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Hardware-efficient quantum error correction via concatenated bosonic qubits

  • Gidney, C. & Ekerå, M. How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum 5, 433 (2021).

    Article 
    MATH 

    Google Scholar
     

  • Dalzell, A. M. et al. Quantum algorithms: a survey of applications and end-to-end complexities. Preprint at https://arxiv.org/abs/2310.03011 (2023).

  • Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Kitaev, A. Y. in Quantum Communication, Computing, and Measurement (eds Hirota, O. et al.), 181–188 (Springer, 1997).

  • Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 (1998).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Cochrane, P. T., Milburn, G. J. & Munro, W. J. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A 59, 2631–2634 (1999).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Aliferis, P. & Preskill, J. Fault-tolerant quantum computation against biased noise. Phys. Rev. A 78, 052331 (2008).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Fukui, K., Tomita, A. & Okamoto, A. Analog quantum error correction with encoding a qubit into an oscillator. Phys. Rev. Lett. 119, 180507 (2017).

    Article 
    ADS 
    MathSciNet 
    PubMed 
    MATH 

    Google Scholar
     

  • Tuckett, D. K., Bartlett, S. D. & Flammia, S. T. Ultrahigh error threshold for surface codes with biased noise. Phys. Rev. Lett. 120, 050505 (2018).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Guillaud, J. & Mirrahimi, M. Repetition cat qubits for fault-tolerant quantum computation. Phys. Rev. X 9, 041053 (2019).

    CAS 
    MATH 

    Google Scholar
     

  • Puri, S. et al. Bias-preserving gates with stabilized cat qubits. Sci. Adv. 6, eaay5901 (2020).

    Article 
    ADS 
    PubMed 
    PubMed Central 
    MATH 

    Google Scholar
     

  • Guillaud, J. & Mirrahimi, M. Error rates and resource overheads of repetition cat qubits. Phys. Rev. A 103, 042413 (2021).

    Article 
    ADS 
    MathSciNet 
    CAS 
    MATH 

    Google Scholar
     

  • Darmawan, A. S., Brown, B. J., Grimsmo, A. L., Tuckett, D. K. & Puri, S. Practical quantum error correction with the xzzx code and kerr-cat qubits. PRX Quantum 2, 030345 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Bonilla Ataides, J. P., Tuckett, D. K., Bartlett, S. D., Flammia, S. T. & Brown, B. J. The xzzx surface code. Nat. Commun. 12, 2172 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Chamberland, C. et al. Building a fault-tolerant quantum computer using concatenated cat codes. PRX Quantum 3, 010329 (2022).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Régent, F.-M.Le, Berdou, C., Leghtas, Z., Guillaud, J. & Mirrahimi, M. High-performance repetition cat code using fast noisy operations. Quantum 7, 1198 (2023).

    Article 

    Google Scholar
     

  • Gouzien, E., Ruiz, D., Le Régent, F.-M., Guillaud, J. & Sangouard, N. Performance analysis of a repetition cat code architecture: Computing 256-bit elliptic curve logarithm in 9 hours with 126 133 cat qubits. Phys. Rev. Lett. 131, 040602 (2023).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ruiz, D., Guillaud, J., Leverrier, A., Mirrahimi, M. & Vuillot, C. LDPC-cat codes for low-overhead quantum computing in 2D. Nat. Commun. 16, 1040 (2025).

  • Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).

    Article 
    ADS 

    Google Scholar
     

  • Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Leghtas, Z. et al. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347, 853–857 (2015).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Touzard, S. et al. Coherent oscillations inside a quantum manifold stabilized by dissipation. Phys. Rev. X 8, 021005 (2018).

    CAS 
    MATH 

    Google Scholar
     

  • Lescanne, R. et al. Exponential suppression of bit-flips in a qubit encoded in an oscillator. Nat. Phys. 16, 509–513 (2020).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Putterman, H. et al. Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression. Preprint at https://arxiv.org/abs/2409.17556 (2024).

  • Krinner, S. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669–674 (2022).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Google Qunatum AI et al. Suppressing quantum errors by scaling a surface code logical qubit. Nature 614, 676–681 (2023).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Sundaresan, N. et al. Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders. Nat. Commun. 14, 2852 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 
    MATH 

    Google Scholar
     

  • Google Quantum AI and Collaborators. Quantum error correction below the surface code threshold. Nature https://doi.org/10.1038/s41586-024-08449-y (2024).

  • Egan, L. et al. Fault-tolerant control of an error-corrected qubit. Nature 598, 281–286 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Bluvstein, D. et al. Logical quantum processor based on reconfigurable atom arrays. Nature 626, 58–65 (2024).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Gottesman, D., Kitaev, A. & Preskill, J. Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Jeong, H. & Kim, M. S. Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Berdou, C. et al. One hundred second bit-flip time in a two-photon dissipative oscillator. PRX Quantum 4, 020350 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Réglade, U. et al. Quantum control of a cat qubit with bit-flip times exceeding ten seconds. Nature 629, 778–783 (2024).

