The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Class of quantum error-correcting codes saturating the quantum Hamming bound
Open accessAbstract
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode k=n-j-2 quantum bits (qubits) in n=${2}^{\mathit{j}}$ qubits and correct t=1 error. \textcopyright{} 1996 The American Physical Society.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Without error corrections, the effect of noise will accumulate and ruin the entire computation[72, 17, 54, 52, 7], and hence the computation must be protected.”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [52]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.722 · Cited by 2,961
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
Flagged first, then by citations
Cited by
Sorted by citations
Items 801–900 of 1,003
Quantum logical states and operators for Josephson-like systems
Faoro, L., Raffa, F. A., & Rasetti, M. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/5/l01 · Cited by 4
Upper bound on quantum stabilizer codes
Li, Z., & Xing, L. (2009) · Physical Review A · doi:10.1103/physreva.79.032342 · Cited by 4
Decoherence suppression for oscillator-assisted geometric quantum gates via symmetrization
Cen, L.-X., & Zanardi, P. (2005) · Physical Review A · doi:10.1103/physreva.71.060307 · Cited by 5
Entanglement in a generalized Jaynes–Cummings model
Zhang, G., & Liu, J. (2007) · Chinese Physics · doi:10.1088/1009-1963/16/12/007 · Cited by 4
Deterministic dense coding and faithful teleportation with multipartite graph states
Huang, C.-Y., Yu, I.-C., Lin, F.-L., & Hsu, L. (2009) · Physical Review A · doi:10.1103/physreva.79.052306 · Cited by 4
Classification of $q$-Ary Perfect Quantum Codes
Li, Z., & Xing, L. (2012) · IEEE Transactions on Information Theory · doi:10.1109/tit.2012.2217475 · Cited by 7
“In quantum coding theory two types of -ary perfect quantum codes were discovered in the early 2000s: i) The cyclic Hamming codes with , see [14]–[16].”
BackgroundProposal for a simple quantum-error-correction test gate in linear optics
Ralph, T. C. (2003) · IEEE Journal of Selected Topics in Quantum Electronics · doi:10.1109/jstqe.2003.820943 · Cited by 3
“The circuit can also be understood in the language of stabilizer codes [ 9 ].”
BackgroundAssadi, L., & Jafarpour, M. (2016) · International Journal of Theoretical Physics · doi:10.1007/s10773-016-3104-x · Cited by 4
All-versus-nothing proofs with n qubits distributed between m parties
Cabello, A., & Moreno, P. (2010) · Physical Review A · doi:10.1103/physreva.81.042110 · Cited by 4
Quantum logical states and operators for Josephson-like systems
Faoro, L., Raffa, F. A., & Rasetti, M. (2006) · PORTO Publications Open Repository TOrino (Politecnico di Torino) · Cited by 4
Quantum MacWilliams IdentitiesPreprint
Shor, P. W., & Laflamme, R. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9610040 · Cited by 4
Unconditionally Secure Quantum Key Distribution In Higher DimensionsPreprint
Chau, H. F. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0212055 · Cited by 4
“on III-B. A. The Unitary Operator T In the analysis of certain quantum error correcting codes, Gottesman introduced a unitary operator that cyclically permutes the σx, σy and σz errors by conjugation [24]. Later on, Lo observed that conjugation by the same operator permutes the three bases used by the six-state scheme…”
MethodInformation flow at the quantum-classical boundaryPreprint
Bény, C. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0901.3629 · Cited by 5
“This yields to the method of quantum error correction [26, 27, 28, 29, 30], or to its refinement which allows for subsystem codes (operator quantum error correction) [31, 32].”
