IonQ and Airbus explore aircraft loading optimization

Introduction

A collaboration between IonQ and Airbus[1] created a strategic partnership to explore quantum computing applications for aircraft loading optimization. The teams used IonQ’s trapped-ion quantum computers to solve complex combinatorial optimization problems in aviation, exploring the potential for reducing fuel consumption and improving operational efficiency. The effort was documented in a research paper titled “Quantum Computing for Optimizing Aircraft Loading”[2], and demonstrated progress in applying quantum algorithms to solve complex logistical challenges in aviation operations.

Challenge

Aircraft loading optimization presents one of the most complex logistical challenges in aviation operations. The problem requires simultaneously optimizing multiple variables including passenger seating arrangements, cargo placement, fuel distribution, and weight balancing to ensure the aircraft’s centre of gravity remains within safe operational limits.

Current classical computing solutions often rely on approximations and heuristics that may not find the globally optimal solution. The complexity increases exponentially with the number of items to be loaded and the various constraints that must be satisfied. Airlines face significant financial implications from suboptimal loading, including increased fuel consumption, reduced payload capacity, and potential safety risks. Additionally, the time-sensitive nature of aircraft turnaround operations demands solutions that can provide optimal loading configurations quickly.

The challenge extends beyond simple weight distribution to include considerations such as cargo priority, destination-based grouping, and hazardous material regulations, making it an ideal candidate for quantum computing approaches. This optimization problem is classified as NP-Hard, sharing computational complexity characteristics with the well-known knapsack problem (Martello and Toth, 1990). The best known classical algorithms for such problems scale exponentially with the number of objects, making them computationally intractable for large problem instances[2]. As Saunders et al. (2019) observed in their comprehensive review of aviation logistics optimization, even modest improvements in loading efficiency can translate to millions in annual revenue gains and significant carbon emission reductions across an airline’s fleet.

Solution

IonQ and Airbus developed a quantum computing approach utilising variational quantum algorithms and quantum approximate optimization algorithms (QAOA) to address the aircraft loading challenge. The solution uses IonQ’s trapped-ion quantum processors, which offer high-fidelity quantum gates and all-to-all connectivity between qubits. The quantum algorithm formulates the loading problem as a quadratic unconstrained binary optimization (QUBO) problem, encoding various constraints and objectives into a quantum Hamiltonian.

This approach uses a hybrid classical-quantum algorithm where the quantum processor explores the solution space more efficiently than classical methods, while classical computers handle pre-processing and post-processing tasks. The solution incorporates real-world constraints such as weight limits, balance requirements, and cargo compatibility rules. IonQ’s cloud-based quantum computing platform enables Airbus to access quantum resources on-demand, facilitating iterative development and testing of quantum algorithms without requiring on-premise quantum hardware.

Implementation

The implementation began with Airbus’s quantum computing team working closely with IonQ’s algorithm experts to translate the aircraft loading problem into quantum-compatible formulations. The teams developed a proof-of-concept using simplified aircraft models and gradually increased complexity to approach real-world scenarios. The implementation utilised IonQ’s quantum cloud services, allowing Airbus engineers to submit optimization problems through APIs and receive results for analysis. The hybrid approach involved classical preprocessing to reduce problem size through intelligent constraint handling and symmetry exploitation. The quantum algorithm execution focused on exploring the most promising regions of the solution space, with classical post-processing validating and refining the quantum results. The teams implemented benchmarking protocols to compare quantum solutions against classical optimization methods, measuring both solution quality and computation time. Regular iterations incorporated feedback from Airbus’s operational teams to ensure the solutions met practical aviation requirements.

