A Novel Quantum Realization of Jet Clustering in High-Energy Physics Experiments

Exploring the application of quantum technologies to fundamental sciences holds the key to fostering innovation for both sides. In high-energy particle collisions, quarks and gluons are produced and immediately form collimated particle sprays known as jets. Accurate jet clustering is crucial as it retains the information of the originating quark or gluon and forms the basis for studying properties of the Higgs boson, which underlies teh mechanism of mass generation for subatomic particles. For the first time, by mapping collision events into graphs–with particles as nodes and their angular separations as edges–we realize jet clustering using the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical algorithm for addressing classical combinatorial optimization problems with available quantum resources. Our results, derived from 30 qubits on quantum computer simulator and 6 qubits on quantum computer hardware, demonstrate that jet clustering performance with QAOA is comparable with or even better than classical algorithms for a small-sized problem. This study highlights the feasibility of quantum computing to revolutionize jet clustering, bringing the practical application of quantum computing in high-energy physics experiments one step closer.

💡 Research Summary

The paper presents the first application of the Quantum Approximate Optimization Algorithm (QAOA) to jet clustering, a fundamental task in high‑energy particle physics. Jets are collimated sprays of particles originating from quarks and gluons produced in collisions; accurate clustering is essential for reconstructing the underlying parton kinematics and for precision studies of the Higgs boson at future electron‑positron colliders such as the CEPC.

The authors map each collision event onto an undirected weighted graph: particles become vertices, and the weight of an edge between two particles is defined as their angular separation. To keep the graph sparse, only the k largest‑weight edges incident on each vertex are retained, yielding a k‑regular graph. Jet clustering of two jets is then cast as a Max‑K‑cut problem with K = 2, i.e., a binary partition of the graph that maximizes the sum of edge weights crossing the cut.

In the QAOA framework, the problem Hamiltonian is ˆH_C = ½ ∑{(i,j)∈E} w{ij}(I − σ_z^iσ_z^j) and the mixer Hamiltonian is ˆH_M = ∑_i σ_x^i. The algorithm alternates p layers of unitary evolutions e^{−iβ_l H_M}e^{−iγ_l H_C}, with the angles {β_l,γ_l} optimized by a classical optimizer (COBYLA combined with an interpolation scheme). For each event the circuit is sampled 1024 times; the bitstring with the lowest measured energy is taken as the clustering solution.

Two experimental regimes are explored. First, a noiseless quantum‑circuit simulator with 30 qubits processes 4000 events each containing 30 particles. The authors vary the QAOA depth (p = 1, 3, 5) and the graph connectivity parameter k (2 – 8). Depths of 3 and 5 give markedly better performance than depth 1, and the optimal k is found to be 7, balancing graph richness against circuit complexity. Performance is quantified by the sum of the angular deviations between the reconstructed jets and the true quark directions; lower sums indicate better clustering.

Second, the algorithm is executed on real hardware: the BAQIS Quafu cloud’s superconducting Baihua processor (123 qubits, average T₁≈74 µs, T₂≈29 µs, single‑qubit fidelity 99.9 %, two‑qubit CZ fidelity 98.8 %). Because of limited qubit connectivity and noise, the study is restricted to 6‑particle events using only 6 qubits. The compiled circuit contains 34 CNOT gates, 27 single‑qubit rotations, and a depth of 26. With QAOA depth = 1 and k = 2, the hardware results on 1217 events match the noiseless simulator, demonstrating that even on current NISQ devices the method can achieve competitive accuracy.

For benchmarking, the authors compare QAOA against two classical jet‑clustering algorithms: k‑Means (using angular distance) and the e⁺e⁻ kt algorithm (the standard sequential recombination method with distance d_{ij}=2 min(E_i²,E_j²)(1−cosθ_{ij})). QAOA’s performance is comparable to e⁺e⁻ kt and consistently superior to k‑Means, indicating that quantum variational optimization can rival state‑of‑the‑art classical techniques for this problem size.

The discussion acknowledges the present hardware limitations—noise, decoherence, and restricted qubit connectivity—that cap the size of solvable instances. Nevertheless, the study shows that careful choice of graph sparsity (k) and shallow circuit depth can mitigate these issues, allowing meaningful results on existing quantum processors. The authors outline future directions: scaling to larger qubit counts, handling multi‑jet (K > 2) scenarios, integrating error‑mitigation strategies, and applying the method to real data from the LHC or CEPC.

In conclusion, the work demonstrates that QAOA can be successfully adapted to a realistic high‑energy‑physics data‑analysis task, achieving performance on par with leading classical algorithms for small‑scale problems. This constitutes a concrete step toward practical quantum‑computing applications in particle physics and suggests that continued advances in quantum algorithms and hardware will enable tackling increasingly complex combinatorial problems in fundamental science.