# Quantum-Efficient Reinforcement Learning Solutions for Last-Mile On-Demand Delivery

arXiv: https://arxiv.org/abs/2508.09183 · HTML: https://mlsanity.com/paper/2508.09183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 4 of 4)

- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Search](https://mlsanity.com/paper/2410.05115/) (2024)
- [An Introduction to Quantum Reinforcement Learning (QRL)](https://mlsanity.com/paper/2409.05846/) (2024)

## Built on by (most cited first, 1 of 1)

- [APGEM: Adaptive Policy-Guided Error Mitigation for Quantum Reinforcement Learning on a Real-World CVRP Case Study](https://mlsanity.com/paper/2609.18219/) (2026)

## Abstract (arXiv)

Quantum computation has demonstrated a promising alternative to solving the NP-hard combinatorial problems. Specifically, when it comes to optimization, classical approaches become intractable to account for large-scale solutions. Specifically, we investigate quantum computing to solve the large-scale Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW). In this regard, a Reinforcement Learning (RL) framework augmented with a Parametrized Quantum Circuit (PQC) is designed to minimize the travel time in a realistic last-mile on-demand delivery. A novel problem-specific encoding quantum circuit with an entangling and variational layer is proposed. Moreover, Proximal Policy Optimization (PPO) and Quantum Singular Value Transformation (QSVT) are designed for comparison through numerical experiments, highlighting the superiority of the proposed method in terms of the scale of the solution and training complexity while incorporating the real-world constraints.