Quantum Computing: Basic knowledge in five video lectures

Although quantum mechanics may be difficult, understanding how a quantum computer works is possible – if it is explained well. In this series of lectures, DLR experts will explain how to make calculations with qubits, what distinguishes a quantum annealer from a quantum computer, how quantum simulation can be used for materials research and much more. This five-part series is aimed at people who are familiar with the concept of quantum computers but would like to know more about what they really are.

Note: We’re currently working on providing the videos.

Quantum annealers are special quantum architectures that, based on the adiabatic theorem, transform one quantum system into another through adiabatic evolution, thereby preserving the ground state – the state of lowest energy. By encoding a function in the target quantum system, its minimum can thus be determined.

However, since the theoretical requirements of the adiabatic theorem can never be completely fulfilled in reality, the quantum annealer represents a heuristic optimiser for these objective functions, which, through repeated execution, finds the optimal solution only with a certain probability.

The company D-Wave Systems Inc. is the first to make a quantum annealer commercially available. The realisation of the qubits by overlapping superconducting loops allows for the optimisation of quadratic objective functions through the use of binary variables. These problems are known as Ising problems and are difficult to solve using conventional methods. An example is the aircraft gate assignment problem, in which the time taken by passengers transiting from one gate to another is optimised.

However, the constrained hardware structure requires several transformation steps. For example, all variables must be binary coded, and constraints must be integrated into the objective function through penalty terms. In addition, the qubit couplings only realise a very specific hardware graph in which what is known as an embedding must be determined before calculations can be performed on the machine. Based on this embedding, the embedded Ising problem must then be formulated, which represents the actual problem to be solved on the machine. Here, the limited machine precision must be taken into account. All these steps have a strong influence on the probability of success and must therefore be carried out with great care to enable meaningful experiments on the quantum annealer.

Classical approaches to simulate the inner processes of nature fail when they are primarily governed by the laws of quantum mechanics. Of particular interest are surface processes in which only a modest number of atoms are involved. Examples include biocatalysts that burn sugar at room temperature or the effects on the electrode surfaces of batteries.

A quantum computer would be able to elegantly solve this problem. Advances in experimental technology make it possible to study single atoms and their interactions. Single-atom chains form the preliminary stage of gate-based quantum computers. The error rate of quantum gates is still too high to program extensive algorithms with them. However, hybrid systems that tackle tasks cooperatively offer a solution in which the intermediate results of a quantum computer flow into the calculations of a classical computer. The classical computer returns improved parameters to the quantum computer and narrows down the parameter range. The quantum computer uses this to perform the next estimation and continue the loop.

Quantum algorithms are algorithms executed on quantum computers. They exploit quantum mechanical phenomena, such as the superposition of states and entanglement, to solve certain problems in fewer steps than a classical computer. This lecture will explain important classes of quantum algorithms and their central building blocks. In addition to an overview of the growing number of quantum algorithms, it will examine selected examples in more detail. These examples will provide a feeling for where the respective algorithms offer an advantage over classical methods.