Jump code[13] 


A CE code designed to detect and correct amplitude damping errors. An \(((n,K))\) jump code is denoted as \(((n,K,t))_w\) (which conflicts with modular-qudit notation), where \(t\) is the maximum number of qubits that can be corrected after each one has undergone a jump error \(|0\rangle\langle 1|\), and where each codeword is a uniform superposition of qubit basis states with Hamming weight \(w\).


Various code bounds, including an upper bound on \(K\) given the other parameters, are provided in Ref. [3]. For example, one can apply bit flips to all qubits of an \(((n,K,t))_w\) jump code to obtain an \(((n,K,t))_{n-w}\) jump code.


An infinite family of jump codes asymptotically attains an upper bound on \(K\) [3; Thm. 27].


Survey of jump codes [4].



  • \([[4,2,2]]\) CSS code — The subcode \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) [1] is a \(((4,2,1))_2\) jump code correcting a single amplitude damping error. This code can be extended to a \(((4,3,1))_2\) jump code \(\{|\overline{01}\rangle,|\overline{10}\rangle,|\overline{11}\rangle\}\) [2].
  • Chuang-Leung-Yamamoto (CLY) code — Jump codes can be thought of as qubit analogues of uniform CLY codes.
  • \([[2m,2m-2,2]]\) error-detecting code — The subcode of the \([[2m,2m-2,2]]\) error-detecting code consisting of codewords labeled by weight-\(m\) bitstrings is a \(((2m,\frac{1}{2}{2m \choose m},1))_{m}\) optimal jump code [2][3; Corr. 9].
  • Combinatorial design code — Certain types of combinatorial designs can be used to obtain jump codes [2,3,5].
  • Self-dual linear code — Iso-dual codes can be used to construct jump codes [3].


G. Alber et al., “Stabilizing Distinguishable Qubits against Spontaneous Decay by Detected-Jump Correcting Quantum Codes”, Physical Review Letters 86, 4402 (2001) arXiv:quant-ph/0103042 DOI
G. Alber et al., “Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation”, Physical Review A 68, (2003) arXiv:quant-ph/0208140 DOI
T. Beth et al., Designs, Codes and Cryptography 29, 51 (2003) DOI
Jimbo, Masakazu, and Keisuke Shiromoto. "Quantum jump codes and related combinatorial designs." Information Security, Coding Theory and Related Combinatorics. IOS Press, 2011. 285-311.
Y. Lin and M. Jimbo, “Extremal properties of t-SEEDs and recursive constructions”, Designs, Codes and Cryptography 73, 805 (2013) DOI
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Zoo Code ID: jump

Cite as:
“Jump code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/jump
@incollection{eczoo_jump, title={Jump code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/jump} }
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Cite as:

“Jump code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/jump

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/nonstabilizer/jump.yml.