Symmetry can help a quantum computer to calculate more efficiently when modelling. Physicists Guido Burkard and Joris Kattemölle from the University of Konstanz show how this works.
Quantum computer research is advancing at a rapid pace. Today's devices, however, still have significant limitations: For example, the length of a quantum computation is severely limited – that is, the number of possible interactions between quantum bits before a serious error occurs in the highly sensitive system. For this reason, it is important to keep computing operations as efficient and lean as possible. Drawing on the example of a quantum simulation, physicists Guido Burkard and Joris Kattemölle from the University of Konstanz illustrate how harnessing symmetry dramatically lowers the computational effort needed: They use recurring patterns in the quantum systems to reduce the required computational effort by a factor of a thousand or more. The method has now been published in the
journal Physical Review Letters.
Accelerating quantum simulations
One of the most important applications of the quantum computer is quantum simulation. In this process, the quantum computer is used to simulate a different, complex quantum system – for example in materials research to calculate the properties of new materials or in pharmacy to predict the interactions of new drugs.
There is just one problem: Before the quantum computer can start its actual calculation, a kind of preliminary calculation is required. In this first step, the structure of the quantum system to be simulated is mapped onto the layout of the quantum bits in the computer. The quantum system typically consists of a periodic lattice, for example a honeycomb lattice. In this lattice, the nodes indicate the possible particle positions, whereas the edges depict the interactions that may occur between them. The quantum computer has to calculate, so to speak, how to transfer this "pattern" of the simulated quantum system to the architecture of its quantum bits. "This calculation is complex – even for a quantum computer", explains Joris Kattemölle, who currently is a researcher at Forschungszentrum Jülich and RWTH Aachen University.
For this sorting work, each individual position of the simulated quantum system previously had to be calculated separately. Now, Kattemölle and Burkard propose a different method that significantly streamlines the calculation process: Instead of calculating individual positions point by point, they use regular, repetitive patterns in the quantum systems to simplify the calculation.
Copying a mosaic
The method can be illustrated through a simple image: picture yourself needing to copy a mosaic. You could transfer the pattern tile by tile onto paper, but the process would be very laborious and take a long time. However, if you know that the mosaic always consists of the same regular pattern, you can also take a characteristic section and simply repeat it. This speeds up the drawing process enormously, because instead of individual stones, you now place a whole group of stones "on one stroke". You end up with the same result, but it's much easier to get there.
Kattemölle and Burkard's quantum simulation method works in a very similar way: The computation no longer relies on single points, but on entire repeating clusters, which significantly streamlines the process. The method is particularly suitable for quantum simulations in the field of materials science, where solids such as crystals consist of an arrangement of atoms that repeats periodically. The process works for two-dimensional as well as three- and higher-dimensional quantum systems. "Our result involves the mathematical proof that the method works for all types of periodic structures and also provides a freely available software (open source), which you can use to transfer the patterns of the simulated quantum bits to your quantum bits' architecture," says Guido Burkard.
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