Design and operation of degenerate quantum dot systems for topological quantum computing
S. Miles (TU Delft - QRD/Wimmer Group)
M.T. Wimmer – Promotor (TU Delft - QN/Wimmer Group, TU Delft - QRD/Wimmer Group)
A.R. Akhmerov – Promotor (TU Delft - QN/Akhmerov Group)
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Abstract
Topological quantum computation is a paradigm of quantum computation anticipated to be resilient to a wide variety of noise sources. In it information is encoded in distributed, exponentially topologically protected degrees of freedom. These would only be deteriorated by significant perturbations of the system.
At the heart of this paradigm lies the Majorana zero mode It is an effective particle excitation akin to a fractionalized electron. Such Majorana zero modes are non-Abelian meaning their exchange changes the quantum state of the system. This can allow to perform operations in a protected and noise resilient way. Isolating and controlling Majorana zero modes is therefore the first step on the way to topological quantum computation. The past decade has seen significant efforts to isolate such Majorana zero modes. Especially semiconductor superconductor hybrid systems in the form of proximitized ballistic one dimensional channels have garnered great attention. With time however, it became apparent that ballisticity puts significant constraints on material and fabrication quality.
As alternative, recent work suggests that the relevant physics can similarly be realized in arrays of quantum dots. The idea is to design quantum dot based arrays to implement the desired physics in their low energy degrees of freedom. By having a number of dots be proximitzed through adjacent superconductors, one can implement the relevant couplings for Majorana zero modes. Tuning the individual quantum dots then allows to control the localization and coupling to possibly allow for probes of their non-Abelianess in the near future.
The quantum dot platform largely avoids the challenges associated with material and fabrication dependent disorder. Rather, the system constituents can be controlled individually offering detailed control over the physics. In contrast to previous approaches, protection of the involved zero modes is not exponential. Instead, protection is generally proportional to a polynomial depending on the number of sites of the array. In this thesis we will discuss designs of systems that can realize Majorana zeromodes and how these can be operated to demonstrate the non-Abelian exchange statistics…