Quantum Tanner code[1]




Minimum distance bound obtained using robustness of dual tensor-product codes [2].


Asymptotically good QLDPC codes.


Linear-time decoder similar to the small-set-flip decoder for quantum expander codes [3].Linear-time decoder [4].Logarithmic-time decoder [2].


Used to obtain explicit lower bounds in the sum-of-squares game [5].States that, on average, achieve small violations of check operators for quantum Tanner codes require a circuit of non-constant depth to make. They are used in the proof [6] of the No low-energy trivial states (NLTS) conjecture [7].


For details, see talk by A. Leverrier.



  • Rotated surface code — Specializing the quantum Tanner construction to the surface code yields the rotated surface code [8][9].


  • Good QLDPC code — Quantum Tanner code construction yields asymptotically good QLDPC codes.
  • Tanner code — Tanner codes are used in constructing quantum Tanner codes.
  • Tensor-product code — Tensor codes are used in constructing quantum Tanner codes.
  • Expander lifted-product code — Quantum Tanner codes are an attempt to construct asymptotically good QLDPC codes that are similar to but simpler than expander lifted-product codes; see Ref. [4] for connection between the codes.
  • CSS classical product code — A \([[512,174,8]]\) classical-product code performed well [10] against erasure and depolarizing noise when compared to a member of an asymptotically good quantum Tanner code family.
  • Left-right Cayley complex code — Applying the CSS construction to two left-right Cayley complex codes yields quantum Tanner codes, and one can simultaneously prove a linear distance for the quantum code and local testability for one of its constituent classical codes [1].


Anthony Leverrier and Gilles Zémor, “Quantum Tanner codes”. 2202.13641
Anthony Leverrier and Gilles Zémor, “Decoding quantum Tanner codes”. 2208.05537
Shouzhen Gu, Christopher A. Pattison, and Eugene Tang, “An efficient decoder for a linear distance quantum LDPC code”. 2206.06557
Anthony Leverrier and Gilles Zémor, “Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes”. 2206.07571
Max Hopkins and Ting-Chun Lin, “Explicit Lower Bounds Against $Ω(n)$-Rounds of Sum-of-Squares”. 2204.11469
Anurag Anshu, Nikolas P. Breuckmann, and Chinmay Nirkhe, “NLTS Hamiltonians from good quantum codes”. 2206.13228
M. H. Freedman and M. B. Hastings, “Quantum Systems on Non-$k$-Hyperfinite Complexes: A Generalization of Classical Statistical Mechanics on Expander Graphs”. 1301.1363
Nikolas P. Breuckmann, private communication, 2022
Anthony Leverrier, Mapping the toric code to the rotated toric code, 2022.
Dimiter Ostrev et al., “Classical product code constructions for quantum Calderbank-Shor-Steane codes”. 2209.13474
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Zoo Code ID: quantum_tanner

Cite as:
“Quantum Tanner code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/quantum_tanner
@incollection{eczoo_quantum_tanner, title={Quantum Tanner code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_tanner} }
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Cite as:

“Quantum Tanner code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/quantum_tanner

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/qldpc/quantum_tanner.yml.