Repetition Cat Qubits for Fault-Tolerant Quantum Computation
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The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches.
“The large physical-qubit overhead associated with error correction motivates the search for more hardware-efficient approaches6–18.”
From Hardware-efficient quantum error correction via concatenated bosonic qubits (2025) · cites this paper as [10]
Various proposals have been put forward to further scale bosonic QEC by concatenating it with an outer code across multiple bosonic modes, leveraging the protection offered in each bosonic mode to reduce the overall resource overhead for QEC.
“At the same time, various proposals have been put forward to further scale bosonic QEC by concatenating it with an outer code across multiple bosonic modes6,8–16,18,40, leveraging the protection offered in each bosonic mode to reduce the overall resource overhead for QEC.”
From Hardware-efficient quantum error correction via concatenated bosonic qubits (2025) · cites this paper as [10]
Although cat qubits can be used as ancilla qubits to implement noise-biased CX gates, these gates can induce substantial control errors and require a complex drive scheme.
“Although cat qubits can be used as ancilla qubits to implement noise-biased CX gates, these gates can induce substantial control errors and require a complex drive scheme10,11,15.”
From Hardware-efficient quantum error correction via concatenated bosonic qubits (2025) · cites this paper as [10]
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Cites
A scheme for efficient quantum computation with linear optics
Knill, E., Laflamme, R., & Milburn, G. J. (2001) · Nature · doi:10.1038/35051009 · Cited by 5,880 · see citing works
Surface codes: Towards practical large-scale quantum computation
Fowler, A. G., Mariantoni, M., Martinis, J. M., & Cleland, A. N. (2012) · Physical Review A · doi:10.1103/physreva.86.032324 · Cited by 3,059 · see citing works
Quantum computations: algorithms and error correction
Kitaev, A. Y. (1997) · Russian Mathematical Surveys · doi:10.1070/rm1997v052n06abeh002155 · Cited by 1,424 · see citing works
Quantum computing with realistically noisy devices
Knill, E. (2005) · Nature · doi:10.1038/nature03350 · Cited by 1,184 · cited 2× · see citing works
“Indeed, the Clifford operations map Pauli operators to Pauli operators and therefore it is only needed to keep track of the errors to update the Pauli frame in software [46].”
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Research works printed but not linked: 35
- P.W. Shor. Fault-tolerant quantum computation. In Proceedings of 37th Conference on Foundations of Computer Science. IEEE Comput. Soc. Press.
- Peter W. Shor. Scheme for reducing decoherence in quan- tum computer memory. Physical Review A, 52(4):R2493- R2496, oct 1995.
- Andrew Steane. Multiple-particle interference and quan- tum error correction. Proceedings: Mathematical, Physical and Engineering Sciences, 452(1954):2551-2577, 1996.
- Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. Topological quantum memory. Journal of Mathematical Physics, 43(9):4452-4505, sep 2002.
- Dorit Aharonov and Michael Ben-Or. Fault-tolerant quantum computation with constant error rate. SIAM Journal on Computing, 38(4):1207-1282, jan 2008.
- Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek. Resilient quantum computation: error mod- els and thresholds. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1969):365-384, jan 1998.
- John Preskill. Reliable quantum computers. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1969):385-410, jan 1998.
- Panos Aliferis, Daniel Gottesman, and John Preskill. Quantum accuracy threshold for concatenated distance-3 codes. Quantum Info. Comput., 6(2):97-165, 2006.
- Seth Lloyd and Jean-Jacques E. Slotine. Analog quantum error correction. Physical Review Letters, 80(18):4088- 4091, may 1998.
- Samuel L. Braunstein. Error correction for contin- uous quantum variables. Physical Review Letters, 80(18):4084-4087, may 1998.
- Daniel Gottesman, Alexei Kitaev, and John Preskill. En- coding a qubit in an oscillator. Physical Review A, 64(1), jun 2001.
- Isaac L. Chuang, Debbie W. Leung, and Yoshihisa Ya- mamoto. Bosonic quantum codes for amplitude damping. Physical Review A, 56(2):1114-1125, aug 1997.
- Marios H. Michael, Matti Silveri, R. T. Brierley, Vic- tor V. Albert, Juha Salmilehto, Liang Jiang, and S. M. Girvin. New class of quantum error-correcting codes for a bosonic mode. Physical Review X, 6(3), jul 2016.
- P. T. Cochrane, G. J. Milburn, and W. J. Munro. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Physical Review A, 59(4):2631-2634, apr 1999.
- Zaki Leghtas, Gerhard Kirchmair, Brian Vlastakis, Robert J. Schoelkopf, Michel H. Devoret, and Maz- yar Mirrahimi. Hardware-efficient autonomous quantum memory protection. Physical Review Letters, 111(12), sep 2013.
- 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(4):045014, 2014.
- S. Puri, A. Grimm, P. Campagne-Ibarcq, A. Eickbusch, K. Noh, G. Roberts, L. Jiang, M. Mirrahimi, M.H. De- voret, and S.M. Girvin. Stabilized cat in driven non- linear cavity: A fault-tolerant error syndrome detector. arXiv:1807.09334, 2018. · arXiv
- Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlas- takis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret. Confining the state of light to a quantum manifold by engineered two-photon loss. Science, 347(6224):853-857, feb 2015.
- S. Rosenblum, P. Reinhold, M. Mirrahimi, Liang Jiang, L. Frunzio, and R. J. Schoelkopf. Fault-tolerant detection of a quantum error. Science, 361(6399):266-270, 2018.
