  Clustering of charged particle tracks along the beam axis is the first step
in reconstructing the positions of hadronic interactions, also known as primary
vertices, at hadron collider experiments. We use a 2036 physical qubit D-Wave
quantum annealer to perform track clustering in a limited capacity on
artificial events where the positions of primary vertices and tracks resemble
those measured by the Compact Muon Solenoid experiment at the Large Hadron
Collider. The algorithm, which is not a classical-quantum hybrid but relies
entirely on quantum annealing, is tested on a variety of event topologies. We
demonstrate a deterministic graph-embedding of the problem on the D-Wave
Chimera architecture, a method for optimizing the coupling strengths within
logical qubits, and a method for optimizing annealing time. Further, we
benchmark it against simulated annealing on a commercial CPU constrained to the
same processor time per anneal as the physical annealer. We note a quantum
advantage against simulated annealing up to a 56 logical qubit problem that
involves 665 physical qubits on average. Our embedding and optimization
methods, and the benchmarking paradigm, can be applied generally to other
clustering problems on quantum annealers. This algorithm may be used as a
building-block for more sophisticated algorithms to reach the number of primary
vertices at the LHC.