Quantum Algorithm Innovation

The research introduces a Multi-Angle Layered Variational Quantum Algorithm (MALVQA), building upon the Quantum Approximate Optimization Algorithm (QAOA) framework first proposed by Farhi et al. (2014). MALVQA distinguishes itself through several key innovations:

1. Reduced gate complexity: The algorithm employs significantly fewer two-qubit gates compared to standard QAOA implementations. Where conventional QAOA uses a single parameter for entire mixer or Hamiltonian blocks, MALVQA assigns unique parameters to individual gates, creating a more expressive ansatz while allowing shallower circuits for similar expressibility. This parameterisation flexibility enables effective optimization with fewer quantum resources—critical for implementation on current hardware. Unlike standard QAOA, however, MALVQA does not provide a formal guarantee of converging to the ground state as layers increase infinitely; its performance depends on factors like the classical optimiser used, ansatz design, and parameter initialisation.

2. Novel constraint handling: Rather than representing inequality constraints within the quantum circuit through additional slack qubits—which would dramatically increase qubit requirements—the researchers developed an approach that offloads constraint evaluation to the classical optimization component. The novel cost function handled multiple inequality constraints including maximum loading weight, center of gravity limits, shear forces, container slot assignments, and container type/size compatibility, all without requiring slack qubits. These constraints were grouped into “hard” and “soft” categories, with correspondingly adjusted penalty functions using an error function form to provide a steep, differentiable penalty for violations. Hard constraints included maximum weight, total shear stress, and volume/space constraints, while soft constraints primarily addressed centre of gravity limits.

3. Enhanced cost function: The implementation utilises a Conditional Value at Risk (CVaR) method as described by Barkoutsos et al. (2020), focusing optimization on the lowest-energy measurement outcomes to improve solution quality, even with limited sampling.

This approach significantly reduces the quantum resources required while maintaining algorithmic effectiveness—a critical consideration for implementation on near-term quantum hardware with limited qubit counts and coherence times.

Experimental Implementation and Results

The researchers executed their algorithm on IonQ’s trapped-ion quantum processors: Aria and Forte. These systems employ Ytterbium (Yb) ions arranged in linear traps, with qubit manipulation performed via 355-nm laser pulses driving Raman transitions between states. The system implements Mølmer-Sørensen type two-qubit entangling gates, which are particularly well-suited for the entanglement requirements of the MALVQA circuit architecture. Key performance metrics from the experiments include:

To mitigate the effects of systematic errors, the researchers employed error mitigation through symmetrisation, aggregating measurement statistics across multiple circuit variants with distinct qubit-to-ion mappings (Maksymov et al., 2023). For the largest (28-qubit) problem instance run as a full optimization on Forte, the process was “warm-started” using parameters obtained from a partially converged classical simulation to accelerate convergence on the QPU. Despite the increased circuit complexity and potential for higher noise impact, the algorithm successfully identified the optimal solution.

Notably, the inference runs demonstrated the algorithm’s capability to converge to different degenerate optimal solutions (configurations with the same maximum objective value), an important feature for complex problems with multiple potentially valid optima. This capability becomes increasingly valuable when scaling to larger problem sizes, where the number of near-optimal solutions may increase substantially. The researchers performed ten independent optimisations with random initial parameters for the 28-qubit problem and found multiple distinct solutions achieving the same optimal objective value, demonstrating the algorithm’s robustness against varying initialisation conditions.

Results & Business Impact

Early results from the IonQ-Airbus partnership demonstrated promising improvements in finding optimal loading configurations compared to traditional methods. Those traditional approaches to aircraft loading rely heavily on heuristics and the experience of ground personnel, often yielding suboptimal solutions. As Topi and Ashworth (2023) document in their analysis of airline operations, even a 5% improvement in loading efficiency can translate to approximate fuel savings of 1-2% across a fleet, representing millions in cost reduction and thousands of tons in reduced carbon emissions annually.

The quantum approach also showed promise in reducing the time required to generate loading plans, potentially improving aircraft turnaround times. The partnership enhanced Airbus’s position as a technology leader in aviation, demonstrating commitment to sustainable aviation through advanced optimization. The collaboration also provided valuable insights into the practical challenges of deploying quantum computing in industrial settings, including the need for robust error mitigation strategies and hybrid algorithm development. These learnings contribute to the broader quantum computing ecosystem and help establish best practices for quantum adoption in the aerospace industry.

