The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot picking and batching in a warehouse. The path to the solution has led to the definition of a new artificial intelligence paradigm with quantum computing, quantum Case-Based Reasoning (qCBR) and to a proof of concept to integrate the capacity of quantum computing within mobile robotics using a Raspberry Pi 4 as a processor (qRobot), capable of operating with leading technology players such as IBMQ, Amazon Braket (D-Wave) and Pennylane. To improve the execution time of variational algorithms in this NISQ era and the next, we have proposed EVA: a quantum Exponential Value Approximation algorithm that speeds up the VQE, and that is, to date, the flagship of the quantum computation. To improve the execution time of variational algorithms in this NISQ era and the next, we have proposed EVA: a quantum Exponential Value Approximation algorithm that speeds up the VQE, and that is, to date, the flagship of the quantum computation.
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot picking and batching in a warehouse. The path to the solution has led to the definition of a new artificial intelligence paradigm with quantum computing, quantum Case-Based Reasoning (qCBR) and to a proof of concept to integrate the capacity of quantum computing within mobile robotics using a Raspberry Pi 4 as a processor (qRobot), capable of operating with leading technology players such as IBMQ, Amazon Braket (D-Wave) and Pennylane. To improve the execution time of variational algorithms in this NISQ era and the next, we have proposed EVA: a quantum Exponential Value Approximation algorithm that speeds up the VQE, and that is, to date, the flagship of the quantum computation. To improve the execution time of variational algorithms in this NISQ era and the next, we have proposed EVA: a quantum Exponential Value Approximation algorithm that speeds up the VQE, and that is, to date, the flagship of the quantum computation.
Artificial Intelligence (AI) and quantum computing are converging to form a new era of ultra-fast computational problem-solving. Quantum optimization algorithms—when integrated with AI-driven heuristics, reinforcement learning, and neural-guided search models—offer unprecedented capabilities for tackling complex problems such as NP-hard optimization, logistics scheduling, cryptographic analysis, and large-scale simulation tasks. This research investigates the combined potential of AI-augmented quantum algorithms, focusing on how machine learning enhances qubit efficiency, error mitigation, quantum annealing performance, and adaptive gate-level optimization. A practical case study evaluates hybrid AI-quantum models applied to combinatorial optimization tasks, demonstrating significant reductions in computational time and improved solution accuracy. Findings highlight a future in which AI-enhanced quantum systems redefine computation, enabling breakthroughs in science, industry, and national innovation systems
Quantum computing is a rapidly developing field that has seen a huge amount of interest in the last couple of decades due to its promise of revolutionizing several domains of business and science. It presents a new way of doing computations by making use of fundamental properties of quantum mechanics such as superposition and entanglement. Optimization, on the other hand, is a field that is omnipresent in the industry and where small improvements can have a significant impact. This thesis aims to tackle optimization problems using quantum algorithms.NP-hard optimization problems are not believed to be exactly solvable through general polynomial time algorithms. Variational quantum algorithms (VQAs) to address such combinatorial problems have been of great interest recently. Such algorithms are heuristic and aim to obtain an approximate solution. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions.An issue with contemporary quantum optimization algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is that they scale linearly with problem size. To tackle this issue, we present the LogQ encoding, using which we can design quantum variational algorithms that scale logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. We show how this algorithm can be applied to several combinatorial optimization problems such as Maximum Cut, Minimum Partition, Maximum Clique and Maximum Weighted Independent Set (MWIS). Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming previous problem sizes by almost tenfold.Next, we apply the LogQ encoding to two use-cases for large companies such as TotalEnergies. Fleet conversion is the process of transitioning a fleet of vehicles to more sustainable and environmentally friendly alternatives. It is modeled as a column generation scheme with the MWIS problem as the sub-problem or worker problem. We use the LogQ method to solve the MWIS Workers and demonstrate how quantum and classical solvers can be used together in a hybrid manner to approach an industrial-sized use-case. Mesh segmentation refers to the process of dividing a complex mesh (composed of vertices, edges, and faces) into meaningful and semantically coherent parts or regions. Mesh segmentation plays an important part in computer modeling, which is extensively used in the core domains of TotalEnergies' activities such as Earth imaging, physical modeling for reservoirs, and others. We define the problem as a graph optimization problem and use the LogQ encoding to solve it.
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor’s algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world problems. It is likely that quantum methods can efficiently solve certain (NP-) hard optimization problems where classical approaches fail. In our perspective, we examine the field of quantum optimization, that is, solving optimization problems using quantum computers. We provide an entry point to quantum optimization for researchers from each topic, optimization or quantum computing, by demonstrating advances and obstacles with a suitable use case. We give an overview on problem formulation, available algorithms, and benchmarking. Although we show a proof-of-concept rather than a full benchmark between classical and quantum methods, this gives an idea of the current quality and capabilities of quantum computers for optimization problems. All observations are incorporated in a discussion on some recent quantum optimization breakthroughs, current status, and future directions.
The major advances in quantum computing over the last few decades have sparked great interest in applying it to solve the most challenging computational problems in a wide variety of areas. One of the most pronounced domains here are optimization problems and a number of algorithmic approaches have been proposed for their solution. For the current noisy intermediate-scale quantum (NISQ) computers the quantum approximate optimization algorithm (QAOA), the variational quantum eigensolver (VQE), and quantum annealing (QA) are the central algorithms for this problem class. The two former can be executed on digital gate-model quantum computers, whereas the latter requires a quantum annealer. Across all hardware architectures and manufactures, the quantum computers available today share the property of being too error-prone to reliably execute involved quantum circuits as they typically arise from quantum optimization algorithms. In order to characterize the limits of existing quantum computers, many component and system level benchmarks have been proposed. However, owing to the complex nature of the errors in quantum systems these benchmark fail to provide predictive power beyond simple quantum circuits and small examples. Application oriented benchmarks have been proposed to remedy this problem, but both, results from real quantum systems as well as use cases beyond constructed academic examples, remain very rare. This paper addresses precisely this gap by considering two industrial relevant use cases: one in the realm of optimizing charging schedules for electric vehicles, the other concerned with the optimization of truck routes. Our central contribution are systematic series of examples derived from these uses cases that we execute on different processors of the gate-based quantum computers of IBM as well as on the quantum annealer of D-Wave.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Quantum computing and artificial intelligence (AI) are positioned as groundbreaking tools capable of tackling complexities inherent to modern computation posed by high-dimensional optimization problems.This research presents a quantum-enhanced optimization framework that leverages the QAOA (Quantum Approximate Optimization Algorithm) and VQE (Variational Quantum Eigen solver) within a hybrid quantum-classical paradigm.Machine learning models, including reinforcement learning and NN (neural networks), are integrated to optimize the quantum circuit parameters, enhance convergence, and improve scalability for complex problem spaces.Experimental evaluations demonstrate that this approach outperforms traditional optimization techniques in terms of efficiency and solution accuracy, particularly for large-scale multi-objective tasks.The framework is applied to key domains such as smart energy systems, logistics, and scientific modeling, illustrating its versatility and alignment with sustainable development goals.This study also explores the limitations of current quantum hardware and discusses future pathways for advancing hybrid quantum AI systems, offering significant contributions to next generation computational methodologies and intelligent problem solving.