  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 jet-like 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(N^3) classical algorithm to an O(N^2) 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(N^2 log N) using a sorting strategy inspired by the
SISCone jet algorithm, which has no natural quantum counterpart. With a
parallel computing model, we achieve O(N log N) 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.
