# Quantum Neural Networks for a Supply Chain Logistics Application

arXiv: https://arxiv.org/abs/2212.00576 · HTML: https://mlsanity.com/paper/2212.00576/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Short Quantum Circuits in Reinforcement Learning Policies for the Vehicle Routing Problem](https://mlsanity.com/paper/2109.07498/) (2021)

## Abstract (arXiv)

Problem instances of a size suitable for practical applications are not likely to be addressed during the noisy intermediate-scale quantum (NISQ) period with (almost) pure quantum algorithms. Hybrid classical-quantum algorithms have potential, however, to achieve good performance on much larger problem instances. We investigate one such hybrid algorithm on a problem of substantial importance: vehicle routing for supply chain logistics with multiple trucks and complex demand structure. We use reinforcement learning with neural networks with embedded quantum circuits. In such neural networks, projecting high-dimensional feature vectors down to smaller vectors is necessary to accommodate restrictions on the number of qubits of NISQ hardware. However, we use a multi-head attention mechanism where, even in classical machine learning, such projections are natural and desirable. We consider data from the truck routing logistics of a company in the automotive sector, and apply our methodology by decomposing into small teams of trucks, and we find results comparable to human truck assignment.