- S. Puri, L. St-Jean, J.A. Gross, A. Grimm, N.E. Frattini, P.S. Iyer, A. Krishna, S. Touzard, L. Jiang, A. Blais, S.T. Flammia, and S.M. Girvin. Bias-preserving gates with stabilized cat qubits arXiv:1905.00450, 2019. · arXiv
- R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas. Exponential suppression of bit flips in a qubit encoded in an oscillator. arXiv:1907.11729, 2019. · arXiv
- A. Grimm, N.E. Frattini, S. Puri, S.O. Mundhada, S. Touzard, M. Mirrahimi, S.M. Girvin, S. Shankar, and M.H. Devoret. The Kerr-cat qubit: stabilization, read- out, and gates. arXiv:1907.12131, 2019. · arXiv
- Panos Aliferis and John Preskill. Fault-tolerant quantum computation against biased noise. Physical Review A, 78(5), nov 2008.
- David K. Tuckett, Stephen D. Bartlett, and Steven T. Flammia. Ultrahigh error threshold for surface codes with biased noise. Physical Review Letters, 120(5), jan 2018.
- Lilian Childress and Ronald Hanson. Diamond NV cen- ters for quantum computing and quantum networks. MRS Bulletin, 38(02):134-138, feb 2013.
- L. Gilles, B. M. Garraway, and P. L. Knight. Generation of nonclassical light by dissipative two-photon processes. Physical Review A, 49(4):2785-2799, apr 1994.
- Paul Webster, Stephen D. Bartlett, and David Poulin. Reducing the overhead for quantum computation when noise is biased. Physical Review A, 92(6), dec 2015.
- Yaoyun Shi. Both toffoli and controlled-not need little help to do universal quantum computing. Quantum Info. Comput., 3(1):84-92, January 2003.
- Dorit Aharonov. A simple proof that toffoli and hadamard are quantum universal, 2003. arXiv:quant- ph/0301040.
- L. Sun, A. Petrenko, Z. Leghtas, B. Vlastakis, G. Kirch- mair, 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(7510):444-448, jul 2014.
- Theodore J. Yoder, Ryuji Takagi, and Isaac L. Chuang. Universal fault-tolerant gates on concatenated stabilizer codes. Physical Review X, 6(3), sep 2016.
- R. Azouit, A. Sarlette, and P. Rouchon. Adiabatic elim- ination for open quantum systems with effective lind- blad master equations. In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, dec 2016.
- Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, New York, NY, USA, 10th edition, 2011.
- Chen Wang, Yvonne Y. Gao, Philip Reinhold, R. W. Heeres, Nissim Ofek, Kevin Chou, Christopher Axline, Matthew Reagor, Jacob Blumoff, K. M. Sliwa, L. Frun- zio, S. M. Girvin, Liang Jiang, M. Mirrahimi, M. H. De- voret, and R. J. Schoelkopf. A schrödinger cat living in two boxes. Science, 352(6289):1087-1091, 2016.
- Chenyang Wang, Jim Harrington, and John Preskill. Confinement-higgs transition in a disordered gauge the- ory and the accuracy threshold for quantum memory. Annals of Physics, 303(1):31 -58, 2003.
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Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes
Chamberland, C., Noh, K., Arrangoiz-Arriola, P., Campbell, E. T., Hann, C. T., Iverson, J., Putterman, H., Bohdanowicz, T. C., Flammia, S. T., Keller, A., et al. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010329 · Cited by 281 · see citing works
Hardware-efficient quantum error correction via concatenated bosonic qubits
Putterman, H., Noh, K., Hann, C. T., MacCabe, G. S., Aghaeimeibodi, S., Patel, R. N., Lee, M., Jones, W. M., Moradinejad, H., Rodriguez, R., et al. (2025) · Nature · doi:10.1038/s41586-025-08642-7 · Cited by 108 · see citing works
One Hundred Second Bit-Flip Time in a Two-Photon Dissipative Oscillator
Berdou, C., Murani, A., Réglade, U., Smith, W. C., Villiers, M., Palomo, J., Rosticher, M., Denis, A., Morfin, P., Delbecq, M., et al. (2023) · PRX Quantum · doi:10.1103/prxquantum.4.020350 · Cited by 75 · see citing works
Self-citationError rates and resource overheads of repetition cat qubits
Guillaud, J., & Mirrahimi, M. (2021) · Physical Review A · doi:10.1103/physreva.103.042413 · Cited by 55 · see citing works
Self-citationHigh-performance repetition cat code using fast noisy operations
Régent, F.-M. L., Berdou, C., Leghtas, Z., Guillaud, J., & Mirrahimi, M. (2023) · Quantum · doi:10.22331/q-2023-12-06-1198 · Cited by 15 · see citing works
Self-citationPractical Quantum Error Correction with the XZZX Code and Kerr-Cat Qubits
Darmawan, A. S., Brown, B. J., Grimsmo, A. L., Tuckett, D. K., & Puri, S. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.030345 · Cited by 2 · see citing works
- Authors
- Guillaud, J., & Mirrahimi, M.
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2019-12-12
- Volume
- 9
- Issue
- 4
- ISSN
- 2160-3308
- Cited by
- 189
- References
- 4
- Language
- en
- Funders
- Army Research Office (W911NF-18-1-0212)
- Domaine Intérêt Majeur Science et Ingénierie en Région Île-de-France pour les Technologies Quantiques
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