MethodOn the Structure of Additive Quantum Codes and the Existence of Nonadditive CodesPreprint
Roychowdhury, V., & Vatan, F. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/9710031 · Cited by 4
“ive code Q with stabilizer HQ there is a sufficient condition in term of the dual of HQ with respect to the inner product defined by equation (1) for Q to be a t–error–correcting code. Theorem 2.2 ([3], [7]) Let Q be an additive code with stabilizer HQ. Let HQ ⊥ be the space orthogonal to HQ with respect to the inner pro…”
BackgroundInfluentialWang, Y., Liu, X.-S., & Gui-Lu, L. (2007) · Communications in Theoretical Physics · doi:10.1088/0253-6102/48/1/015 · Cited by 4
Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption
Seyfarth, U. (2019) · TUbilio (Technical University of Darmstadt) · doi:10.48550/arxiv.1907.02726 · Cited by 8
Binary construction of quantum codes
Li, R., & Li, X. (2006) · Cited by 4
Glisic, S., & Lorenzo, B. (2022) · Wiley eBooks · doi:10.1002/9781119790327.ch10 · Cited by 4
(2008) · CRC Press eBooks · doi:10.1201/b15868-2 · Cited by 4
Joint Interoperability: Fog or Lens for Joint Vision 2010
Reddy, P. C. (1997) · Defense Technical Information Center (DTIC) · doi:10.21236/ada388057 · Cited by 4
QKD parameter estimation by two-universal hashing
Ostrev, D. (2023) · Quantum · doi:10.22331/q-2023-01-13-894 · Cited by 3
“The present paper also uses a number of technical lemmas related to the stabilizer formalism [6, 3].”
MethodEstimating Fock-state linear optics evolution using coherent states
Lund, A. P. (2023) · AVS Quantum Science · doi:10.1116/5.0136828 · Cited by 3
Park, M., Maskara, N., Kalinowski, M., & Lukin, M. D. (2025) · Physical Review A · doi:10.1103/physreva.111.012419 · Cited by 7
“Stabilizer codes are a particularly important class, as they come equipped with efficient circuits for identifying and correcting errors without affecting the encoded information [7, 8].”
Saurav, K., & Lidar, D. A. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.010335 · Cited by 3
“Namely, unlike in quantum error avoidance [21, 22] or correction [23–25], we explicitly avoid introducing any encoding or measurement-based feedback, whether classical or coherent [26].”
Cylindrical and Möbius Quantum Codes for Asymmetric Pauli Errors
Valentini, L., Forlivesi, D., & Chiani, M. (2025) · IEEE Transactions on Information Theory · doi:10.1109/tit.2025.3546769 · Cited by 5
“In fact, despite the increased overhead associated with CSS codes compared to their non-CSS counterparts, their use simplifies the design of fault-tolerant quantum computing procedures [19], [20].”
Constructing quantum error correcting code via logic function
Shuqin, Z., Ma, Z., & Ya-jie, X. (2010) · Science China Information Sciences · doi:10.1007/s11432-010-0060-6 · Cited by 3
A New Error Correction Intuitive Approach in Quantum Communications Protocols
Aris, S., Nadjim, M., & Benslama, M. (2007) · American Journal of Applied Sciences · doi:10.3844/ajassp.2007.597.604 · Cited by 3
“These methods have been developed much further by a large number of researchers, notably Gottesman [23] and Calderbank et al [24] , who developed a powerful framework for the study of quantum codes and by Preskill [25] and Shor [26] , who developed methods for performing quantum information…”
MethodA fermionic code related to the exceptional group E 8
Lévay, P., & Holweck, F. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aac192 · Cited by 3
Topological Quantum Codes from Lattices Partition on the n-Dimensional Flat Tori
de Carvalho, E. D., Soares, W. S., & da Silva, E. B. (2021) · Entropy · doi:10.3390/e23080959 · Cited by 3
“In 1996, a fundamental step in the quantum coding theory was made due to the discovery of a new class of codes, now known as CSS codes, by Robert Calderbank, Peter Shor and Andrew Steane [1,2] and which originated a richer code structure—the stabilizer quantum codes [3].”
BackgroundLaflamme, R., & Knill, E. H. (2000) · Springer eBooks · doi:10.1007/978-94-010-0948-5_7 · Cited by 3
Quantum error precompensation for quantum noisy channels
Zhang, C., Li, L., Lu, G., Yuan, H., & Duan, R. (2022) · Physical Review A · doi:10.1103/physreva.106.042440 · Cited by 3
Stabilizer quantum codes defined by trace-depending polynomials
Galindo, C., Hernando, F., Martín-Cruz, H., & Ruano, D. (2022) · Finite Fields and Their Applications · doi:10.1016/j.ffa.2022.102138 · Cited by 3
“Seminal papers on quantum error-correcting codes studied binary codes [8, 9, 19] (see also [2, 3, 22]).”
BackgroundNew quantum surface codes from semi-regular tessellations
da Silva, E. B., Brizola, E. M., Soares, W. S., & Copatti, D. F. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04147-2 · Cited by 3
“CSS codes are part of an even more general class of quantum codes called stabilizer codes, [13].”
