High-performance repetition cat code using fast noisy operations

Francois-Marie Le Régent1,2, Camille Berdou2, Zaki Leghtas2, Jérémie Guillaud1, and Mazyar Mirrahimi2

1Alice&Bob, 53 boulevard du Général Martial Valin, 75015 Paris
2Laboratoire de Physique de l'Ecole Normale Supérieure, Ecole normale supérieure, MINES Paris, Université PSL, Sorbonne Université, CNRS, Inria, 75005 Paris

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Abstract

Bosonic cat qubits stabilized by two-photon driven dissipation benefit from exponential suppression of bit-flip errors and an extensive set of gates preserving this protection. These properties make them promising building blocks of a hardware-efficient and fault-tolerant quantum processor. In this paper, we propose a performance optimization of the repetition cat code architecture using fast but noisy CNOT gates for stabilizer measurements. This optimization leads to high thresholds for the physical figure of merit, given as the ratio between intrinsic single-photon loss rate of the bosonic mode and the engineered two-photon loss rate, as well as an improved scaling below threshold of the required overhead, to reach an expected level of logical error rate. Relying on the specific error models for cat qubit operations, this optimization exploits fast parity measurements, using accelerated low-fidelity CNOT gates, combined with fast ancilla parity-check qubits. The significant enhancement in the performance is explained by: 1- the highly asymmetric error model of cat qubit CNOT gates with a major component on control (ancilla) qubits, and 2- the robustness of the repetition cat code error correction performance in presence of the leakage induced by fast operations. In order to demonstrate these performances, we develop a method to sample the repetition code under circuit-level noise that also takes into account cat qubit state leakage.

The cat qubits are bosonic codes benefitting from exponentially suppressed bit-flip rates with increasing number of encoding photons. In conjunction with bias-preserving operations, they can be used to drastically reduce the hardware overhead required for error correction towards fault-tolerant quantum computation. In this paper we investigate another useful property of such qubits, the asymmetry in the phase-flip errors of a bias-preserving CNOT gate. While performing a fast CNOT gate, the probability of such an error increases on the control cat qubit while it decreases on the target one. By exploiting this property, we demonstrate an improved performance of error correction in a concatenated repetition cat code architecture. A central contribution of our paper is to propose a way to handle the further leakage out of code space induced by such fast operations. The numerical tools developed in the paper demonstrate the viability of this approach towards further reduction of hardware overhead.

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► References

[1] Atharv Joshi, Kyungjoo Noh, and Yvonne Y Gao. ``Quantum information processing with bosonic qubits in circuit QED''. Quantum Science and Technology 6, 033001 (2021).
https:/​/​doi.org/​10.1088/​2058-9565/​abe989

[2] Weizhou Cai, Yuwei Ma, Weiting Wang, Chang-Ling Zou, and Luyan Sun. ``Bosonic quantum error correction codes in superconducting quantum circuits''. Fundamental Research 1, 50–67 (2021).
https:/​/​doi.org/​10.1016/​j.fmre.2020.12.006

[3] Mazyar Mirrahimi, Zaki Leghtas, Victor V Albert, Steven Touzard, Robert J Schoelkopf, Liang Jiang, and Michel H Devoret. ``Dynamically protected cat-qubits: a new paradigm for universal quantum computation''. New Journal of Physics 16, 045014 (2014).
https:/​/​doi.org/​10.1088/​1367-2630/​16/​4/​045014

[4] Jérémie Guillaud and Mazyar Mirrahimi. ``Repetition cat qubits for fault-tolerant quantum computation''. Physical Review X 9 (2019).
https:/​/​doi.org/​10.1103/​physrevx.9.041053

[5] Christopher Chamberland, Kyungjoo Noh, Patricio Arrangoiz-Arriola, Earl T. Campbell, Connor T. Hann, Joseph Iverson, Harald Putterman, Thomas C. Bohdanowicz, Steven T. Flammia, Andrew Keller, Gil Refael, John Preskill, Liang Jiang, Amir H. Safavi-Naeini, Oskar Painter, and Fernando G.S.L. Brandão. ``Building a fault-tolerant quantum computer using concatenated cat codes''. PRX Quantum 3 (2022).
https:/​/​doi.org/​10.1103/​prxquantum.3.010329

[6] Raphaël Lescanne, Marius Villiers, Théau Peronnin, Alain Sarlette, Matthieu Delbecq, Benjamin Huard, Takis Kontos, Mazyar Mirrahimi, and Zaki Leghtas. ``Exponential suppression of bit-flips in a qubit encoded in an oscillator''. Nature Physics 16, 509–513 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0824-x

