Computation is not limited to electronic computers, but many natural systems can process information as well. Studying such systems is interesting because it can lead to new unconventional computers, for example in synthetic biology. Understanding computation in natural systems, however, also reveals gaps in our understanding of what it means to compute. In this talk I will concentrate on computation in and by biological systems and describe under which conditions biochemical reactions can be understood as processing information and how this relates to thermodynamics.
Ultra cold atoms are remarkable systems with a truly unprecedented level of experimental control and one application of this control is creating topological band structures. The most natural approach centers on creating suitable real-space lattice potentials that the atoms experience. Here we present our experimental work which uses the internal atomic states as an additional ``synthetic'' dimension. We engineered a two-dimensional magnetic lattice in an elongated strip geometry, with effective per-plaquette flux about 4/3 times the flux quanta. The long direction of this strip is formed from a 1D optical lattice while the short direction is built from the 5 mF states comprising the f=2 ground state hyperfine manifold of Rb-87. We imaged the localized edge and bulk states of atomic Bose-Einstein condensates in this strip, with single lattice-site resolution along the narrow direction. In this 5-site wide strip we are able to delineate between bulk behavior quantified by Chern numbers and edge behavior which is not.
Since the mid-nineties of the 20th century, it became apparent that one of the centuries’ most important technological inventions, computers in general and many of their applications could possibly be further enhanced by using operations based on quantum physics. This is timely since the classical roadmap for the development of computational devices, commonly known as Moore’s law, will cease to be applicable within the next decade. This is due to the ever-smaller sizes of the electronic components that will enter the realm of quantum physics. Computations, whether they happen in our heads or with any computational device, always rely on real physical devices and processes. Data input, data representation in a memory, data manipulation using algorithms and finally, data output require physical realizations with devices and practical procedures. Building a quantum computer then requires the implementation of quantum bits (qubits) as storage sites for quantum information, quantum registers and quantum gates for data handling and processing as well as the development of quantum algorithms. In this talk, the basic functional principle of a quantum computer will be reviewed. It will be shown how strings of trapped ions can be used to build a quantum information processor and how basic computations can be performed using quantum techniques. In particular, the quantum way of doing computations will be illustrated with analog and digital quantum simulations, which range from the simulation of quantum many-body spin systems over open quantum systems to the quantum simulation of a lattice gauge theory.