BackgroundMethodNew three- and four-dimensional toric and burst error-correcting quantum codes
Trinca, C. C., Palazzo, R., Watanabe, R. A., de Albuquerque, C. D., Interlando, J. C., & de Andrade, A. A. (2024) · Quantum Information Processing · doi:10.1007/s11128-023-04213-9 · Cited by 3
“Thus, C = {| ψ〉 ∈ H | M | ψ〉 = | ψ〉, ∀ M ∈ S} [17].”
Stabilizer Codes with Exotic Local-dimensions
Gunderman, L. G. (2024) · Quantum · doi:10.22331/q-2024-02-12-1249 · Cited by 4
“One of the earliest theoretical methods for correcting quantum information is the stabilizer formalism which encapsulated many of the existing example schemes and put them into a general framework [1], [2].”
BackgroundAll-optical correlated noisy channel and its application in recovering quantum coherence
Lei, D., Guo, D., Xin, J., & Lu, X.-M. (2024) · Physical Review A · doi:10.1103/physreva.109.062410 · Cited by 3
Generalizing Quantum Tanner Codes
Mostad, O. Å., Rosnes, E., & Lin, H.-Y. (2024) · doi:10.1109/isit-w61686.2024.10591772 · Cited by 2
“CSS codes allowing to build a quantum code from two classical codes with the requirement that the dual of one should be contained in the other [3], [4] were introduced shortly after and then followed by quantum stabilizer codes [5], [6] which are in many ways analogous to classical linear codes.”
BackgroundCelestial Quantum Error Correction. Part II. From qudits to celestial CFT
Guevara, A., & Hu, Y. (2025) · Journal of High Energy Physics · doi:10.1007/jhep06(2025)121 · Cited by 3
“This picture is one of our guiding motivations, and even though not strictly necessary for the construction, we find it useful to keep in mind.”
Quantum CSS Duadic and Triadic Codes: New Insights and Properties
Dastbasteh, R., Larrarte, O. S., Martínez, J. E., iOlius, A. D., del Moral, J. O., & Crespo, P. M. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-81824-0_5 · Cited by 3
Hardware-optimal quantum algorithms
Muroya, S., Chatterjee, K., & Henzinger, T. A. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2419273122 · Cited by 6
Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes
Chen, X., Zhao, L.-Y., Xu, G., Pan, X.-B., Chen, S., Cheng, Z., & Yang, Y. (2021) · Chinese Physics B · doi:10.1088/1674-1056/ac3817 · Cited by 3
(2018) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789813238411_0015 · Cited by 3
Williams, C. P. (2010) · Texts in computer science · doi:10.1007/978-1-84628-887-6_14 · Cited by 3
Quantum Communication and Decoherence
Aschauer, H., & Briegel, H. J. (2002) · Lecture notes in physics · doi:10.1007/3-540-45855-7_6 · Cited by 3
“The observable M1 = σz,1σz,2, for example, tells us whether on qubit 1 or 2 a spin flip has occurred without revealing any information on which of the qubits: M1(|000〉 + |111〉) = +(|000〉 + |111〉), M1(|100〉 + |011〉) = 3 These observables generate an Abelian group, the so-called stabilizer of the Shor code [23].”
BackgroundMethodInfluentialGhiu, I., & Ghiu, C. (2014) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(14)60031-8 · Cited by 3
How to Combat Quantum Bursts of Errors Efficiently
Guo, Y., & Zeng, G. (2006) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.75.034402 · Cited by 3
Cryptanalysis of an Improved Flexible Ping-Pong Protocol in Perfect and Imperfect Quantum Channels
Bin-Bin, Z., Da-Qing, W., Huang, S.-S., & Yu, L. (2009) · Chinese Physics Letters · doi:10.1088/0256-307x/26/10/100305 · Cited by 3
Dephasing in nonlinear quantum scissors systems
Kowalewska-Kudłaszyk, A. (2012) · Optics Communications · doi:10.1016/j.optcom.2012.06.093 · Cited by 3
Scattering theory in relation to quantum computing
Myers, J. M., & Wu, T. T. (2007) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.721693 · Cited by 2
“(14) The result is decoherence Imp(ρ) ∼ ∫ T/2”
Conditions for degradability of tripartite quantum states
Fung, C. F., Li, C.-K., Sze, N.-S., & Chau, H. F. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/11/115306 · Cited by 3
“1 Introduction In quantum information processing, information is often encoded in quantum states which are transformed under quantum computation in order to carry out tasks such as the generation of secret keys [1, 2], encoding of error correcting codes [3, 4, 5, 6], and secret sharing [7, 8].”
