Qubit seriation: Undoing data shuffling using spectral ordering

With the advent of quantum and quantum-inspired machine learning, adaptingthe structure of learning models to match the structure of target datasets has beenshown to be crucial for obtaining high performance. Probabilistic models basedon tensor networks (TNs) are prime candidates to benefit from data-dependentdesign considerations, owing to their bias towards correlations that are localwith respect to the topology of the model. In this work, we use methods fromspectral graph theory to search for optimal permutations of model sites that areadapted to the structure of an input dataset. Our method uses pair-wise mutualinformation estimates from the target dataset to ensure that strongly correlated bitsare placed closer to each other relative to the model’s topology. We demonstratethe effectiveness of such prepossessing for probabilistic modeling tasks, findingsubstantial improvements in the performance of generative models based on matrixproduct states (MPS) across a variety of datasets. We also show how spectralembedding, a dimensionality reduction technique from spectral graph theory, canbe used to gain further insights into the structure of datasets of interest.