arXiv subjects

Mainak Bhattacharyya

Publications and source records attributed to Mainak Bhattacharyya.

4 recordsLinked to original sources

arXiv2026

A Highly Accurate Fast Decoding Framework for QLDPC codes Accelerated by Noise Perturbation and Ensemble Decoding

A well-balanced decoder has been central to the development of modern fault-tolerant quantum computing. However, the inherent topologies of quantum error correcting codes can limit the performance of many well-studied decoding algorithms. In this work, we introduce Noise Assisted Ensemble Decoding (NAED), a highly accurate decoding framework with a significant advantage in real-time speed. NAED constructs an ensemble of Tanner forests, obtained as acyclic subgraphs of the original Tanner graph, and performs exact inference on each Tanner forest using a lightweight dynamic programming algorithm. The forest construction is guided by synthetic soft information derived jointly from the measured syndrome and channel statistics, with controlled noise perturbations generating diverse yet informative decoding matrix column orderings for the Tanner forest construction across the ensemble. Our benchmark results show that the proposed synthetic soft information-driven construction and inference on the Tanner forests can achieve improved or comparable decoding performances to the state-of-the-art decoding solutions, such as BP+OSD$0$, while also providing orders-of-magnitude improvements in per-round decoding speed under circuit-level noise.

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arXiv2025

Fault-tolerant syndrome extraction in [[n,1,3]] non-CSS code family generated using measurements on graph states

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.}

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arXiv2025

Decoding Quantum LDPC Codes using Collaborative Check Node Removal

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.

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arXiv2023

Quantum Approximation Optimization Algorithm for the Trellis based Viterbi Decoding of Classical Error Correcting Codes

We construct a hybrid quantum-classical Viterbi decoder for the classical error-correcting codes. Viterbi decoding is a trellis-based procedure for maximum likelihood decoding of classical error-correcting codes. In this article, we demonstrate that the quantum approximate optimization algorithm can find any path on the trellis with the minimum Hamming distance relative to the received erroneous vector. We construct a generalized method to map the Viterbi decoding problem into optimization of a parameterized quantum circuit for any classical linear block code. Also, we propose a uniform parameter optimization strategy to optimize the parameterized quantum circuit using a classical optimizer. We observe that the proposed method efficiently generates low-depth trainable parameterized quantum circuits. Our approach makes the hybrid decoder more efficient than previous attempts at making quantum Viterbi algorithm. We show that using uniform parameter optimization, we obtain parameters more efficiently for the parameterized quantum circuit than previously used methods such as random sampling and fixing the parameters.

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