BackgroundQuantum Computation: Theory and Implementation
Boyden, E. S. (1999) · Cited by 3
Cabello, A., Gühne, O., Moreno, P., & Rodríguez, D. (2008) · Laser Physics · doi:10.1134/s1054660x08030249 · Cited by 3
Protograph Quantum LDPC Codes from Tensor Product of Parity-Check Matrices
Xie, Y., & Yuan, J. (2015) · IEEE Globecom Workshops (GC Wkshps) · doi:10.1109/glocomw.2015.7414205 · Cited by 3
“A Stabilizer code is a code space CS that is stabilized by an Abelian subgroup S of the N -qubit Pauli group PN , such that all the elements of S simultaneously generate eigenvalues +1 [5].”
BackgroundMethodGeneralized Concatenation for Quantum Codes
Grassl, M., Shor, P. W., & Zeng, B. (2009) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 3
Kasirajan, V. (2021) · Springer eBooks · doi:10.1007/978-3-030-63689-0_9 · Cited by 3
Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
Burkard, G., Engel, H., & Loss, D. (2002) · Springer eBooks · doi:10.1007/978-94-010-0419-0_4 · Cited by 3
A stabilizer code for uncorrelated errors can correct spatially correlated ones
Hayashi, T., Arimitsu, T., Kitajima, S., & Shibata, F. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/24/f04 · Cited by 3
Grassl, M. (2016) · Wiley eBooks · doi:10.1002/9783527805785.ch7 · Cited by 3
Quantum Cyclic CodePreprint
Dutta, S., & Kurur, P. P. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1007.1697 · Cited by 4
“obtained from classical cyclic codes via the CSS construction. However, the codes that we study are much more general. In particular, we construct cyclic stabiliser codes with parameters [[5,1,3]], [[17,1,7]] and [[17,9,3]], all of which are not CSS. The [[5,1,3]] code is the well known Laflamme code and to the best of…”
BackgroundMethodInfluential5-qubit quantum error correction in a charge qubit quantum computerPreprint
Touchette, D., Ali, H., & Hilke, M. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1010.3242 · Cited by 5
Dynamical Aspects of Information Storage in Quantum-Mechanical SystemsPreprint
Raginsky, M. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0207162 · Cited by 3
“Using the theory of the so-called stabilizer codes [51], it can be shown that the dimension of the protected subspace is equal to 2 = 4.”
MethodMatsumoto, R. (2002) · Physical Review A · doi:10.1103/physreva.66.059901 · Cited by 4
Three quantum error-correcting codes constructed from self-orthogonal codes over GF(4)
Ma, Y., Li, R., Zhao, X., & Feng, Y. (2007) · International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS) · doi:10.1109/ispacs.2007.4446005 · Cited by 2
“Quaternary code, self-orthogonal code, linear quantum error-correcting code”
MethodBeyond Stabilizer Codes II: Clifford CodesPreprint
Klappenecker, A., & Roetteler, M. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0010076 · Cited by 3
“We recover the definition of binary stabilizer codes as used in [2], [3] by taking E to be the generalized extraspecial 2-group which is generated by k-fold tensor products of Pauli matrices.”
BackgroundMethodSeveral Classes of Concatenated Quantum Codes: Constructions and BoundsPreprint
Fujita, H. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0608063 · Cited by 3
“Gottesman states code concatenation in his PhD thesis and gives the stabilizer of a quantum code constructed by concatenating the five-qubit code with itself.”
MethodRobust universal Hamiltonian quantum computing using two-body interactionsPreprint
Marvian, M., & Lloyd, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.01354 · Cited by 6
“We first briefly review subsystem stabilizer codes [13] which are the generalization of subspace stabilizer codes [14].”
MethodRobust decoding in monitored dynamics of open quantum systems with Z_2 symmetryPreprint
Li, Y., & Fisher, M. P. A. (2021) · arXiv (Cornell University) · Cited by 3
Towards fault-tolerant quantum computation with higher-dimensional systems
Anwar, H. (2014) · UCL Discovery (University College London) · Cited by 3
Design of Regular Reversible Quantum Circuits
Shah, D. (2000) · doi:10.15760/etd.129 · Cited by 4
“[Gottesman96] D. Gottesman, ―”
Single-shot quantum error correction with the three-dimensional subsystem toric code
Kubica, A., & Vasmer, M. (2022) · Nature Communications · doi:10.1038/s41467-022-33923-4 · Cited by 49
Ternary Quantum Codes Constructed from a Class of Quasi-Twisted Codes
Li, Z., Li, R., Guan, C., Lü, L., Song, H., & Fu, Q. (2024) · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · doi:10.1587/transfun.2024eap1055 · Cited by 2
“Gottesman [4] articulates the theory of stabilizer quantum codes through mathematical tools such as group theory.”
