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Optimization-based Unfolding in High-Energy Physics

Simone Gasperini, Gianluca Bianco, Marco Lorusso, Carla Rieger, Michele Grossi

Abstract

In High-Energy Physics, unfolding is the process of reconstructing true distributions of physical observables from detector-distorted measurements. Starting from its reformulation as a regularized quadratic optimization, we develop a framework to tackle this problem 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.

Optimization-based Unfolding in High-Energy Physics

Abstract

In High-Energy Physics, unfolding is the process of reconstructing true distributions of physical observables from detector-distorted measurements. Starting from its reformulation as a regularized quadratic optimization, we develop a framework to tackle this problem 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.
Paper Structure (10 sections, 15 equations, 1 figure)

This paper contains 10 sections, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Unfolding problem definition
  4. State-of-the-art methods
  5. Log-likelihood maximization
  6. Methods
  7. Quadratic optimization problem formulation
  8. QUBO model formulation
  9. Results and discussion
  10. Conclusion

Figures (1)

  • Figure 1: Comparison of unfolding methods on four synthetic datasets. Each histogram contains $12$ equally spaced bins and $10\,000$ total events. The detector-level data are generated by applying Gaussian smearing, a fixed bias, and limited detection efficiency. True distributions are shown in blue, measured spectra in orange, and unfolded results as colored markers with statistical uncertainties. The methods compared are Matrix Inversion (MI), Iterative Bayesian Unfolding (IBU), Singular Value Decomposition (SVD), classical optimization using Gurobi (GRB), and hybrid quantum-classical solver (HYB).