Hyperdimensional Quantum Approximate Optimization: Accelerating Quantum Advantage in Combinatorial Problems

<b>Hyperdimensional Quantum Approximate Optimization: Accelerating Quantum Advantage in Combinatorial Problems</b><b>Abstract:</b><br>This work introduces <b>Hyperdimensional Quantum Approximate Optimization Algorithm (HQAOA)</b>, an extension of QAOA that integrates <b>hyperdimensional resonance operators</b> to accelerate solution discovery in combinatorial optimization problems. We propose a novel Hamiltonian modification that embeds higher-order quantum correlations, enabling improved quantum mixing and non-local state transitions. The approach is benchmarked on <b>Max-Cut</b> problems, demonstrating enhanced performance in convergence speed, approximation ratio, and energy landscape exploration. By leveraging both quantum-inspired tensor representations and circuit optimizations, HQAOA presents a <b>new paradigm for quantum advantage</b> with reduced computational overhead.<b>Key Contributions:</b><br>✅ <b>Hyperdimensional Resonance Operator</b>: Introducing <b>H_d</b>, a structured interaction term that facilitates <b>non-local energy feedback</b> for more efficient optimization.<br>✅ <b>Enhanced Variational Quantum Optimization</b>: Extending QAOA to explore higher-dimensional solution spaces <b>beyond classical constraints</b>.<br>✅ <b>Empirical Benchmarks &amp; Feasibility</b>: Testing on small-scale quantum hardware (IBM Q, AWS Braket) and evaluating resilience to noise.<br>✅ <b>Quantum Acceleration Metrics</b>: Measuring HQAOA's <b>solution quality, convergence rates, and required quantum resources</b> relative to traditional QAOA.This research aligns with <b>XPRIZE Quantum's objective</b> of accelerating quantum advantage through real-world applications, setting a foundation for future explorations into <b>hyperdimensional quantum computing</b>.