AI summaryⓘ
The authors create simpler and faster decoders for certain quantum error-correcting codes, aiming to lessen how long decoding takes despite faults in the system. They focus on two main slow parts: a complicated cleanup step called order-statistics decoding (OSD), and the many extra nodes needed to track certain fault correlations during error checking. By noticing that specific faults cause recognizable error patterns, the authors design message-passing decoders that handle these patterns directly without extra nodes. Their approach uses insights from classical code decoders and treats some faults as equivalent to simpler syndrome measurement errors, which lowers complexity. Tests show their method reduces or matches error rates compared to traditional methods but with less effort in decoding.
Quantum LDPC codesDecoding latencyCircuit-level noiseOrder-statistics decoding (OSD)CNOT faultsStabilizer codesTrapping setsMessage-passing decoderPhenomenological Tanner graphLifted-product codes
Authors
Asit Kumar Pradhan, Nithin Raveendran, David Declercq, Bane Vasić
Abstract
We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes with the goal of reducing decoding latency. We target two major bottlenecks of decoding under the \emph{circuit-level} noise model: (i) post-processing via order-statistics decoding (OSD), and (ii) the large number of auxiliary variable nodes commonly introduced to represent CNOT-induced correlations during syndrome extraction. Our key observation is that propagating CNOT faults (\emph{hook errors}) create \emph{stabilizer-induced} trapping sets (TSs) that are intrinsic to hypergraph-product (HGP) and lifted-product (LP) constructions. Therefore, instead of modeling each such fault with an explicit correlation node and relying on OSD to clean up the resulting failures, we design message-passing decoders that resolve the corresponding \emph{stabilizer-induced} TSs directly. We obtain these decoders by deriving QLDPC decoders from decoders for the parent classical LDPC codes and using them collectively to correct broad families of \emph{stabilizer-induced} TSs. For CNOT faults that manifest primarily as syndrome errors, we show that their effect is equivalent to a data error together with syndrome-bit measurement errors. Consequently, given repeated measurements and a decoding graph that already includes nodes representing syndrome-bit errors, no distinct variable node is needed for each CNOT fault. Using a \emph{phenomenological} Tanner graph with nodes representing only data errors and syndrome-bit errors, simulations on the LP codes show a reduction in, or comparable, logical error rates relative to BP+OSD, at substantially lower decoding complexity.