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Paper 1

Optimizing Qubit Mapping with Quasi-Orthogonal Space-Time Block Codes and Quaternion Orthogonal Designs

Valentine Nyirahafashimana, Nurisya Mohd Shah, Umair Abdul Halim, Mohamed Othman, Sharifah Kartini Said Husain

Year

2024

Journal

arXiv preprint

DOI

arXiv:2412.06145

arXiv

2412.06145

This study explores the qubit mapping through the integration of Quasi-Orthogonal Space-Time Block Codes (QOSTBCs) with Quaternion Orthogonal Designs (QODs) in quantum error correction (QEC) frameworks. QOSTBCs have gained prominence for enhancing performance and reliability in quantum computing and communication systems. These codes draw on stabilizer group formalism and QODs to boost error correction, with QOSTBCs mapping logical qubits to physical ones, refines error handling in complex channels environments. Simulations results demonstrate the effectiveness of this approach by comparing the percentage improvement under various detected and corrected error conditions for four different cases, \textbf{$Z_1$} up to \textbf{$Z_4$}. The obtained simulations and implemental results show that QOSTBCs consistently achieve a higher correction improvement percentage than stabilizer Group for \textbf{$Z_1$}, \textbf{$Z_2$}, and \textbf{$Z_4$}; QOSTBCs can correct more errors than those detected, achieving over 100\% correction rates for first two cases, which indicates their enhanced resilience and redundancy in high-error environments. While for \textbf{$Z_3$}, stabilizer consistently remains above that of QOSTBCs, reflecting its slightly better performance. These outcomes indicate that QOSTBCs are reliable in making better logarithmic efficiency and error resilience, making them a valuable asset for quantum information processing and advanced wireless communication.

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Paper 2

Lottery BP: Unlocking Quantum Error Decoding at Scale

Yanzhang Zhu, Chen-Yu Peng, Yun Hao Chen, Yeong-Luh Ueng, Di Wu

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.00038

arXiv

2605.00038

To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code, toric code, and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. This paper contributes in three aspects, including decoder, decoder architecture, and decoding simulator. First, we propose Lottery BP, a decoder that introduces randomness during decoding. Lottery BP improves the decoding accuracy over BP by 2~8 orders of magnitude for topological codes. To efficiently decode multi-round measurement errors, we propose syndrome vote as a pre-processing step before Lottery BP, which compresses multiple rounds of syndromes into one. Syndrome vote increases the latency margin of decoding and mitigates the backlog problem. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, and it is configurable for surface/toric code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., 3~5 orders of magnitude less for topological codes. Third, to evaluate decoders fairly, we develop a PyTorch-based decoding simulator, Syndrilla, that modularizes the simulation pipeline and allows to extend new decoders flexibly. We formulate multiple metrics to quantify the performance of decoders and integrate them in Syndrilla. Running on GPUs, Syndrilla is 1~2 orders of magnitude faster than CPUs.

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