Thrust can be computed in O(N^2) time with a Grover-based quantum algorithm under a sequential data-loading model, and in O(N^2 log N) time classically with sorting, but the quantum advantage is only formal for very restrictive memory models.
Jet reconstruction in hadronic collisions by Gaussian filtering
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abstract
A new algorithm for jet finding in hadronic collisions is presented. The algorithm, based on a Gaussian filter in $(\eta,\phi)$, is specifically intended for use in heavy ion collisions and/or for detectors with limited acceptance. The performance of the algorithm is compared to two conventional algorithms, a seedless cone algorithm and a $k_\perp$ algorithm, for Pythia simulated di-jet events in $\sqrt{s} = 200 \mathrm{GeV}$ $p + p$ collisions with $4 \mathrm{GeV}/c \le \sqrt{Q^2} \le 16 \mathrm{GeV}/c$. The Gaussian filter is found to perform as well as, and in some instances better than, the conventional algorithms.
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Quantum Algorithms for Jet Clustering
Thrust can be computed in O(N^2) time with a Grover-based quantum algorithm under a sequential data-loading model, and in O(N^2 log N) time classically with sorting, but the quantum advantage is only formal for very restrictive memory models.