A team of researchers led by Professor Kavan Modi from the Singapore University of Technology and Design (SUTD) has taken a conceptual leap into this complexity by developing a new quantum framework for analysing higher-order network data. Their work centres on a mathematical field called topological signal processing (TSP), which encodes more than connections between pairs of points but also among triplets, quadruplets, and beyond. Here, “signals” are information that lives on higher-dimensional shapes (triangles or tetrahedra) embedded in a network. The team introduced a quantum version of this framework, called Quantum Topological Signal Processing (QTSP). It is a mathematically rigorous method for manipulating multi-way signals using quantum linear systems algorithms. Unlike prior quantum approaches to topological data analysis, which often suffer from impractical scaling, the QTSP framework achieves linear scaling in signal dimension. It is an improvement that opens the door to efficient quantum algorithms for problems previously considered out of reach. The technical insight behind QTSP is in the structure of the data itself. Classical approaches typically require costly transformations to fit topological data into a form usable by quantum devices. However, in QTSP, the data’s native format is already compatible with quantum linear systems solvers, due to recent developments in quantum topological data analysis. This compatibility allows the team to circumvent a major bottleneck, efficient data encoding, while ensuring the algorithm remains mathematically grounded and modular. Still, loading data into quantum hardware and retrieving it without overwhelming the quantum advantage remains an unsolved challenge. Even with linear scaling, quantum speedups can be nullified by overheads in pre- and post-processing. The framework achieves linear scaling and has been demonstrated through a quantum extension of the classical HodgeRank algorithm, with potential applications in recommendation systems, neuroscience, physics and finance.