| Summary: | <p>Many important physical and mathematical problems do not allow analytical treatment, and are difficult to solve numerically on classical computers. Quantum computing is anticipated to perform vastly better for some of these problems. Examples include simulating other quantum mechanical systems like molecules, some optimisation tasks (e.g. combinatorial optimisation and data fitting), and number-theoretical problems like prime factorisation. Being able to efficiently find answers to these questions would enable the accelerated development in other fields of science, like chemistry and engineering.</p>
<p>This work uses analytical and numerical methods to tackle several sub-problems in the field of quantum computing, and provides tools and algorithms that allow more efficient utilisation of the (anticipated) hardware capabilities. The considered problems span a wide range of possible quantum device capacities, from their classical simulation, via near-term intermediate scale (NISQ) and early fault-tolerant hardware, all the way to fully error corrected platforms. Covered topics include an exploration of the problem to automatically generate an efficient implementation of any arbitrary quantum algorithm using the available resources, more accurate techniques for simulating electrons in molecules, a method for extracting information about energy levels in a system from minimal data, and an effort to prepare defined states in a controlled manner. The challenge of modelling perfect or noisy quantum computers themselves using conventional computers is also addressed through the development of an easy-to-use interface to a powerful quantum emulator.</p>
<p>Each one of the discussed contributions represents an advance of the theoretical capabilities towards the goal of utilising quantum hardware — which is rapidly being developed alongside theoretical efforts — to its full potential.</p>
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