Prototype-Based Classifiers and Vector Quantization on a Quantum Computer-Implementing Integer Arithmetic Oracles for...

Area of Science:

• Quantum Computing
• Machine Learning
• Computational Science

Background:

• The superposition principle in quantum mechanics allows encoding vast solution spaces in single quantum states.
• Quantum algorithms like amplitude amplification and QAOA efficiently explore these spaces for optimal solutions.

Purpose of the Study:

• To propose quantum circuits for winner determination in prototype-based classification and representation learning.
• To investigate quantum search for nearest prototype identification and quantum optimization for prototype selection.

Main Methods:

• Design of quantum circuits operating on binary data representations.
• Development of arithmetic circuit-based oracles leveraging quantum parallelism.
• Integration of a novel oracle for prototype selection within a learning routine.

Main Results:

• Demonstrated quantum search algorithms for efficient nearest prototype identification.
• Implemented quantum optimization schemes for prototype selection, reducing auxiliary variables.
• Empirical validation of proposed oracles using PennyLane on synthetic datasets.

Conclusions:

• Quantum circuits offer a computationally efficient approach to winner determination in machine learning.
• The proposed methods leverage quantum parallelism for simultaneous mathematical operations.
• Novel oracles simplify prototype selection, avoiding complex binary optimization formulations.