    Article 
    ADS 
    PubMed 
    MATH 

    Google Scholar
     

  • Ni, Z. et al. Beating the break-even point with a discrete-variable-encoded logical qubit. Nature 616, 56–60 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 
    MATH 

    Google Scholar
     

  • Flühmann, C. et al. Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513–517 (2019).

    Article 
    ADS 
    PubMed 
    MATH 

    Google Scholar
     

  • Campagne-Ibarcq, P. et al. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368–372 (2020).

    Article 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Sivak, V. V. et al. Real-time quantum error correction beyond break-even. Nature 616, 50–55 (2023).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Xu, Q., Zeng, P., Xu, D. & Jiang, L. Fault-tolerant operation of bosonic qubits with discrete-variable ancillae. Phys. Rev. X 14, 031016 (2024).

  • Yan, F. et al. Tunable coupling scheme for implementing high-fidelity two-qubit gates. Phys. Rev. Appl. 10, 054062 (2018).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Sung, Y. et al. Realization of high-fidelity cz and zz-free iSWAP gates with a tunable coupler. Phys. Rev. X 11, 021058 (2021).

    CAS 

    Google Scholar
     

  • Walter, T. et al. Rapid high-fidelity single-shot dispersive readout of superconducting qubits. Phys. Rev. Appl. 7, 054020 (2017).

    Article 
    ADS 

    Google Scholar
     

  • Magnard, P. et al. Fast and unconditional all-microwave reset of a superconducting qubit. Phys. Rev. Lett. 121, 060502 (2018).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Lutterbach, L. G. & Davidovich, L. Method for direct measurement of the Wigner function in cavity QED and ion traps. Phys. Rev. Lett. 78, 2547–2550 (1997).

    Article 
    ADS 
    CAS 
    MATH 

    Google Scholar
     

  • Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Leghtas, Z. et al. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett. 111, 120501 (2013).

    Article 
    ADS 
    PubMed 
    MATH 

    Google Scholar
     

  • Sun, L. et al. Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 511, 444–448 (2014).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Rosenblum, S. et al. Fault-tolerant detection of a quantum error. Science 361, 266–270 (2018).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Reinhold, P. et al. Error-corrected gates on an encoded qubit. Nat. Phys. 16, 822–826 (2020).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Ma, W.-L. et al. Path-independent quantum gates with noisy ancilla. Phys. Rev. Lett. 125, 110503 (2020).

    Article 
    ADS 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Higgott, O. & Gidney, C. Pymatching v.2. GitHub https://github.com/oscarhiggott/PyMatching (2022).

  • Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article 
    ADS 

    Google Scholar
     

  • Google Quantum AI Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383–387 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Miao, K. C. et al. Overcoming leakage in quantum error correction. Nat. Phys. 19, 1780–1786 (2023).

    Article 
    CAS 
    MATH 

    Google Scholar
     

  • Lacroix, N. et al. Fast flux-activated leakage reduction for superconducting quantum circuits. Preprint at https://arxiv.org/abs/2309.07060 (2023).

  • Bennett, C. H., DiVincenzo, D. P. & Smolin, J. A. Capacities of quantum erasure channels. Phys. Rev. Lett. 78, 3217–3220 (1997).

    Article 
    ADS 
    MathSciNet 
    CAS 
    MATH 

    Google Scholar
     

  • Grassl, M., Beth, T. & Pellizzari, T. Codes for the quantum erasure channel. Phys. Rev. A 56, 33–38 (1997).

    Article 
    ADS 
    MathSciNet 
    CAS 
    MATH 

    Google Scholar
     

  • Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002).

    Article 
    ADS 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Hann, C. T. et al. Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction. Preprint at https://arxiv.org/abs/2410.23363 (2024).

  • Cohen, J., Smith, W. C., Devoret, M. H. & Mirrahimi, M. Degeneracy-preserving quantum nondemolition measurement of parity-type observables for cat qubits. Phys. Rev. Lett. 119, 060503 (2017).

    Article 
    ADS 
    PubMed 
    MATH 

    Google Scholar
     

  • Xu, Q. et al. Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits. npj Quantum Inf. 9, 78 (2023).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Gautier, R., Mirrahimi, M. & Sarlette, A. Designing high-fidelity zeno gates for dissipative cat qubits. PRX Quantum 4, 040316 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Place, A. P. M. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 
    MATH 

    Google Scholar
     

  • Reagor, M. et al. Quantum memory with millisecond coherence in circuit QED. Phys. Rev. B 94, 014506 (2016).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Putterman, H. Data from “Hardware-efficient quantum error correction using concatenated bosonic qubits”. Zenodo https://doi.org/10.5281/zenodo.14257632 (2024).

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