Quantum Motif Clustering

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use approximate counting, and all them obtain square-root like speedups over fastest classical in various settings. In order to counting context clustering, we show that general weighted performance spectral is mostly left unchanged by presence constant (relative) errors edge weights. Finally, extend original analysis better understand role multiple `anchor nodes' motifs types relationships this method can cannot capture.