Vehicle Loading Optimization Software for Quantum-Brilliance computer systems

A frequent problem amongst various transportation companies is determining the optimal loading strategy for packing their merchandise in different vehicles, such as boats, aircrafts, trains or trucks with potentially multiple cargo decks. This project aims at determining the optimal configuration of maximizing the loading of cargo vehicles – subject to appropriate constraints—by using quantum algorithms developed by Quantum-South in the quantum computing platform provided by Quantum-Brilliance. The problem, succinctly, can be stated as follows: - Let there be N packages to be transported. Each package i, has a weight wi and a volume vi. The vehicle has a maximum load capacity M and a maximum volume V. - The objective is to identify the optimal selection of the individual packages to be transported that maximizes the weight transported in each trip, subject to the load and volume constraints of the given vehicle. - Given the exponential increase in the number of possible combinations as N increases, the problem poses a serious challenge to be solved by classical means

Principal investigator

Rafael Sotelo
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Area of science


Systems used


Applications used

Quantum Brilliance Quantum Emulator
Partner Institution: Quantum South / Universidad de Montevideo | Project Code:

The Challenge

Our original approach is based on the use of the Variational Quantum Eigensolver (VQE) algorithm.
In this project, we will implement our algorithm on the Quantum Brilliance Quantum Emulator platform, which can simulate a gate-based quantum computer using scalable tensor network backends.

The Solution

We address the problem inspired by the well-known knapsack problem, which is NP-complete. In our case, the knapsack is the cargo aircraft, the “profit” to maximize is the total weight of the load, and the capacity is the volume available in the aircraft.
We consider a set of given packages with weights pj with integer values, and container types wj, where wj is 0.5 if container j occupies half position, 1 for one, and 2 for two positions. n the number of items, and N the maximum available positions in the payload. We include a Hamiltonian to solve the problem that consists of three terms (HA+HB+HC). Once obtained the Hamiltonian, we use it to run the VQE algorithm in the Quantum Brilliance platform. VQE identifies the lowest eigenvalue of the Hamiltonian. The corresponding eigenvector will be the solution to the problem.

The Outcome

We were able to implement our algorithm in Quantum Brilliance Quantum Emulator (QBQE). The results obtained were correct compared to other solutions we already had on other platforms.
Our work together with Quantum Brilliance is very fruitful. It allowed us to give them valuable feedback on their VQE implementation as they were developing it. For us, it is an excellent experience to test our algorithms in this platform, on state of the art technology.

List of Publications

We have no publications derived from this project yet.
On the other hand, during 2021 we mentioned our participation in this project in many international and regional events.

IP Identified

No IP derived from this project yet.

Commercial Advantage of this Project

A demo was made to the extended team of Quantum Brilliance showing the procedure and the algorithm working. This demo was recorded so it can be used to be shown to possible clients and stakeholders.

Additionally, all along 2021 we participated in events, together with Quantum Brilliance or not, and talked about this experience.