Dynamic Programming for Quantum Circuit Optimization with Error Modeling

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Quantum circuit optimization is a critical step in realizing the full potential of quantum computing. However, the inherent noise and decoherence present in quantum systems introduce significant challenges to traditional optimization techniques. This paper proposes a novel approach that leverages dynamic programming (DP) to optimize quantum circuits while explicitly incorporating probabilistic error models. The core idea is to extend the DP table to represent not only the cost (gate count) of minimizing the circuit but also the estimated error probability associated with each sub-circuit. This allows for a more accurate assessment of the trade-off between circuit complexity and fidelity. The algorithm iteratively builds the DP table, considering different circuit decompositions and their corresponding error rates. The resulting optimized quantum circuit minimizes the overall expected error, providing a more robust solution compared to purely gate-count-based optimization. The methodology is presented with detailed formulas and mathematical notation, providing a comprehensive understanding of the approach. This work addresses a key limitation of existing optimization methods by integrating error modeling directly into the dynamic programming framework.

DOI: 10.5281/zenodo.22333632

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