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.

## 1| What is a quantum computer?

Speaker: Dr. Roland Pleger

DLR Institute for Software Technology

A computer calculates with bits, a quantum computer with qubits. This statement would be rather straightforward, were it not for the fact that a qubit is such an alien concept to us. Thankfully, there are vivid experiments that illustrate the superposition of states. In essence, this superposition is expressed in the highly simplified model of wave-particle duality: a photon is sometimes described as a particle, and other times as a wave. In the wave model, the wave function is locally smeared, collapsing into a discrete particle at the moment of a measurement.

The second key concept, entanglement, is familiar to anyone who has ever dealt with atomic models. The electrons of a helium atom are indistinguishable from each other and are described by a common wave function.

These basics are enough to comprehend the concept of a quantum computer. Qubits are brought into an excited state and entangled with other qubits. As long as the system is left to itself, it performs computing miracles.

## 2| How is a quantum computer programmed?

Speaker: Dr. Roland Pleger, DLR-Institute for Software Technology

To participate, you have to measure – and you only get one of the many possible states as a result. If the measurements are repeated often enough, the statistical distribution gives an idea of what has happened inside the quantum computer.

The practical implementation of controllable qubits is an engineering masterpiece. Cooled far below the temperatures typically experienced in space, superconducting qubits are individually produced with a clock rate far above one gigahertz and energy precisely administered on the scale of a tenth of one part per thousand. There are other qubit implementations that attempt similar things at room temperature. The calculations must be finished and read out before the states collapse due to interaction with the environment. This is no easy task, as the proneness to errors is only mitigated by the addition of further qubits, which are themselves also error-prone.

## Dr. Roland Pleger

Roland Pleger is a physicist who, in his time as a researcher, enjoyed cooling intermetallic alloys to temperatures below the boiling point of helium. As an ESA delegate, he deepened his expertise in the space sector, specifically in satellite communications and navigation. He is now a lecturer in data science and machine learning.

## 3| Quantum Annealing

Speaker: Dr. Elisabeth Lobe

DLR Institute for Software Technology

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.

## Dr. Elisabeth Lobe

Elisabeth Lobe completed her master’s degree in mathematics at Otto von Guericke University (OVGU) Magdeburg in 2016. Since then, she has been a research associate at the DLR Institute for Software Technology, conducting research in the field of quantum computing and optimisation. In May 2022, she successfully defended her doctoral thesis on ‘Combinatorial Problems in Programming Quantum Annealers’, which was supervised by Professor Volker Kaibel at OVGU Magdeburg.

## 4| Materials research with quantum simulation

Speaker: Dr. Benedikt Fauseweh

DLR Institute for Software Technology

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.

## Dr. Benedikt Fauseweh

Theoretical quantum physics led Benedikt Fauseweh to the modelling of superconductors. He arrived at his current field of research, quantum computers, via the investigation of quantum Many-particle systems. At the DLR Institute for Software Technology, he leads the ‘Quantum Computing Applications’ group. He is interested in the effective characterisation of strongly correlated quantum systems using quantum computers.

## 5| Quantenalgorithmen

Speaker: Dr. Michael Epping

DLR Institute for Software Technology

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.

## Dr. Michael Epping

Michael Epping studied physics in Siegen and Vienna with a focus on quantum information. He received his PhD in Düsseldorf under Professor Dagmar Bruß, providing contributions to the field of quantum non-locality and networks of quantum signal amplifiers. He continued his research in quantum communications at the Institute for Quantum Computing (IQC) in Waterloo, Canada. After a brief foray into the topic of safeguarding autonomous vehicles, he began researching quantum algorithms, their compilation and quantum error correction at DLR’s Institute for Software Technology in early 2021. Here he leads the ‘Quantum Computing – Methods and Implementation’ group.

## 6| Project ALQU

Speaker: Dr. Peter Ken Schuhmacher of the DLR Institute for Software Technology

It is not at all easy to find algorithms for error-prone quantum computers that promise a quantum advantage despite their susceptibility to errors. This is currently a key challenge! For current quantum computers of the NISQ era, no algorithms are known that have a guaranteed improvement in runtime compared to classic computers. Although many of these algorithms can do without quantum error correction, accurate knowledge of the errors is essential to achieve the quantum advantage. The research and development work in the QCI project ALQU supports the quantum computing ecosystem with the development of innovative products and applications.

## Dr. Peter Ken Schuhmacher

Peter Ken Schuhmacher is in charge of the ALQU project at the DLR Institute of Software Technology. His core tasks include hardware-related research and here in particular error-aware and hardware-specific compilation. His main research areas and expertise are open quantum systems, QC hardware (superconducting circuits), quantum annealing and quantum algorithms.

## 7| Project R-QIP

Speaker: Dr.-Ing. Francisco Lazaro Blasco of the DLR Institute for Communications and Navigation

Quantum computers promise exponential acceleration in solving certain classes of problems. However, quantum information is inherently prone to errors and information loss. Quantum computing hardware is inherently error-prone, while actual quantum computation only takes place in a virtually error-free environment. So for quantum computation to be practical, the information in the qubits must be protected. This requires the introduction of a quantum error correction. The R-QIP project addresses such quantum error correction techniques to protect quantum calculations from errors.

## Dr.-Ing. Francisco Lazaro Blasco

Dr.-Ing. Francisco Lázaro Blasco was born in Spain and graduated in Telecommunications Engineering from the University of Zaragoza in 2006. After a brief stint as a test engineer at Rohde and Schwarz from 2007-2008, he moved to the Institute for Communications and Navigation at DLR in 2008. At the DLR, Francisco did his doctorate in electrical engineering at the Technical University of Hamburg with a focus on (classic) error correction. Since then, his research has focused on the field of error correction, first on classical codes and more recently on quantum error correction. Francisco has been working as an external lecturer at the Karlsruhe Institute of Technology (KIT) since 2020 and is currently leading the QCI project R-QIP.