Core Concepts
Quantum Tanner codes facilitate single-shot quantum error correction under adversarial noise, where a single round of constant-weight parity check measurements suffices to reliably correct errors even in the presence of measurement errors.
Abstract
The content discusses the problem of decoding quantum Tanner codes, a family of quantum low-density parity-check (QLDPC) codes with good parameters, in the presence of measurement errors.
Key highlights:
- Quantum Tanner codes admit computationally efficient decoding algorithms, such as the sequential and parallel mismatch decomposition decoders.
- The authors show that these decoders are single-shot, meaning they can reliably correct errors using a single round of noisy syndrome measurements.
- Specifically, the sequential decoder is shown to be (α=0, β)-single-shot, while the parallel decoder is (α, β)-single-shot for any α>0, with α decreasing exponentially with the number of parallel decoding iterations.
- The authors further analyze the performance of these single-shot decoders under multiple rounds of errors and decoding, showing that the residual error can be kept bounded under mild assumptions on the error and syndrome noise weights.
- The single-shot decoding property and the constant-time overhead of the parallel decoder make quantum Tanner codes attractive for fault-tolerant quantum computing protocols.
Stats
The content does not provide specific numerical data or metrics. It focuses on theoretical analysis and properties of the decoding algorithms.
Quotes
"Quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors."
"There exists a constant β such that the sequential decoder (Algorithm 1) is (α = 0, β)-single-shot."
"There exists a constant β such that for all α > 0, the O(log(1/α))-iteration parallel decoder (Algorithm 3) is (α, β)-single-shot."