[7] C. Berdou, A. Murani, U. Réglade, W.C. Smith, M. Villiers, J. Palomo, M. Rosticher, A. Denis, P. Morfin, M. Delbecq, T. Kontos, N. Pankratova, F. Rautschke, T. Peronnin, L.-A. Sellem, P. Rouchon, A. Sarlette, M. Mirrahimi, P. Campagne-Ibarcq, S. Jezouin, R. Lescanne, and Z. Leghtas. ``One hundred second bit-flip time in a two-photon dissipative oscillator''. PRX Quantum 4 (2023).
https:/​/​doi.org/​10.1103/​prxquantum.4.020350

[8] L. G. Lutterbach and L. Davidovich. ``Method for direct measurement of the wigner function in cavity qed and ion traps''. Phys. Rev. Lett. 78, 2547–2550 (1997).
https:/​/​doi.org/​10.1103/​PhysRevLett.78.2547

[9] P. Bertet, A. Auffeves, P. Maioli, S. Osnaghi, T. Meunier, M. Brune, J. M. Raimond, and S. Haroche. ``Direct measurement of the wigner function of a one-photon fock state in a cavity''. Phys. Rev. Lett. 89, 200402 (2002).
https:/​/​doi.org/​10.1103/​PhysRevLett.89.200402

[10] L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirchmair, K. M. Sliwa, A. Narla, M. Hatridge, S. Shankar, J. Blumoff, L. Frunzio, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf. ``Tracking photon jumps with repeated quantum non-demolition parity measurements''. Nature 511, 444–+ (2014).
https:/​/​doi.org/​10.1038/​nature13436

[11] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. ``Surface codes: Towards practical large-scale quantum computation''. Phys. Rev. A 86, 032324 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.032324

[12] Shruti Puri, Lucas St-Jean, Jonathan A. Gross, Alexander Grimm, Nicholas E. Frattini, Pavithran S. Iyer, Anirudh Krishna, Steven Touzard, Liang Jiang, Alexandre Blais, Steven T. Flammia, and S. M. Girvin. ``Bias-preserving gates with stabilized cat qubits''. Science Advances 6 (2020).
https:/​/​doi.org/​10.1126/​sciadv.aay5901

[13] Qian Xu, Joseph K. Iverson, Fernando G. S. L. Brandão, and Liang Jiang. ``Engineering fast bias-preserving gates on stabilized cat qubits''. Phys. Rev. Res. 4, 013082 (2022).
https:/​/​doi.org/​10.1103/​PhysRevResearch.4.013082

[14] Harald Putterman, Joseph Iverson, Qian Xu, Liang Jiang, Oskar Painter, Fernando G. S. L. Brandão, and Kyungjoo Noh. ``Stabilizing a bosonic qubit using colored dissipation''. Physical Review Letters 128 (2022).
https:/​/​doi.org/​10.1103/​physrevlett.128.110502

[15] Ronan Gautier, Alain Sarlette, and Mazyar Mirrahimi. ``Combined dissipative and hamiltonian confinement of cat qubits''. PRX Quantum 3, 020339 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.020339

[16] Diego Ruiz, Ronan Gautier, Jérémie Guillaud, and Mazyar Mirrahimi. ``Two-photon driven kerr quantum oscillator with multiple spectral degeneracies''. Physical Review A 107 (2023).
https:/​/​doi.org/​10.1103/​physreva.107.042407

[17] Qian Xu, Guo Zheng, Yu-Xin Wang, Peter Zoller, Aashish A. Clerk, and Liang Jiang. ``Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits''. npj Quantum Information 9, 78 (2023).
https:/​/​doi.org/​10.1038/​s41534-023-00746-0

[18] Jérémie Guillaud and Mazyar Mirrahimi. ``Error rates and resource overheads of repetition cat qubits''. Physical Review A 103 (2021).
https:/​/​doi.org/​10.1103/​physreva.103.042413

[19] Austin G. Fowler, Adam C. Whiteside, and Lloyd C. L. Hollenberg. ``Towards practical classical processing for the surface code''. Phys. Rev. Lett. 108, 180501 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.108.180501

[20] Oscar Higgott. ``Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching''. ACM Transactions on Quantum Computing (2021).
https:/​/​doi.org/​10.1145/​3505637

[21] P. Aliferis and B.M. Terhal. ``Fault-tolerant quantum computation for local leakage faults''. Quantum Information and Computation 7, 139–156 (2007).
https:/​/​doi.org/​10.26421/​qic7.1-2-9

[22] F. Battistel, B.M. Varbanov, and B.M. Terhal. ``Hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits''. PRX Quantum 2 (2021).
https:/​/​doi.org/​10.1103/​prxquantum.2.030314

