Drone delivery packing problem on a neutral-atom quantum computer

TL;DR

This work addresses the Drone Delivery Packing Problem via a hybrid quantum-classical framework leveraging a neutral-atom quantum processing unit (QPU) and reformulate the optimization task as a graph-partitioning problem based on the independent sets of a scheduling graph that encodes delivery incompatibilities.

Abstract

Quantum architectures based on neutral atoms have gained significant attention in recent years as specialized computational machines due to their ability to directly encode the independent set constraint on graphs, exploiting the Rydberg blockade mechanism. In this work, we address the Drone Delivery Packing Problem via a hybrid quantum-classical framework leveraging a neutral-atom quantum processing unit (QPU). We reformulate the optimization task as a graph-partitioning problem based on the independent sets (ISs) of a scheduling graph that encodes delivery incompatibilities. Each partition corresponds to deliveries assigned to a single drone, with the objective of minimizing the total number of partitions. While the ISs represent time-feasible schedules, battery-duration constraints are enforced through a classical post-processing routine. This methodology enables the recovery of optimal delivery schedules, provided a sufficient number of samples is collected from the QPU to resolve the solution space. We benchmark the hybrid workflow through numerical emulations and demonstrate its effectiveness on Pasqal's Fresnel QPU, reporting hardware experiments with configurations of up to 100 atoms.

Figures (6)

• Figure 1: Delivery schedule for a DDPP instance with $N=8$ deliveries in the center of Turin, Italy. The DDPP is a (battery-constrained) minimum vertex coloring of the scheduling graph $\mathcal{G}$ shown in the inset, with edges indicating time-conflicting deliveries. The optimal solution is represented by nodes colors, which denote deliveries assigned to the same drone.
• Figure 2: Box plots showing the approximation ratio $\rho$ (left panel) and additive gap $\Delta$ (right panel) for DDPP instances with $5$ to $50$ deliveries ($20$ instances per size), using Pasqal's emulator. $N_{\rm meas}$ is fixed to 500 samples.
• Figure 3: Approximation ratio as a function of the number of measurements $N_{\rm meas}$ for DDPP of different sizes $N$ (indicated by different colors). Data points correspond to the median value of $\rho$ obtained across 30 different sample sets, with relative error bars.
• Figure 4: Results for the 20-delivery DDPP instance used in the experiments on Pasqal's QPU. Top panel: histogram showing the Hamming weight distribution of the neutral atom samples. Purple and orange bars represent results obtained on the QPU and by emulation, respectively. The solid (hatched) portions of the bars denote the number of samples that are (are not) valid IS of the scheduling graph. Bottom panel: analogous histogram for the post-processed samples forming the $\mathcal{S}_B$ set.
• Figure 5: Scheduling graph of 100 deliveries used in the experiments on Pasqal's QPU. Nodes denote individual deliveries, while edges represent temporal conflicts. The coloring indicates the assignment of deliveries to specific drones, illustrating the solution to the battery-constrained graph coloring problem.