Optimization-based Unfolding in High-Energy Physics

TL;DR

This paper introduces a novel optimization-based framework for unfolding in high-energy physics, leveraging quantum-compatible methods and an open-source Python package to improve distribution estimation from detector data.

Contribution

It reformulates unfolding as a quadratic optimization problem, derives a QUBO representation for quantum implementation, and benchmarks the approach against traditional methods.

Findings

Achieves competitive accuracy in reconstructing distributions.

Provides a quantum-compatible formulation for unfolding.

Demonstrates the effectiveness of the open-source QUnfold package.

Abstract

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 dataset 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.