October 17, 2025
While quantum error-correcting codes have been studied extensively, there is still ample design space to explore. The quantum LEGO (QL) framework, invented by Cao and Lackey, is a tensor network description of QEC codes that may facilitate the discovery of new codes. Duke Ph.D. student Balint Pato and Master's student June Vanlerberghe extended the QL framework with hyper-optimized contraction schedules, demonstrating significant performance advantages. The QL framework can also provide a deep analysis of QEC codes through weight enumerator calculations. Weight enumerator polynomials (WEPs) are notoriously hard to compute; in general, computing them is #P-hard. However, if the underlying code's entanglement is not too complex, the WEP calculation can be exponentially faster using the QL framework, with an optimal QL tensor network and contraction schedule. Well-known tensor network layouts, such as tree and grid structures, have been shown to achieve a large speedup over the brute-force, exponential solution. In the new preprint https://arxiv.org/abs/2510.08210, the students show that by combining QL with Cotengra (https://cotengra.readthedocs.io/), arbitrary layouts can be contracted. Furthermore, they showed that significantly better hyper-optimized contraction schedules can be found using a so-called Sparse Stabilizer Tensor (SST) cost function instead of the default Cotengra cost function. This work opens the possibility of analyzing the structure of QL layouts more rigorously and, hopefully, will lead to better QEC codes.
Balint Pato presented the work at the 27th annual SQuInT conference on October 10th in Albuquerque, New Mexico, alongside the International Balloon Fiesta and musical exploration of quantum computing with Mark Wilde and Cole Mauer.