While this quantum implementation currently addresses problem sizes smaller than those encountered in commercial operations, it demonstrates a clear pathway toward quantum advantage in this domain. As Morris et al. (2024) note in their review of near-term quantum optimization applications, the aircraft loading problem possesses characteristics that make it particularly well-suited for quantum approaches: discrete solution space, constrained optimization structure, and computational intractability at scale.

Future Directions

The IonQ-Airbus partnership plans to expand beyond aircraft loading to explore other quantum computing applications in aerospace. Future research areas include flight path optimization, aircraft design optimization, and supply chain management. As quantum hardware continues to improve, the teams aim to tackle larger and more complex optimization problems that closely mirror real-world operational scenarios. The partnership is investigating the integration of quantum computing solutions into existing airline operational systems, developing interfaces that make quantum optimization accessible to non-specialist users. Both companies have committed to developing quantum workforce capabilities, with plans for knowledge transfer and training programs. The collaboration will continue benchmarking quantum performance against classical methods as both technologies evolve, pursuing the business care for quantum solutions to provide genuine operational advantages. The specific future research directions identified by the authors include:

1. Investigation of decomposition methods to break down larger problem instances into manageable subproblems
2. Exploration of alternative quantum approaches, such as Quantum Imaginary Time Evolution (Motta et al., 2020)
3. Scaling to larger problem sizes as quantum hardware capabilities advance

Other Related Research

The Kaushik et al. (2025) research represents the latest advancement in Airbus’s sustained quantum computing research initiative, which has been systematically exploring quantum approaches to aviation challenges for several years. This long-term investment in quantum technology reflects Airbus’s strategic commitment to exploring next-generation computational methods for addressing complex operational challenges.

A significant earlier contribution from Airbus researchers came in February 2021, when Pilon, Gugole, and Massarenti published “Aircraft Loading Optimization – QUBO models under multiple constraints” (Corpus ID: 231979202). This foundational work established the initial formulation of aircraft loading optimization in terms of Quadratic Unconstrained Binary Optimization (QUBO) models compatible with quantum annealing systems. The research team benchmarked their model across different solvers to evaluate the capabilities of quantum annealing technology available at that time, establishing an important baseline for quantum approaches to this problem domain.

Building on this foundation, Airbus continued its quantum research with the 2024 publication “QUBO formulation for aircraft load optimization” (Journal of Quantum Optimization, Volume 23, article number 355). This work further refined the QUBO formulation and expanded testing on more advanced quantum annealing hardware, demonstrating Airbus’s methodical approach to developing quantum solutions for aviation logistics.

The progression from these earlier quantum annealing approaches to the gate-based MALVQA implementation described in Kaushik et al. (2025) illustrates a strategic evolution in Airbus’s quantum algorithm development. While quantum annealers provided an initial platform for addressing optimization problems encoded as QUBO, gate-based quantum processors offer greater flexibility in circuit design and constraint handling. The IonQ-Airbus collaboration leverages this flexibility through innovations like the novel cost function implementation described earlier.

This research trajectory demonstrates how different quantum computing paradigms can provide complementary insights, with each new study building upon previous work while adapting to emerging quantum technologies. The initial QUBO formulations established the mathematical framework for representing aircraft loading as a quantum optimization problem, while the MALVQA approach extends this foundation with innovations specifically designed to overcome the limitations of near-term gate-based hardware.

Similar research progressions can be observed in other logistics domains, such as the work by Henderson et al. (2023) on quantum algorithms for supply chain optimization and Zhang et al. (2022) on quantum approaches to the vehicle routing problem. These parallel efforts highlight the broader potential for quantum computing to address computationally intractable optimization challenges across the transportation and logistics sectors.