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.
A Simple Alternative to Jet-Clustering Algorithms
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abstract
I describe a class of iterative jet algorithms that are based on maximizing a fixed function of the total 4-momentum rather than clustering of pairs of jets. I describe some of the properties of the simplest examples of this class, appropriate for jets at an $e^+e^-$ machine. These examples are sufficiently simple that many features of the jets that they define can be determined analytically with ease. The jets constructed in this way have some potentially useful properties, including a strong form of infrared safety.
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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.