Quantum Error Correction For Dummies
Abstract
In the current Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, qubit technologies are prone to imperfections, giving rise to various errors such as gate errors, decoherence/dephasing, measurement errors, leakage, and crosstalk. These errors present challenges in achieving error-free computation within NISQ devices. A proposed solution to this issue is Quantum Error Correction (QEC), which aims to rectify the corrupted qubit state through a three-step process: (i) detection: identifying the presence of an error, (ii) decoding: pinpointing the location(s) of the affected qubit(s), and (iii) correction: restoring the faulty qubits to their original states. QEC is an expanding field of research that encompasses intricate concepts. In this paper, we aim to provide a comprehensive review of the historical context, current state, and future prospects of Quantum Error Correction, tailored to cater to computer scientists with limited familiarity with quantum physics and its associated mathematical concepts. In this work, we, (a) explain the foundational principles of QEC and explore existing Quantum Error Correction Codes (QECC) designed to correct errors in qubits, (b) explore the practicality of these QECCs with regard to implementation and error correction quality, and (c) highlight the challenges associated with implementing QEC within the context of the current landscape of NISQ computers.
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Recent analyses estimate feasible RSA-2048 factoring anywhere between fifteen and thirty-five years depending on hardware error rates and algorithmic progress.
“Recent analyses estimate feasible RSA-2048 factoring anywhere between fifteen and thirty-five years depending on hardware error rates and algorithmic progress, implying wide confidence bounds on the temporal risk curves [45,46].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [46]
The quantum decryption horizon Ha(t) is highly uncertain because projections of qubit availability Q(t) and error-correction efficiency ECC(t) vary by orders of magnitude across studies.
“In practice, the quantum decryption horizon Ha ( t ) is highly uncertain because projections of qubit availability Q ( t ) and error-correction efficiency ECC ( t ) vary by orders of magnitude across studies [45,46].”
From Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition (2025) · cites this paper as [46]
Cites
A single quantum cannot be cloned
Wootters, W. K., & Zurek, W. H. (1982) · Nature · doi:10.1038/299802a0 · Cited by 5,406 · see citing works
Ladd, T. D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., & O’Brien, J. L. (2010) · Nature · doi:10.1038/nature08812 · Cited by 3,592 · see citing works
Good quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516 · see citing works
Edmonds, J. (1965) · Canadian Journal of Mathematics · doi:10.4153/cjm-1965-045-4 · Cited by 2,428 · 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
An introduction to quantum machine learning
Schuld, M., Sinayskiy, I., & Petruccione, F. (2015) · Contemporary Physics · doi:10.1080/00107514.2014.964942 · Cited by 1,381 · see citing works
Realizing repeated quantum error correction in a distance-three surface code
Krinner, S., Lacroix, N., Remm, A., Di Paolo, A., Genois, E., Leroux, C., Hellings, C., Lazar, S., Swiadek, F., Herrmann, J., et al. (2022) · Nature · doi:10.1038/s41586-022-04566-8 · Cited by 686 · see citing works
Photonic quantum information processing: a concise review
Slussarenko, S., & Pryde, G. J. (2019) · Applied Physics Reviews · doi:10.1063/1.5115814 · Cited by 644 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Simple quantum error-correcting codes
Steane, A. M. (1996) · Physical Review A · doi:10.1103/physreva.54.4741 · Cited by 522 · see citing works
Realization of quantum error correction
Chiaverini, J., Leibfried, D., Schaetz, T., Barrett, M. D., Blakestad, R. B., Britton, J., Itano, W. M., Jost, J. D., Knill, E., Langer, C., et al. (2004) · Nature · doi:10.1038/nature03074 · Cited by 517 · see citing works
Stim: a fast stabilizer circuit simulator
Gidney, C. (2021) · Quantum · doi:10.22331/q-2021-07-06-497 · Cited by 415 · see citing works
Realization of an Error-Correcting Surface Code with Superconducting Qubits
Zhao, Y., Ye, Y., Huang, H.-L., Zhang, Y., Wu, D., Guan, H., Zhu, Q., Wei, Z., He, T., Cao, S., et al. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.030501 · Cited by 321 · see citing works
Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits
Takita, M., Cross, A. W., Córcoles, A. D., Chow, J. M., & Gambetta, J. M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.180501 · Cited by 228 · see citing works
Error-protected qubits in a silicon photonic chip
Vigliar, C., Paesani, S., Ding, Y., Adcock, J. C., Wang, J., Morley-Short, S., Bacco, D., Oxenløwe, L. K., Thompson, M. G., Rarity, J. G., et al. (2021) · Nature Physics · doi:10.1038/s41567-021-01333-w · Cited by 118 · see citing works
Fault-Tolerant Operation of a Quantum Error-Correction Code
Egan, L., Debroy, D. M., Noel, C., Risinger, A., Zhu, D., Biswas, D., Newman, M., Li, M., Brown, K. R., Cetina, M., et al. (2020) · arXiv · doi:10.48550/arxiv.2009.11482 · Cited by 65 · see citing works
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Harvest-Now, Decrypt-Later: A Temporal Cybersecurity Risk in the Quantum Transition
Kagai, F., Branch, P., But, J., & Allen, R. (2025) · Telecom · doi:10.3390/telecom6040100 · Cited by 15 · see citing works
“Recent analyses estimate feasible RSA-2048 factoring anywhere between fifteen and thirty-five years depending on hardware error rates and algorithmic progress, implying wide confidence bounds on the temporal risk curves [45,46].”
- Authors
- Chatterjee, A., Phalak, K., & Ghosh, S.
- Affiliations
- Pennsylvania State University (US)
- Venue
- 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)
- Publisher
- IEEE
- Published
- 2023-09-17
- Pages
- 70-81
- OpenAlex
- W4389168214
- Cited by
- 35
- References
- 16
- Citations by year
- 2026: 9 · 2025: 16 · 2024: 8 · 2023: 2
- FWCI
- 6.20
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE International Conference on Quantum Computing and Engineering (QCE) (publishedVersion)
- Funders
- National Science Foundation (NSF) (CNS-1722557,CCF-1718474,OIA-2040667,DGE-1723687,DGE-1821766)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum error correction, quantum error-correcting codes, NISQ devices, decoherence, gate errors, measurement error, quantum computing hardware
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