Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering

Area of Science:

• Quantum computing
• Machine learning
• Optical communications

Background:

• Nearest-neighbor clustering is vital for optical-fibre signal decoding.
• Quantum k-means clustering has not yet achieved speed-ups for this application due to data embedding issues.
• Existing methods face inaccuracies and slowdowns in quantum clustering for optical signals.

Purpose of the Study:

• To propose an improved embedding method for quantum machine learning algorithms, specifically for clustering optical-fibre signals.
• To develop and benchmark a 'quantum-inspired' classical clustering algorithm for optical-fibre communications.
• To enhance the accuracy and convergence rate of clustering algorithms in this domain.

Main Methods:

• Utilized the generalized inverse stereographic projection for improved embedding into the Bloch sphere for quantum distance estimation.
• Developed a classical clustering algorithm based on the generalized inverse stereographic projection and spherical centroid.
• Benchmarked the proposed classical algorithm's accuracy, runtime, and convergence using real-world optical-fibre communication data.

Main Results:

• The generalized inverse stereographic projection brings quantum distance estimation closer to classical performance.
• The proposed 'quantum-inspired' classical algorithm demonstrates improved accuracy and convergence rate compared to standard k-means.
• Optimizing the radius in the classical algorithm consistently enhances accuracy and convergence.

Conclusions:

• The generalized inverse stereographic projection offers a superior embedding strategy for quantum machine learning, exemplified by optical-fibre signal clustering.
• A novel classical clustering algorithm, inspired by quantum methods, provides practical improvements for optical-fibre communications.
• This work bridges quantum and classical approaches, offering a more efficient solution for signal decoding.