A bstract High-energy physics is replete with hard computational problems and it is one of the areas where quantum computing could be used to speed up calculations. We present an implementation of likelihood-based regularized unfolding on a quantum computer. The inverse problem is recast in terms of quadratic unconstrained binary optimization (QUBO), which has the same form of the Ising hamiltonian and hence it is solvable on a programmable quantum annealer. We tested the method using a model that captures the essence of the problem, and compared the results with a baseline method commonly used in precision measurements at the Large Hadron Collider (LHC) at CERN. The unfolded distribution is in very good agreement with the original one. We also show how the method can be extended to include the effect of nuisance parameters representing sources of systematic uncertainties affecting the measurement.
A bstract High-energy physics is replete with hard computational problems and it is one of the areas where quantum computing could be used to speed up calculations. We present an implementation of likelihood-based regularized unfolding on a quantum computer. The inverse problem is recast in terms of quadratic unconstrained binary optimization (QUBO), which has the same form of the Ising hamiltonian and hence it is solvable on a programmable quantum annealer. We tested the method using a model that captures the essence of the problem, and compared the results with a baseline method commonly used in precision measurements at the Large Hadron Collider (LHC) at CERN. The unfolded distribution is in very good agreement with the original one. We also show how the method can be extended to include the effect of nuisance parameters representing sources of systematic uncertainties affecting the measurement.
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.
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 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.
Abstract The reconstruction of charged particles will be a key computing challenge for the high-luminosity Large Hadron Collider (HL-LHC) where increased data rates lead to a large increase in running time for current pattern recognition algorithms. An alternative approach explored here expresses pattern recognition as a quadratic unconstrained binary optimization (QUBO), which allows algorithms to be run on classical and quantum annealers. While the overall timing of the proposed approach and its scaling has still to be measured and studied, we demonstrate that, in terms of efficiency and purity, the same physics performance of the LHC tracking algorithms can be achieved. More research will be needed to achieve comparable performance in HL-LHC conditions, as increasing track density decreases the purity of the QUBO track segment classifier.
Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical qubits and couplers of the quantum chip, from which a solution is read after a process called quantum annealing. However, this process is subject to multiple sources of biases, including poor calibration, leakage between adjacent qubits, control biases, etc., which might negatively influence the quality of the annealing results. In this work, we aim at mitigating the effect of such biases for solving constrained optimization problems, by offering a two-step method, and apply it to Graph Partitioning. In the first step, we measure and reduce any biases that result from implementing the constraints of the problem. In the second, we add the objective function to the resulting bias-corrected implementation of the constraints, and send the problem to the quantum annealer. We apply this concept to Graph Partitioning, an important NP-hard problem, which asks to find a partition of the vertices of a graph that is balanced (the constraint) and minimizes the cut size (the objective). We first quantify the bias of the implementation of the constraint on the quantum annealer, that is, we require, in an unbiased implementation, that any two vertices have the same likelihood of being assigned to the same or to different parts of the partition. We then propose an iterative method to correct any such biases. We demonstrate that, after adding the objective, solving the resulting bias-corrected Ising problem on the quantum annealer results in a higher solution accuracy.
Abstract Charged particle reconstruction or track reconstruction is one of the most crucial components of pattern recognition in high-energy collider physics. It is known to entail enormous consumption of computing resources, especially when the particle multiplicity is high, which will be the conditions at future colliders, such as the High Luminosity Large Hadron Collider and Super Proton–Proton Collider. Track reconstruction can be formulated as a quadratic unconstrained binary optimization (QUBO) problem, for which various quantum algorithms have been investigated and evaluated with both a quantum simulator and hardware. Simulated bifurcation algorithms are a set of quantum-annealing-inspired algorithms, known to be serious competitors to other Ising machines. In this study, we show that simulated bifurcation algorithms can be employed to solve the particle tracking problem. The simulated bifurcation algorithms run on classical computers and are suitable for parallel processing and usage of graphical processing units, and they can handle significantly large amounts of data at high speed. These algorithms exhibit reconstruction efficiency and purity comparable to or sometimes improved over those of simulated annealing, but the running time can be reduced by as much as four orders of magnitude. These results suggest that QUBO models together with quantum-annealing-inspired algorithms are valuable for current and future particle tracking problems.
The detection and localization of gamma-ray sources via maximum-likelihood analysis is a complex parameter optimization problem. We address this challenge using quantum annealing, a computational approach that solves optimization tasks by encoding them into the ground state of an Ising Hamiltonian. Specifically, we apply this method to observations from AGILE's Gamma-Ray Imaging Detector (GRID) in the 30 MeV-50 GeV band. We reformulated the standard analysis as a Quadratic Unconstrained Binary Optimization (QUBO) problem. We tested this method on a set of AGILE observations generated with AGILEpy, solving the QUBO with simulated quantum annealing. The method reproduces the classical flux and position estimates within their statistical uncertainty and identifies the correct grid node among the candidate positions in 97% of the maps. These promising results demonstrate that quantum annealing could be used in this optimization problem, laying the ground for its deployment on actual quantum annealers.