Quantum internet building blocks state of research and development
Meddeb, A. (2025) · Computer Networks · doi:10.1016/j.comnet.2025.111151 · Cited by 5
Applications of Quantum Computing in AI
Mummadi, S., Jambek, A. B., Siripuram, A., Vadla, S., & Mohammed, N. (2025) · Advances in computational intelligence and robotics book series · doi:10.4018/979-8-3373-1210-1.ch001 · Cited by 2
CaliQEC: In-situ Qubit Calibration for Surface Code Quantum Error Correction
Fang, X., Yin, K., Zhu, Y., Ruan, J., Tullsen, D. M., Liang, Z., Sornborger, A. T., Li, A., Humble, T. S., Ding, Y., et al. (2025) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1145/3695053.3731042 · Cited by 6
“Each syndrome qubit is linked to a stabilizer [24, 25, 55], a Pauli operator involving adjacent data qubits, as shown in Fig.3b,c.”
Fault tolerance against amplitude-damping noise using Bacon-Shor codes
My, L. D. H., Jayashankar, A., Mandayam, P., & Ng, H. K. (2025) · Physical Review Research · doi:10.1103/89td-45nl · Cited by 2
Sunami, S., Hirano, Y., Hinokuma, T., & Yamasaki, H. (2026) · PRX Quantum · doi:10.1103/tz8f-6xwk · Cited by 3
Techniques for Formal Modelling and Analysis of Quantum Systems
Gay, S. J., & Nagarajan, R. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-38164-5_18 · Cited by 2
Symplectic isometries of stabilizer codes
Pllaha, T. (2018) · Journal of Algebra and Its Applications · doi:10.1142/s0219498820500218 · Cited by 5
The Gilbert-Varshamov Bound for Stabilizer Codes Over $\mathbb{Z}_m$
Tang, N., Li, Z., Xing, L., & Zhang, M. (2018) · IEEE Access · doi:10.1109/access.2018.2865918 · Cited by 2
“Gottesman [2] showed that quantum codes can be represented by stabilizers in an appropriate error group.”
BackgroundMutually Unbiased Bases and Their Symmetries
Alber, G., & Charnes, C. (2019) · Quantum Reports · doi:10.3390/quantum1020020 · Cited by 2
“Current applications range from quantum state discrimination [2] and quantum state reconstruction [3,4], to quantum error correction [5,6] and quantum key distribution [7].”
BackgroundMUB-like structures and tomographic reconstruction for N -ququart systems
Guevara, J. J. J. D., Sainz, I., & Klimov, A. B. (2021) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ac07ea · Cited by 2
Some quantum synchronizable codes with explicit distance
Liu, T., & Kai, X. (2022) · Journal of Applied Mathematics and Computing · doi:10.1007/s12190-022-01811-1 · Cited by 2
“C1 = 〈m1(x)m2(x)m3(x)m4(x)m5(x)〉 and C2 = 〈m3(x)m4(x)m5(x)〉 are [48, 38, 6] and [48, 42, 4] cyclic codes overF7, respectively.”
Quantum Codes Do Not Increase Fidelity against Isotropic Errors
de Lacalle, J. G. L., Coronado, L. M. P., de Oliveira, A. L. F., & Martin-Cuevas, R. (2023) · Journal of Applied Mathematics and Physics · doi:10.4236/jamp.2023.112034 · Cited by 3
“developed: quantum error correction codes [1, 2, 3, 4, 5, 6] in combination with fault tolerant quantum computing [7, 8, 9, 10, 11, 12, 13].”
BackgroundBarbero-Lucas, B., Hernando, F., Martín-Cruz, H., & McGuire, G. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04297-x · Cited by 2
“Over the last twenty-five years, error-correction has proved to be one of the main obstacles to scaling up quantum computing and quantum information processing.”
