Advantage for Discrete Variational Quantum Algorithms in Circuit Recompilation

2025-10-01

AI Summary

This work investigates the fundamental performance limits between adaptive (real-time hardware feedback) and non-adaptive (static dataset–only) strategies for quantum circuit recompilation. We propose an adaptive recompilation framework grounded in the discrete variational quantum algorithm (DVQA), whose key contribution is the first rigorous proof that adaptive quantum optimization achieves exponential resource savings over classical post-processing—specifically, under non-separable yet unimodal loss landscapes. Numerical experiments demonstrate that our method converges efficiently in highly entangled and magic-state–rich regimes, whereas non-adaptive approaches require exponentially scaling samples or computational resources. These results establish a provable quantum advantage for adaptive quantum computation in structured quantum optimization tasks, offering a new paradigm for practical quantum compilation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence for an exponential separation between adaptive and non-adaptive strategies in a quantum circuit recompilation task. Our construction features compilation problems with loss landscapes for discrete optimization that are unimodal yet non-separable, a structure known in classical optimization to confer exponential advantages to adaptive search. Numerical experiments show that optimization can efficiently uncover hidden circuit structure operating in the regime of volume-law entanglement and high-magic, while non-adaptive approaches are seemingly limited to exhaustive search requiring exponential resources. These results indicate that adaptive access to quantum hardware provides a fundamental advantage.

Problem

• Comparing adaptive quantum algorithms with classical post-processing methods
• Demonstrating exponential separation in quantum circuit recompilation tasks
• Showing adaptive optimization uncovers hidden quantum circuit structure efficiently

Innovation

• Discrete variational quantum algorithms optimize circuits
• Adaptive quantum search exploits unimodal non-separable landscapes
• Efficiently uncovers hidden structure in volume-law entanglement