基于优化的高能物理展开
Optimization-based Unfolding in High-Energy Physics
AI总结：
本文提出基于优化的展开方法，结合经典和量子算法，通过QUBO形式实现展开目标，对比传统方法验证了其在不同分布下的重建精度和正则化能力。
摘要：
在高能物理实验中，展开是指从探测器层面数据估计物理可观测量底层分布的问题，存在统计涨落和系统不确定因素。本文将展开重新表述为正则化二次优化问题，开发出经典和量子兼容的展开框架。推导出展开目标的二次无约束二元优化（QUBO）表示，允许在量子退火和混合量子-经典求解器上直接实现。所提方法在QUnfold开源Python包中实现，整合经典混合整数求解器和D-Wave混合量子求解器。通过合成数据集对比RooUnfold常用展开技术，包括响应矩阵求逆、迭代贝叶斯展开和奇异值分解展开。结果表明，基于优化的方法在多种分布下实现竞争性重建精度，同时自然地在目标函数中容纳正则化。本文建立了展开的统一优化视角，为探索量子增强的实验HEP数据分析提供了实用路径。
英文摘要：
In experimental High-Energy Physics, unfolding refers to the problem of estimating the underlying distribution of a physical observable from detector-level data, in the presence of statistical fluctuations and systematic uncertainties. Starting from its reformulation as a regularized quadratic optimization problem, we develop a framework to address unfolding using both classical and quantum-compatible methods. In particular, we derive a Quadratic Unconstrained Binary Optimization (QUBO) representation of the unfolding objective, allowing direct implementation on quantum annealing and hybrid quantum-classical solvers. The proposed approach is implemented in QUnfold, an open-source Python package integrating classical mixed-integer solvers and D-Wave's hybrid quantum solver. We benchmark the method against widely used unfolding techniques in RooUnfold, including response Matrix Inversion, Iterative Bayesian Unfolding, and Singular Value Decomposition unfolding, using synthetic datasets with controlled distortion effects. Our results demonstrate that the optimization-based approach achieves competitive reconstruction accuracy across multiple distributions while naturally accommodating regularization within the objective function. This work establishes a unified optimization perspective on unfolding and provides a practical pathway for exploring quantum-enhanced methods in experimental HEP data analysis.
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