In the first week of this course we will learn the basic concepts of quantum chemistry applications and how to use quantum algorithms to determine the ground state of molecules. We start with a review of the Schrödinger equation, the fundamental equation of quantum dynamics. Next, we will introduce the second quantization notation which we can later use to transform our quantum chemical problem into its qubit representation. We will then get to know the variational quantum eigensolver, a hybrid quantum-classical algorithm for finding the minimum eigenvalue (or in this case the ground state energy) of our problem. We conclude the week with a brief introduction to embedding routines which enable the treatment of larger molecular systems than we could otherwise fit on state-of-the-art quantum computers.

The second course week will delve deeper into tackling problems from the natural sciences with quantum computers. In the first week, we learned some basics and focussed on ground-state calculations. These are not the only kind of problems we face in computational quantum chemistry and physics, however. The computation of excited states and time-dependent properties can often be much more complicated. Therefore, devising clever quantum algorithms for these tasks is crucial. This will be our focus for the beginning of the second week. Another aspect we have not discussed so far is how to actually extract information from our quantum computation and we will continue with discussing how to efficiently measure expectation values. Lastly, current quantum processors are far from error-free. In fact, they come with many different sources of error, or noise as we say. These can potentially ruin any calculation and vast research efforts are spent on finding ways to work around this noise. In our last lecture, we talk about such methods to work around device errors. The second week concludes with an interview of Dr. Ivano Tavernelli, discussing what challenges we researchers are facing and giving an outlook on how we might be able to make use of quantum technologies in the future.

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