I-Chi Chen

Topological codes often rely on overcomplete parity-check matrices (PCMs) containing redundant metachecks to achieve single-shot error correction. Single-shot error correction is vital for reducing decoding latency and circuit depth, as it allows the decoder to correct both data and measurement errors from a single round of syndrome extraction. The prevailing consensus is that these explicit metachecks are a strict geometric prerequisite for single-shot capabilities. In this work, we investigate the decoding performance of CSS-T codes using both overcomplete PCMs of geometric codes (e.g., 3D color codes) and minimal PCMs of algebraic codes containing only linearly independent rows. By leveraging the heuristic A* search of the Tesseract decoder, we demonstrate that single-shot decoding properties are largely preserved even when using minimal PCMs without metachecks. Furthermore, simulations reveal that under realistic circuit-level depolarizing noise, the Tesseract decoder achieves similar logical accuracy on both overcomplete and minimal PCMs, whereas the minimum-weight-parity-factor (MWPF) decoder exhibits a performance degradation of over two orders of magnitude. These findings suggest a pathway to achieving high-accuracy, single-shot fault tolerance while utilizing significantly shallower and less resource-intensive syndrome extraction circuits.