| Abstract: |
Combinatorial optimization problems are pervasive in such important areas as logistics, finance, drug discovery and machine learning; however, most of them are NP-hard when formulated for classical computers which makes them prohibitively complex to solve. Quantum computing promises theoretically exponential speedup for some classical problem classes through algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). However, state-of-the-art Noisy Intermediate-Scale Quantum (NISQ) computers here matured in a niche with a few dozens of qubits and coherence times to measure this contest time in sub-second precision are presently limited by noisy sensor performance and have yet short coherence times. In this work we present the adaptive layered variational optimization (ALVO) framework, a new hybrid quantum-classical paradigm that overcomes these shortcomings with three major technical innovations: 1) An adaptive ansatz construction technique that dynamically grows circuit depth according to an analysis of the underlying optimization landscape, reducing gate needs by 47.3% while maintaining solution quality; 2) A hierarchical problem decomposition method for mapping large-scale problems onto available quantum resources through intelligent partitioning with classical coordination; and 3) A comprehensive error mitigation apparatus composed of zero-noise extrapolation, probabilistic error cancellation and post-selection to achieve achievable effective error rates below 10⁻³. Extensive experiments on IBM Quantum and Google Sycamore processors on benchmark problems such as MaxCut (up to 127 qubits), portfolio optimization (50 assets) and traveling salesman (20 cities) show that ALVO achieves approximations ratios within 3.2% of classical state-of-the-art using 5.4× less quantum operations. The framework provides a realistic set of guidelines for using quantum optimization on state-of-the-art hardware and predicts perf |
