"Every technology requires methods and protocols that check its functionality," explains Dr. Jens Eisert, a professor of quantum physics at Freie Universität Berlin. Complicated devices can only work reliably, if it can be guaranteed that the components work together properly. In many cases there are standardized test methods – for example, with cars. "Quantum technologies are no exception," says Eisert. Quantum technologies are new technologies that function on the basis of other physical laws than we know in everyday life. Eisert continues, "The world of atoms, molecules, and light particles, i.e., the world in miniature, is described by quantum mechanics, which functions according to very different rules." For example, it is not possible to measure an object without changing its state a little – an insight formulated by the so-called Heisenberg uncertainty principle.

Quantum mechanics is suitable not only for describing nature on small scales, but also for technological applications. Thus, communication resistant to eavesdropping, new fast super computers, and simulation methods are all possible based on the special laws of quantum mechanics. It is, however, particularly difficult to develop protocols for quantum technologies that ensure functional reliability. As Eisert explains, "This has to do with the rules of quantum mechanics. Not only does the measuring change the object, but the configuration space of quantum mechanics is gigantic in size, i.e., the abstract space in which quantum mechanical systems are described." Without new ideas and methods, it would be completely unrealistic to conceptualize test methods: one would be lost in the huge configuration space of possibilities.

The method now developed by researchers from Berlin, Innsbruck, Cologne, and Sydney relies on novel ideas that come from so-called compressed sensing in applied mathematics. They are used in signal and image processing, where instead of recording complete data, much less is recorded in a completely random way. The central insight is that current methods of image processing are actually based on a misunderstanding. "If you can compress image data so extensively and reduce it exponentially, you must have recorded the data incorrectly," says Eisert. Therefore, there must be methods for recording information such as image data more efficiently. Compressed sensing, which was originally developed by Emmanuel Candès, Terence Tao, and David Donoho for thinly populated vectors and by Emmanuel Candès and Benjamin Recht for matrices, allows this: the savings in the amount of data that must be recorded to reconstruct images is enormous.

The scientists transferred these ideas to quantum mechanics, developed them further, and tested them in experiments. "In this genuinely interdisciplinary project, we used methods from applied mathematics, theoretical physics, and experimental physics," explained Eisert. In order to test the techniques, the scientists used single ions and lined them up similar to a chain of beads, thus very exactly reconstructing the quantum state of seven ions in an error-correcting code. If carried farther, it should be possible to use similar methods to design tests for the preparation of quantum systems, similar to a TÜV, or a technical inspection, for quantum technology.

The project was supported by the German Research Foundation (DFG) in the field of applied mathematics and by the Templeton Foundation for the implications and applications in the quantum mechanics of complex systems.

The Publication

Jens Eisert, Rainer Blatt, Thomas Monz, David Gross, Steve Flammia (2017): Experimental quantum compressed sensing for a seven-qubit system. In: Nature Communications. DOI: 10.1038/ncomms15305. URL: www.nature.com/articles/ncomms15305

Contact

• Prof. Dr. Jens Eisert, Department of Physics, Freie Universität Berlin, Tel.: +49 30 838-54781, Email: jenseisert@gmail.com
• Dr. Christian Flatz, Science Communication & Digitalization, University of Innsbruck, Tel.: +43 512 507-32022, Email: christian.flatz@uibk.ac.at