  In this paper, we present the Parallel Quantum Rapidly-Exploring Random Tree
(Pq-RRT) algorithm, a parallel version of the Quantum Rapidly-Exploring Random
Trees (q-RRT) algorithm. Parallel Quantum RRT is a parallel quantum algorithm
formulation of a sampling-based motion planner that uses Quantum Amplitude
Amplification to search databases of reachable states for addition to a tree.
In this work we investigate how parallel quantum devices can more efficiently
search a database, as the quantum measurement process involves the collapse of
the superposition to a base state, erasing probability information and
therefore the ability to efficiently find multiple solutions. Pq-RRT uses a
manager/parallel-quantum-workers formulation, inspired by traditional parallel
motion planning, to perform simultaneous quantum searches of a feasible state
database. We present results regarding likelihoods of multiple parallel units
finding any and all solutions contained with a shared database, with and
without reachability errors, allowing efficiency predictions to be made. We
offer simulations in dense obstacle environments showing efficiency,
density/heatmap, and speed comparisons for Pq-RRT against q-RRT, classical RRT,
and classical parallel RRT. We then present Quantum Database Annealing, a
database construction strategy for Pq-RRT and q-RRT that uses a temperature
construct to define database creation over time for balancing exploration and
exploitation.
