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As first noted in [1], single-component fermionic polar molecules confined to two dimensions at sufficiently low temperatures form a topologically non-trivial px +ipy superfluid. For NaK, the critical temperature is theoretically predicted to be at around 15% of the Fermi temperature [2] and in our lab at MPQ we can currently reach temperatures as cold as 25%. It has been proposed in [3] to use blue-detuned tweezers to potentially braid Majoranas hosted at vortex cores in the px + ipy superfluid phase and also a topological qubit read-out scheme was suggested specific for ultracold molecules. Using these techniques it becomes feasible to build a prototype of a topological qubit, apply a gate operation by braiding Majoranas and measure the state of the qubit afterwards. This would directly show the non-Abelian character of the exchange of two vortices and thus provide a clear signature for the existence of Majoranas at their cores. Within this talk I will provide a detailed description of the experimental techniques necessary for such a prototypical topological qubit and outline its significance, but also the shortcomings mainly due to the finite lifetime of the superfluid making it unfortunately not immediately suitable for a full topological quantum computer. [1] N. R. Cooper and G. V. Shlyapnikov, “Stable topological superfluid phase of ultracold polar fermionic molecules,” vol. 103, no. 15, p. 155302. [2] F. Deng, X.-Y. Chen, X.-Y. Luo, W. Zhang, S. Yi, and T. Shi, “Effective potential and superfluidity of microwave-shielded polar molecules,” vol. 130, no. 18, p. 183001. [3] S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and majorana zero modes of a p x + i p y superfluid of fermionic cold atoms,” vol. 98, no. 1, p. 010506.

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Leonard Bleiziffer, TUM/LMU München (MSc. ongoing)
Seminar Room 0.03, ETP
Contact: Matteo Rizzi