Quantum hardware comes with a different computing paradigm and new ways to tackle applications. Much effort has to be put into understanding how to leverage this technology to give real-world... Show moreQuantum hardware comes with a different computing paradigm and new ways to tackle applications. Much effort has to be put into understanding how to leverage this technology to give real-world advantages in areas of interest for industries such as combinatorial optimization or machine learning. Variational quantum algorithms (VQAs) have been introduced as a way to work within the scope of reach of the current imperfect and unstable hardware. A VQA boils down to a parameterized quantum circuit, which is a quantum circuit with adjustable real-valued parameters. These parameters are generally tweaked by a classical optimization algorithm to optimize a quantity of interest. As VQAs are most often used as heuristics, it is not clear whether they genuinely outperform current classical state-of-the-art algorithms in relevant domains of application. Plus, a VQA can come with many components (which can also be calledhyperparameters) making it a (growing) complex system to analyze performances on many considered tasks. Consequently, we will face the issues of algorithm selection and configuration, which we tackle through this thesis on many examples relevant to industrial applications. In this thesis, VQAs for combinatorial optimization, chemistry/material science, and machine learning problems were considered. Show less
Combinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to... Show moreCombinatorial optimization is an important application targeted by quantum computing. However, near-term hardware constraints make quantum algorithms unlikely to be competitive when compared to high-performing classical heuristics on large practical problems. One option to achieve advantages with near-term devices is to use them in combination with classical heuristics. In particular, we propose using quantum methods to sample from classically intractable distributions -- which is the most probable approach to attain a true provable quantum separation in the near-term -- which are used to solve optimization problems faster. We numerically study this enhancement by an adaptation of Tabu Search using the Quantum Approximate Optimization Algorithm (QAOA) as a neighborhood sampler. We show that QAOA provides a flexible tool for exploration-exploitation in such hybrid settings and can provide evidence that it can help in solving problems faster by saving many tabu iterations and achieving better solutions. Show less
