Tesseract: A Dynamic Spacetime-Folding Decoder

Tesseract is a Most-Likely Error (MoLE) decoder designed for topological quantum error-correcting codes. It is built on two foundational principles: (1) dynamic exploration of a multi-dimensional solution space represented by a trellis-like data structure, and (2) recursive folding of both space and time dimensions to enhance efficiency. While Tesseract's worst-case runtime is exponential, it demonstrates strong practical performance at low error rates. To address performance challenges, the decoder employs an A* search algorithm for efficient traversal and utilizes a lazy Viterbi approach to optimize resource management. Benchmarking results show that Tesseract is competitive with integer programming-based decoders, particularly on surface and color code memory circuits, under moderately low physical error rates (e.g., SI1000 circle level noise with $p=0.001$).