Adaptive Quantum Circuit Architecture for Combinatorial Optimization: Structured Amplitude Shaping and Real-Time Feedback on NISQ Hardware

This work presents a novel quantum circuit architecture that achieves consistent 4-6× performance improvements over standard quantum optimization methods on near-term quantum processors. The approach uses real-time ancilla feedback and structured amplitude shaping to bias quantum state evolution toward valid solution regions without requiring classical optimization loops or deep variational circuits. Key Contributions: Novel "meta-floor" architecture with dual-layer adaptive feedback system that monitors circuit evolution and applies corrections only when needed Real-time circuit modification based on intermediate ancilla measurements, enabling self-correction without external classical processing Structured amplitude shaping that directly encodes problem constraints in circuit geometry rather than penalty functions Comprehensive experimental validation across four distinct combinatorial problems on IBM quantum hardware Experimental Results: 3-Exact Cover: 19.82% solution success rate vs. 16.4% random baseline (21% relative improvement) Traveling Salesman (6-city): 7.61% success rate - first quantum hardware demonstration of symbolic TSP optimization MAXCUT (50-node): Consistent optimal cut values (65) across five independent hardware runs Graph 3-Coloring: 12.9% valid colorings achieved without penalty functions or QUBO encoding All results demonstrated on real quantum hardware without classical optimization loops, Grover oracles, or post-selection Technical Innovation: The architecture introduces adaptive quantum error correction (QEC) floor-shaping that engages correction only upon detecting symbolic drift, creating a "delayed decoherence" effect that allows structured collapse patterns to complete before environmental noise dominates. This technical report demonstrates reproducible improvements in combinatorial optimization on IBM and IonQ quantum processors using structured amplitude shaping and real-time ancilla feedback. Over 75,000 measurements across multiple problem classes confirm the predictions of entropy-guided dynamics. Companion work: The theoretical framework underlying these results is developed in Structured Quantum State Evolution: Exploring Entropy-Guided Dynamics as an Alternative to Standard Decoherence Models (Knudsen 2025a), available at DOI: https://zenodo.org/records/16937598 Significance: This research demonstrates that structured quantum circuits with adaptive feedback can consistently outperform variational and search-based quantum algorithms while remaining compatible with current NISQ hardware limitations. The approach represents a paradigm shift from energy-landscape optimization to geometric constraint encoding, opening new possibilities for practical quantum advantage in combinatorial optimization. Reproducibility: Complete experimental datasets (75,000+ measurements), OpenQASM circuit implementations, statistical analysis scripts, and visualization tools are publicly archived on Zenodo with permanent DOIs. All results independently validated across multiple IBM quantum processors (Sherbrooke, Brisbane). Open Science: Full experimental data, circuit source code, and analysis tools available for community validation and extension. © 2025 Kristopher Knudsen / Axion Metrics LLC. This work is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).You are free to share, adapt, and build upon this work for any purpose, provided appropriate credit is given.License details: https://creativecommons.org/licenses/by/4.0/ Contact: [email protected]