BackgroundMultipartite standard nonlocality sharing by m-sided independent sequential observers
Sun, H., Guo, F.-Z., Dong, H., & Gao, F. (2024) · Quantum Information Processing · doi:10.1007/s11128-024-04460-4 · Cited by 2
An efficient combination of quantum error correction and authentication
Dulek, Y., Muguruza, G., & Speelman, F. (2025) · IACR Communications in Cryptology · doi:10.62056/ah2i5w7sf · Cited by 2
A coherence monotone from Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases
Liu, Y., Guo, Z., Ma, Z., & Fei, S.-M. (2025) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/add805 · Cited by 2
AMDS constacyclic codes and quantum AMDS codes
Dinh, H. Q., Nguyen, B. T., & Thi, H. L. (2024) · Filomat · doi:10.2298/fil2433889d · Cited by 2
Multiparty Quantum Secret Sharing of Classical Message Under Noisy Scenario
Basak, N., & Paul, G. (2025) · IEEE International Conference on Quantum Control, Computing and Learning (qCCL) · doi:10.1109/qccl65142.2025.11158800 · Cited by 1
Quantum error correction fundamentals
Djordjević, I. B. (2022) · Elsevier eBooks · doi:10.1016/b978-0-12-822942-2.00003-0 · Cited by 3
Multihop fault-tolerant joint remote state preparation of an arbitrary single-qubit state
Gong, R., & Jiang, M. (2022) · Journal of the Optical Society of America B · doi:10.1364/josab.464741 · Cited by 2
Enhanced quantum teleportation using multi-qubit logical states
Kim, D.-G., Anjum, A., Farooq, M. A., Mushtaq, A., & Shamsi, Z. H. (2023) · Results in Physics · doi:10.1016/j.rinp.2023.106565 · Cited by 2
Quantum Error Correction and Fault Tolerant Quantum Computing
Grassl, M., & Rötteler, M. (2011) · Springer eBooks · doi:10.1007/978-1-4614-1800-9_152 · Cited by 3
Feedback iterative decoding of sparse quantum codes
Wang, Y.-J., Bao-Ming, B., & Wang, X. (2010) · Acta Physica Sinica · doi:10.7498/aps.59.7591 · Cited by 2
Translating Between the Roots of the Identity in Quantum Computers
Castryck, W., Demeyer, J., Vos, A. D., Keszöcze, O., & Soeken, M. (2018) · IEEE International Symposium on Multiple-Valued Logic (ISMVL) · doi:10.1109/ismvl.2018.00051 · Cited by 2
“The Clifford group is a finite group and has applications in so-called stabilizer circuits [2] while the Clifford+T group can be used for the exact synthesis of all unitary matrices [4], [3].”
MethodLie algebras and suppression of decoherence in open quantum systems
Ritter, W. G. (2005) · Physical Review A · doi:10.1103/physreva.72.012305 · Cited by 2
Bipartite entanglement and hypergraph states
Qu, R., Shang, B.-J., Wang, J., Bao, Y.-R., Li, Z.-S., Ma, Y.-P., & Song, D. (2014) · Quantum Information Processing · doi:10.1007/s11128-014-0890-z · Cited by 2
“Although graph states can describe a large family of entangled states including cluster states [7], GHZ states, stabilizer states [8,9], it is clear that they cannot represent all entangled states.”
BackgroundPhysical Implementation of Large-Scale Quantum Computation
Suominen, K. (2012) · Springer eBooks · doi:10.1007/978-3-540-92910-9_44 · Cited by 3
A new approach to constructing CSS codes based on factor graphs
Huisong, W., Jun, W., Du, Q., & Zeng, G. (2007) · Information Sciences · doi:10.1016/j.ins.2007.10.027 · Cited by 2
Almlöf, J., & Bjork, G. G. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.09.006 · Cited by 2
Metadata
- Authors
- Gottesman, D.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Gottesman, Daniel
- ORCID
- Gottesman, Daniel
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1996-09-01
- Volume
- 54
- Issue
- 3
- Pages
- 1862-1868
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2069711632
- Cited by
- 1,227
- References
- 3
- Citations by year
- 2026: 26 · 2025: 75 · 2024: 48 · 2023: 56 · 2022: 45 · 2021: 65 · 2020: 44 · 2019: 36 · 2018: 34 · 2017: 36 · 2016: 33 · 2015: 32 · 2014: 41 · 2013: 38 · 2012: 34
- FWCI
- 38.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (FG0392ER40701)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum error-correcting codes, code construction, single error correction, qubit encoding, code rate, quantum information
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
