量子近似优化算法中依赖于参数的噪声鲁棒性
Parameter-Dependent Noise Resilience in the Quantum Approximate Optimization Algorithm
浏览论文内容
中文总结 AI 辅助
本研究针对QAOA受噪声影响的问题，推导了含噪声与无噪声电路输出总变差距离的参数相关上界，提出误差惩罚与截断搜索优化法，并将分析扩展至QAA，为提升量子算法噪声鲁棒性提供了理论与方法支撑。
中文摘要 AI 辅助
量子近似优化算法（QAOA）是一种用于求解组合优化问题的变分量子算法，被认为是近期量子硬件的有前景应用方向。然而，这类设备中的高噪声率会掩盖有意义的结果，因此理解并抑制噪声对算法输出的影响至关重要。本研究发现，算法在噪声存在时的稳定性依赖于其变分参数；利用泡利噪声模型，我们推导了含噪声与无噪声量子电路输出间总变差距离的上界，该上界是这些参数的函数。含噪声模拟的结果验证了该上界，并为噪声存在时参数生成的最佳方法提供了见解。我们还基于该上界引入了两种优化新方法：误差惩罚法和截断搜索法，以构建噪声鲁棒性。我们通过对QAOA取连续极限，将该分析扩展到了量子绝热算法（QAA）。
英文摘要
The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm used for solving combinatorial optimization problems, which is thought to be a promising application of near-term quantum hardware. However, high rates of noise in these devices can obscure meaningful results. Therefore, it is crucial to understand and suppress the effects of noise on the algorithm's output. Here, we find that the stability of the algorithm in the presence of noise is dependent on its variational parameters. Using a Pauli noise model, we derive an upper bound on the total variation distance between the noisy and noiseless circuit output as a function of these parameters. Results from noisy simulations support this bound and give insight into the best methods to use for parameter generation in the presence of noise. We also introduce new methods of optimization using error penalties and truncated search based on this bound to manufacture error resilience. We extend this analysis to the quantum adiabatic algorithm (QAA) by taking the continuous limit of the QAOA.
发表机构
- School of Mathematics, University of Bristol（布里斯托大学数学学院）
- Phasecraft Ltd.（Phasecraft有限公司）
机构由 AI 辅助整理，请以论文原文为准。