[23] M. McEwen et al. ``Removing leakage-induced correlated errors in superconducting quantum error correction''. Nature Communications 12 (2021).
https:/​/​doi.org/​10.1038/​s41467-021-21982-y

[24] Zijun Chen et al. ``Exponential suppression of bit or phase errors with cyclic error correction''. Nature 595, 383–387 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03588-y

[25] Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. ``Topological quantum memory''. Journal of Mathematical Physics 43, 4452–4505 (2002).
https:/​/​doi.org/​10.1063/​1.1499754

[26] Jérémie Guillaud, Joachim Cohen, and Mazyar Mirrahimi. ``Quantum computation with cat qubits''. SciPost Physics Lecture Notes (2023).
https:/​/​doi.org/​10.21468/​scipostphyslectnotes.72

[27] Giacomo Pantaleoni, Ben Q. Baragiola, and Nicolas C. Menicucci. ``Modular bosonic subsystem codes''. Physical Review Letters 125 (2020).
https:/​/​doi.org/​10.1103/​physrevlett.125.040501

[28] Andrew S. Darmawan, Benjamin J. Brown, Arne L. Grimsmo, David K. Tuckett, and Shruti Puri. ``Practical quantum error correction with the XZZX code and kerr-cat qubits''. PRX Quantum 2 (2021).
https:/​/​doi.org/​10.1103/​prxquantum.2.030345

[29] Scott Aaronson and Daniel Gottesman. ``Improved simulation of stabilizer circuits''. Phys. Rev. A 70, 052328 (2004).
https:/​/​doi.org/​10.1103/​PhysRevA.70.052328

[30] Jack Edmonds. ``Paths, trees, and flowers''. Canadian Journal of Mathematics 17, 449–467 (1965).
https:/​/​doi.org/​10.4153/​CJM-1965-045-4

[31] Vladimir Kolmogorov. ``Blossom v: a new implementation of a minimum cost perfect matching algorithm''. Mathematical Programming Computation 1, 43–67 (2009).
https:/​/​doi.org/​10.1007/​s12532-009-0002-8

Cited by

[1] Adrian Copetudo, Clara Yun Fontaine, Fernando Valadares, and Yvonne Y. Gao, "Shaping photons: Quantum information processing with bosonic cQED", Applied Physics Letters 124 8, 080502 (2024).

[2] Ofir Milul, Barkay Guttel, Uri Goldblatt, Sergey Hazanov, Lalit M. Joshi, Daniel Chausovsky, Nitzan Kahn, Engin çiftyürek, Fabien Lafont, and Serge Rosenblum, "Superconducting Cavity Qubit with Tens of Milliseconds Single-Photon Coherence Time", PRX Quantum 4 3, 030336 (2023).

[3] Diego Ruiz, Jérémie Guillaud, Anthony Leverrier, Mazyar Mirrahimi, and Christophe Vuillot, "LDPC-cat codes for low-overhead quantum computing in 2D", arXiv:2401.09541, (2024).

[4] Élie Gouzien, Diego Ruiz, Francois-Marie Le Régent, Jérémie Guillaud, and Nicolas Sangouard, "Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126 133 Cat Qubits", Physical Review Letters 131 4, 040602 (2023).

[5] Adrian Copetudo, Clara Yun Fontaine, Fernando Valadares, and Yvonne Y. Gao, "Shaping photons: quantum computation with bosonic cQED", arXiv:2311.03846, (2023).

[6] Ronan Gautier, Mazyar Mirrahimi, and Alain Sarlette, "Designing High-Fidelity Zeno Gates for Dissipative Cat Qubits", PRX Quantum 4 4, 040316 (2023).

[7] Lucas Berent, Timo Hillmann, Jens Eisert, Robert Wille, and Joschka Roffe, "Analog information decoding of bosonic quantum LDPC codes", arXiv:2311.01328, (2023).

[8] Jaehak Lee, Nuri Kang, Seok-Hyung Lee, Hyunseok Jeong, Liang Jiang, and Seung-Woo Lee, "Fault-tolerant quantum computation by hybrid qubits with bosonic cat-code and single photons", arXiv:2401.00450, (2023).

[9] Antoine Marquet, Antoine Essig, Joachim Cohen, Nathanaël Cottet, Anil Murani, Emanuele Abertinale, Simon Dupouy, Audrey Bienfait, Théau Peronnin, Sébastien Jezouin, Raphaël Lescanne, and Benjamin Huard, "Autoparametric resonance extending the bit-flip time of a cat qubit up to 0.3 s", arXiv:2307.06761, (2023).

[10] Florian Hopfmueller, Maxime Tremblay, Philippe St-Jean, Baptiste Royer, and Marc-Antoine Lemonde, "Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes", arXiv:2402.09333, (2024).

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