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In the early days of quantum mechanics in 1932, four famous physicists—Lev Landau, Clarence Zener, Ernst Stückelberg, and Ettore Majorana—found a mathematical formula for the probability of jumps between two states in a system whose energy is time-dependent. Their formula has since had countless applications in various systems across physics and chemistry.

Now physicists at Aalto University’s Department of Applied Physics showed that the jump between different states can be realised in systems with more than two energy levels via a virtual transition to an intermediate state and by a linear chirp of the drive frequency. This process can be applied to systems where it is not possible to modify the energy of the levels.

The team, consisting of Doctoral Researcher Isak Björkman, Postdoctoral Researcher Marko Kuzmanovic and Associate Professor Sorin Paraoanu, implemented the 1932 process in a superconducting circuit similar to the ones employed in superconducting quantum computers. 

The paper was published today in Physical Review Letters:

The team managed to take the device from its ground energy level to what is known as the second excited level, even though no direct coupling between the levels exists. This was done by simultaneously applying two Landau-Zener-Stückelberg-Majorana processes. The first excited state was left empty at the end of the protocol, as if it had been skipped entirely. The technique circumvents a physics constraint that forbids going from the ground level to the second level directly. The result is a more robust and information-efficient protocol that could be applied to domains like quantum computers to increase their power.

‘We developed an electric control pulse that changes the state of the qubit from the ground level to the second by using a virtual process involving the first level. There are many benefits to our method, including that we don’t need to know the transition frequency perfectly, but a rough estimate is enough,’ first author Björkman says.

Conventionally, similar results required highly sophisticated control schemes and delicate fine-tuning.

‘Increasing the number of levels in this type of system drastically increases its complexity. One of the benefits of our approach is that it makes adding a third state much easier,’ Kuzmanovic says.

Even better, the new method demonstrated high transfer probabilities and showed impressive robustness to drifts in the qubit frequency. It is also suitable as a control method for multilevel quantum-computing architectures.

‘Usually, if you have a multilevel system, you can of course put some radiation in, but you will most likely excite a lot of states that you may not want. Our result shows how to target very precisely the intended state, even in systems with frequency drift. Imagine that you are scanning for your preferred radio station: our method would allow you to jump over frequencies and listen to the one you like even if you cannot tune in very precisely,’ Paraoanu says.

In addition to better control, bypassing an energy state paves the way for squeezing more computational power out of the same number of qubit-like devices.

‘This method cuts away some hardware overhead in quantum computers,’ Paraoanu says.

The team used the Low-Temperature Laboratory and the Micronova fabrication facilities in their pioneering study. Both belong to. 

The project received funding from the European Union project , and the work was performed as part of the Academy of Finland  programme.