Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called ``thrust'' in electron-positron collision events. We find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.
Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called ``thrust'' in electron-positron collision events. We find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.
Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jetlike separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A key component of our analysis is the consideration of realistic models for interfacing classical data with a quantum algorithm. With a sequential computing model, we show how to speed up the well-known O(N3) classical algorithm to an O(N2) quantum algorithm, including the O(N) overhead of loading classical data from N final-state particles. Along the way, we also identify a way to speed up the classical algorithm to O(N2logN) using a sorting strategy inspired by the siscone jet algorithm, which has no natural quantum counterpart. With a parallel computing model, we achieve O(NlogN) scaling in both the classical and quantum cases. Finally, we consider the generalization of these quantum methods to other jet algorithms more closely related to those used for proton-proton collisions at the Large Hadron Collider.
The currently predicted increase in computational demand for the upcoming High-Luminosity Large Hadron Collider (HL-LHC) event reconstruction, and in particular jet clustering, is bound to challenge present day computing resources, becoming an even more complex combinatorial problem. In this paper, we show that quantum annealing can tackle dijet event clustering by introducing a novel quantum annealing binary clustering algorithm. The benchmarked efficiency is of the order of 96%, thus yielding substantial improvements over the current quantum state-of-the-art. Additionally, we also show how to generalize the proposed objective function into a more versatile form, capable of solving the clustering problem in multijet events.
Clustering is one of the most frequent problems in many domains, in particular, in particle physics where jet reconstruction is central in experimental analyses. Jet clustering at the CERN's Large Hadron Collider (LHC) is computationally expensive and the difficulty of this task will increase with the upcoming High-Luminosity LHC (HL-LHC). In this paper, we study the case in which quantum computing algorithms might improve jet clustering by considering two novel quantum algorithms which may speed up the classical jet clustering algorithms. The first one is a quantum subroutine to compute a Minkowski-based distance between two data points, whereas the second one consists of a quantum circuit to track the maximum into a list of unsorted data. The latter algorithm could be of value beyond particle physics, for instance in statistics. When one or both of these algorithms are implemented into the classical versions of well-known clustering algorithms (K-means, affinity propagation, and kT-jet) we obtain efficiencies comparable to those of their classical counterparts. Even more, exponential speed-up could be achieved, in the first two algorithms, in data dimensionality and data length when the distance algorithm or the maximum searching algorithm are applied.
Experimental High-Energy Physics (HEP), especially the Large Hadron Collider (LHC) programme at the European Organization for Nuclear Research (CERN), is one of the most computationally intensive activities in the world. This demand is set to increase significantly with the upcoming High-Luminosity LHC (HL-LHC), and even more in future machines, such as the Future Circular Collider (FCC). As a consequence, event reconstruction, and in particular jet clustering, is bound to become an even more daunting problem, thus challenging present day computing resources. In this work, we present the first digital quantum algorithm to tackle jet clustering, opening the way for digital quantum processors to address this challenging problem. Furthermore, we show that, at present and future collider energies, our algorithm has comparable, yet generally lower complexity relative to the classical state-of-the-art kt clustering algorithm.
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of qubits and their connectivity, the QA hardware did not show such an advantage over classical methods in past benchmarking studies. Recent advancements in QA with more than 5000 qubits, enhanced qubit connectivity, and the hybrid architecture promise to realize the quantum advantage. Here, we use a quantum annealer with state-of-the-art techniques and benchmark its performance against classical solvers. To compare their performance, we solve over 50 optimization problem instances represented by large and dense Hamiltonian matrices using quantum and classical solvers. The results demonstrate that a state-of-the-art quantum solver has higher accuracy (~0.013%) and a significantly faster problem-solving time (~6561×) than the best classical solver. Our results highlight the advantages of leveraging QA over classical counterparts, particularly in hybrid configurations, for achieving high accuracy and substantially reduced problem solving time in large-scale real-world optimization problems.
Quantum annealing (QA) is a promising quantum computing paradigm for solving optimization problems. However, the performance of QA is often limited by issues such as slow convergence rates and sensitivity to parameter settings. This paper presents a novel optimization method designed to address these limitations. The approach introduces refined parameters and an adaptive strategy to enhance the algorithm's convergence speed and solution accuracy. We explore the application of this optimized QA method to complex problems, demonstrating its potential for improved performance. The core of the optimization lies in modifying the annealing schedule and incorporating a dynamic adjustment of the magnetic field strength, denoted as H(t), where t represents time. The objective function to be minimized is typically represented as E[s], where s is the state vector of the quantum annealer. We introduce a variance reduction technique, denoted as σ(t), which is dynamically adjusted based on the error estimates of the current state. The overall optimization process can be summarized as: minsE[s]subject todtdS=−β(t)E[s]−γ(t)H(t)s where β(t) is the annealing rate and γ(t) is the magnetic field strength. The adaptive strategy involves updating β(t) and γ(t) based on the error in the current solution, aiming to reduce the variance σ(t) and improve the convergence. The theoretical analysis suggests that this approach can significantly reduce the computational cost and improve the solution quality compared to traditional QA methods. Furthermore, we investigate the impact of different parameter settings on the algorithm's performance, highlighting the importance of careful tuning for optimal results. The results demonstrate a notable improvement in solution quality and convergence speed across various benchmark problems.