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Chapitre 5. L’horizon quantique : les défis et les promesses d’un nouveau monde

Giuliano Benenti, Giulio Casati, Simone Montangero, Michel Le Bellac

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

This paper investigates the application of quantum computing technology to airline gate-scheduling quadratic assignment problems (QAP).We explore the quantum computing hardware architecture and software environment required for porting classical versions of these type of problems to quantum computers.We discuss the variational quantum eigensolver and the inclusion of space-efficient graph coloring to the Quadratic Unconstrained Binary Optimization (QUBO).These enhanced quantum computing algorithms are tested with an 8 gate and 24 flight test case using both the IBM quantum computing simulator and a 27 qubit superconducting transmon IBM quantum computing hardware platform.

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This paper investigates the application of quantum computing technology to airline gate-scheduling quadratic assignment problems (QAP).We explore the quantum computing hardware architecture and software environment required for porting classical versions of these type of problems to quantum computers.We discuss the variational quantum eigensolver and the inclusion of space-efficient graph coloring to the Quadratic Unconstrained Binary Optimization (QUBO).These enhanced quantum computing algorithms are tested with an 8 gate and 24 flight test case using both the IBM quantum computing simulator and a 27 qubit superconducting transmon IBM quantum computing hardware platform.
This paper investigates the application of quantum computing technology to airline gate-scheduling quadratic assignment problems (QAP). We explore the quantum computing hardware architecture and software environment required for porting classical versions of these type of problems to quantum computers. We discuss the variational quantum eigensolver and the inclusion of space-efficient graph coloring to the Quadratic Unconstrained Binary Optimization (QUBO). These enhanced quantum computing algorithms are tested with an 8 gate and 24 flight test case using both the IBM quantum computing simulator and a 27 qubit superconducting transmon IBM quantum computing hardware platform.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
Abstract Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present a focussed, application-level hardware case study of near-term quantum optimisation algorithms applied to a dense quadratic unconstrained binary optimisation (QUBO) materials science problem. To solve this problem, we implement two methods, the variational quantum eigensolver and quantum annealing (QA), on commercially-available gate-based and QA devices that are accessible via Quantum-Computing-as-a-Service (QCaaS) models. To analyse the performance of these algorithms on our chosen problem, we use a toolbox of relevant metrics and compare performance against three classical algorithms. We employ quantum methods to solve our fully-connected QUBO of up to 72 variables, and find that algorithm performance beyond this is restricted by device connectivity, noise and classical computation time overheads. The classical method—simulated annealing—demonstrates the best performance, exhibiting polynomial scaling on the tested problem sizes.
Quantum computing has the potential to revolutionize the way we solve problems that are computationally infeasible for classical computers. This paper explores the application of quantum computing to NP-complete problems, and by focusing on the Graph Coloring Problem (GCP) we benchmark the performance of two prominent quantum computing devices: D-Wave's quantum annealer and IBM's gatebased quantum processors. After mapping instances of the GCP native formulation, we evaluate the effectiveness and limitations of quantum annealing and gate-based approaches in tackling such combinatorial problems. For annealers, the problem is cast into Quadratic Unconstrained Binary Optimization (QUBO) forms, while gate-based quantum devices employ variational algorithms like the Quantum Approximate Optimization Algorithm (QAOA). The research includes a comparative analysis, highlighting the scalability, accuracy, and practical challenges faced by current quantum hardware.
Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems with emerging quantum computing technology and propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. We investigate several ways to inject permutation matrix constraints in a quadratic unconstrained binary optimization problem which can be mapped to quantum hardware. We focus on obtaining a sufficient spectral gap, which further increases the probability to measure optimal solutions and valid permutation matrices in a single run. We perform our experiments on the quantum computer D-Wave 2000Q (2^11 qubits, adiabatic). Despite the observed discrepancy between simulated adiabatic quantum computing and execution on real quantum hardware, our reformulation of permutation matrix constraints increases the robustness of the numerical computations over other penalty approaches in our experiments. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures, which opens up multiple new directions for solving matching problems in 3D computer vision and graphics.
The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of these new devices. These problems are recurrent in industrial applications and they are in general difficult for classical computing hardware. In this work, we provide a survey of the approaches to solving different types of combinatorial optimization problems, in particular quadratic unconstrained binary optimization (QUBO) problems on a gate model quantum computer. We focus mainly on four different approaches including digitizing the adiabatic quantum computing, global quantum optimization algorithms, the quantum algorithms that approximate the ground state of a general QUBO problem, and quantum sampling. We also discuss the quantum algorithms that are custom designed to solve certain types of QUBO problems.