Ankur Raina

Harsh Gupta, Mainak Bhattacharyya, Ritik Jain et al.

The reliability of quantum computation critically depends on the performance of quantum error-correcting codes (QECCs). Performance of QECCs can be severely degraded by hook errors, which effectively reduce the code distance. In this work, we construct a family of $[[n,1,3]]$ non-CSS QECCs, which are fault-tolerant (FT) against noisy syndrome measurements. We employ the bare-ancilla method of Muyuan Li \emph{et al.} to demonstrate fault tolerance against hook errors during syndrome extraction. We present a systematic protocol for generating these QECCs using graph codes and propose a family of $[[n,1,3]]$ codes that preserve the fault-tolerant properties of the bare ancilla codes. We use a custom lookup-table decoder and simulate the code's performance under both anisotropic and circuit-level depolarizing noise. Our results reveal a trade-off in performance with respect to the code rate and identify optimized codes under these noise models. We benchmark our results against the flag-qubit method of Chao \emph{et al}. Notably, we report a new bare ancilla code with improved code rate while maintaining the same distance compared to the bare code used in the work of Muyuan Li \emph{et al.}

Mainak Bhattacharyya, Ankur Raina

Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and efficient decoders. Iterative message passing-based decoders, although fast, fail to produce suitable success rates due to the colossal degeneracy and short cycles intrinsic to these codes. In this work we present a strategy to improve the performance of the Belief Propagation (BP) decoding, specifically the min-sum algorithm. We propose a collaborative decoding framework that integrates message passing with stabilizer check node removals. We further introduce the concept of ``qubit separation" and show that the improved decoding performance is directly related to the generation of highly separated trapped data qubits. To guide a more selective removal of check nodes that constrain the separation of the trapped data qubits, we introduce information measurements (IMs) for the data qubits and their adjacent stabilizer checks. We evaluate the performance of the proposed collaborative decoder on Generalized Hypergraph Product (GHP) codes and demonstrate that appropriate decoder configurations mitigate trapping sets in min-sum decoding without significant overhead.