Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength

By Jean-Pierre Tillich, G. Zémor. IEEE Transactions on Information Theory, 2009

440 citations recorded by the source corpus.

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with a fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.

Subfields: Artificial Intelligence, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/4ec8143dad4bd2bec0352c6c8ad6be76292f9e8f

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Citations in the corpus

High-threshold and low-overhead fault-tolerant quantum memory (2023, positive): “Multiple variants of the LDPC codes have been proposed recently including hyperbolic surface codes [30], hypergraph product [31], balanced product codes [32], two-block codes based on finite groups [33, 34, 35, 36], and quantum Tanner codes [37, 38].”
Fusion-based quantum computation (2021, methodology): “We can introduce a notion of low-density parity check (LDPC) fusion networks that is analogous to other similar constructions in error correction [45, 46].”
Asymptotically good Quantum and locally testable classical LDPC codes (2021, background): “…that for every a, a ′ ∈ A , b, b ′ ∈ B , and r, r ′ ∈ R we have: and for every λ ∈ F q we get: We should note that if R = F q , then the lifted product is equivalent to the product construction from [29], while if, in addition, we have m = n = 1, then it is the same as the hypergraph product [31].”
Quantum error correction (2001, positive): “The main new idea in this direction was the hypergraph product code construction due to Jean-Pierre Tillich and Gilles Zémor [TZ14].”
The future of quantum computing with superconducting qubits (2022, background): “For example, quantum LDPC codes can achieve a constant encoding rate independent of the code size 44 .”