Phys. Rev. B 88, 094512 (2013). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.88.094512

[43] A. B. Zorin and F. Chiarello. ``Superconducting phase qubit based on the josephson oscillator with strong anharmonicity''. Phys. Rev. B 80, 214535 (2009). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.80.214535

[44] Fei Yan, Youngkyu Sung, Philip Krantz, Archana Kamal, David K. Kim, Jonilyn L. Yoder, Terry P. Orlando, Simon Gustavsson, and William D. Oliver. ``Engineering Framework for Optimizing Superconducting Qubit Designs'' (2020). arXiv:2006.04130. Appearances:.
https:/​/​doi.org/​10.48550/​arXiv.2006.04130
arXiv:2006.04130

[45] Eric Hyyppä, Suman Kundu, Chun Fai Chan, András Gunyhó, Juho Hotari, David Janzso, Kristinn Juliusson, Olavi Kiuru, Janne Kotilahti, Alessandro Landra, Wei Liu, Fabian Marxer, Akseli Mäkinen, Jean-Luc Orgiazzi, Mario Palma, Mykhailo Savytskyi, Francesca Tosto, Jani Tuorila, Vasilii Vadimov, Tianyi Li, Caspar Ockeloen-Korppi, Johannes Heinsoo, Kuan Yen Tan, Juha Hassel, and Mikko Möttönen. ``Unimon qubit''. Nature Communications 13, 6895 (2022). Appearances:.
https:/​/​doi.org/​10.1038/​s41467-022-34614-w

[46] K. A. Matveev, A. I. Larkin, and L. I. Glazman. ``Persistent current in superconducting nanorings''. Phys. Rev. Lett. 89, 096802 (2002). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.89.096802

[47] Peter Brooks, Alexei Kitaev, and John Preskill. ``Protected gates for superconducting qubits''. Phys. Rev. A 87, 052306 (2013). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevA.87.052306

[48] Nicholas A. Masluk, Ioan M. Pop, Archana Kamal, Zlatko K. Minev, and Michel H. Devoret. ``Microwave characterization of josephson junction arrays: Implementing a low loss superinductance''. Phys. Rev. Lett. 109, 137002 (2012). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.137002

[49] David Niepce, Jonathan Burnett, and Jonas Bylander. ``High kinetic inductance $\mathrm{Nb}\mathrm{N}$ nanowire superinductors''. Phys. Rev. Appl. 11, 044014 (2019). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevApplied.11.044014

[50] R. Kuzmin, R. Mencia, N. Grabon, N. Mehta, Y. H. Lin, and V. E. Manucharyan. ``Quantum electrodynamics of a superconductor–insulator phase transition''. Nature Physics 15, 930–934 (2019). Appearances:.
https:/​/​doi.org/​10.1038/​s41567-019-0553-1

[51] Lukas Grünhaupt, Martin Spiecker, Daria Gusenkova, Nataliya Maleeva, Sebastian T. Skacel, Ivan Takmakov, Francesco Valenti, Patrick Winkel, Hannes Rotzinger, Wolfgang Wernsdorfer, Alexey V. Ustinov, and Ioan M. Pop. ``Granular aluminium as a superconducting material for high-impedance quantum circuits''. Nature Materials 18, 816–819 (2019). Appearances:.
https:/​/​doi.org/​10.1038/​s41563-019-0350-3

[52] Plamen Kamenov, Wen-Sen Lu, Konstantin Kalashnikov, Thomas DiNapoli, Matthew T. Bell, and Michael E. Gershenson. ``Granular aluminum meandered superinductors for quantum circuits''. Phys. Rev. Appl. 13, 054051 (2020). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevApplied.13.054051

[53] David G. Ferguson, A. A. Houck, and Jens Koch. ``Symmetries and collective excitations in large superconducting circuits''. Phys. Rev. X 3, 011003 (2013). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevX.3.011003

[54] T. Weißl, B. Küng, E. Dumur, A. K. Feofanov, I. Matei, C. Naud, O. Buisson, F. W. J. Hekking, and W. Guichard. ``Kerr coefficients of plasma resonances in josephson junction chains''. Phys. Rev. B 92, 104508 (2015). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.92.104508

[55] Luca Chirolli and Guido Burkard. ``Decoherence in solid-state qubits''. Advances in Physics 57, 225–285 (2008). Appearances:.
https:/​/​doi.org/​10.1080/​00018730802218067

[56] Fei Yan, Simon Gustavsson, Archana Kamal, Jeffrey Birenbaum, Adam P Sears, David Hover, Ted J. Gudmundsen, Danna Rosenberg, Gabriel Samach, S. Weber, Jonilyn L. Yoder, Terry P. Orlando, John Clarke, Andrew J. Kerman, and William D. Oliver. ``The flux qubit revisited to enhance coherence and reproducibility''. Nature Communications 7, 12964 (2016). Appearances:.
https:/​/​doi.org/​10.1038/​ncomms12964

[57] Dmitri A. Ivanov, Lev B. Ioffe, Vadim B. Geshkenbein, and Gianni Blatter. ``Interference effects in isolated josephson junction arrays with geometric symmetries''. Phys. Rev. B 65, 024509 (2001). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.65.024509

[58] Jonathan R. Friedman and D. V. Averin. ``Aharonov-casher-effect suppression of macroscopic tunneling of magnetic flux''. Phys. Rev. Lett. 88, 050403 (2002). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevLett.88.050403

[59] I. M. Pop, B. Douçot, L. Ioffe, I. Protopopov, F. Lecocq, I. Matei, O. Buisson, and W. Guichard. ``Experimental demonstration of aharonov-casher interference in a josephson junction circuit''. Phys. Rev. B 85, 094503 (2012). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.85.094503

[60] Ari Mizel and Yariv Yanay. ``Right-sizing fluxonium against charge noise''. Phys. Rev. B 102, 014512 (2020). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.102.014512

[61] Luca Chirolli and Guido Burkard. ``Full control of qubit rotations in a voltage-biased superconducting flux qubit''. Phys. Rev. B 74, 174510 (2006). Appearances:.
https:/​/​doi.org/​10.1103/​PhysRevB.74.174510

[62] Uri Vool and Michel Devoret. ``Introduction to quantum electromagnetic circuits''. International Journal of Circuit Theory and Applications 45, 897–934 (2017). Appearances:.
https:/​/​doi.org/​10.1002/​cta.2359

[63] P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver. ``A quantum engineer's guide to superconducting qubits''. Applied Physics Reviews 6, 021318 (2019). Appearances:.
https:/​/​doi.org/​10.1063/​1.5089550

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