Simplifying quantum computing: from theory to applications

The field of quantum computing has seen a tremendous advancement in the last decade. In 2019, for the first time in history, Google demonstrated that a quantum computer can outperform a classical computer. This is known as quantum supremacy, and since then it has been confirmed by other independent groups. Despite its tremendous importance, quantum supremacy was shown for an on-purpose designed model, with limited connections with reality. One could thus say that the first fundamental quantum question was answered, namely, whether it is possible to design a quantum computer faster (for specific purposes) than a classical one. The second question is however still open, and has deeper implications. It is about when it will be possible to integrate quantum algorithms into the texture of the society, particularly within its scientific and economical branches. There is a wide variety of proposals on how to use a quantum computer for practical purposes, that include the development of new materials and drugs, cryptography, finance, the simulation of physical models, and possibly even fighting climate change. However, these proposals have mostly been applied to small problem instances that can be reached by classical computers as well and are of limited practical use.

There are still challenges to be addressed in order to exploit all advantages of quantum machines, such as increasing the number of qubits and their coherence time, lowering the gate errors, and constructing all-to-all connected architectures that can be easily scaled up. While quantum machines improve to face these challenges, there is an immense amount of work from the theoretical side to be made. In its essence, one of the main duties from the theory side consists in finding new ways to lower the requirements on the quantum hardware, in order to run a desired algorithm. This is what this project is about, and in the short term will reduce the time required to quantum technologies to be employed in...