Promising signals in quantum computing

Whenever we mull over what film to watch on Netflix, or deliberate between different products on an e-commerce platform, the gears of recommendation algorithms spin under the hood. These systems sort through sprawling datasets to deliver personalised suggestions. However, as data becomes richer and more interconnected, today’s algorithms struggle to keep pace with capturing relationships that span more than just pairs, such as group ratings, cross-category tags, or interactions shaped by time and context.

 

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.

 

In their recent paper, “Topological signal processing on quantum computers for higher-order network analysis”, 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.

 

“Much of the excitement around quantum computing lies in its potential to outperform classical computers in certain tasks,” said Prof Modi. “With QTSP, we’ve identified a class of problems—those with inherently higher-order structure—where this advantage could be more than just speculative.”

 

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.

 

“Quantum computing as a field is grappling with these issues,” explained Prof Modi. “But theoretical progress matters as it tells us where to look and what to build towards.”

 

To show how QTSP might be used in practice, the team applied it to a well-known classical algorithm called HodgeRank, commonly used in ranking problems like recommendation systems. This extension, detailed in a companion paper titled “Quantum HodgeRank: Topology-based rank aggregation on quantum computers”, demonstrates how QTSP can be plugged into existing frameworks to tackle real-world problems.

 

While classical HodgeRank handles pairwise comparisons, quantum HodgeRank allows for higher-order interactions. This enables systems to incorporate nuances like overlapping preferences among groups of users or cross-modal influences.

 

“When we look at recommendation systems through the lens of QTSP, we’re not just ranking things. We’re analysing how complex signals propagate across a network,” added Prof Modi.

 

While many of the immediate applications may remain classical, laying the theoretical foundation now helps prepare for a future where quantum hardware is robust enough to handle such tasks. The team’s framework could potentially influence fields where the shape of data matters: biology, chemistry, neuroscience, and finance among them.

 

One potential frontier is neuroscience, where some theorists have speculated that cognitive processes may be underpinned by topological structures.

 

“If information in the brain is processed via topological embeddings, our algorithm could, one day, support experimental neuroscience by pairing with quantum sensors and processors,” shared Prof Modi.

 

The team is currently focusing on refining the theory, finding stronger use cases and exploring new domains where topological and quantum tools might converge.

 

“We’re especially excited about applying these ideas to physics. There’s potential to study phases of matter in ways that classical tools don’t easily allow,” Prof Modi said.

 

He added: “Our research is in line with SUTD’s ethos of combining technology with thoughtful design—the QTSP framework was built to be modular and adaptable, ensuring that its mathematical components can be repurposed for diverse applications.”

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