**Engineering Topological States**

Emergent quasiparticles in superconductors, such as Majorana bound states (MBS), are neither Fermions, nor Bosons. Instead, exchanging MBS yields a non-commutative phase, a sign of non-Abelian statistics and non-local degrees of freedom to implement fault-tolerant topological quantum computing. Despite impressive experimental progress in fabricating one-dimensional structures to realize MBS these architectures are inherently limited. Our research takes a new path to create and manipulate topological excitations on a new 2D platform for MBS. It combines proximity-induced superconductivity in a 2D electron gas (2DEG) with magnetic textures from the fringing fields of spin-valve structures, such a magnetic tunnel junctions or magnetic nanopillars. These magnetic textures engineer an effective Hamiltonian in the 2DEG that supports the creation of MBS.

Read more:

A. Matos-Abiague, J. Shabani, A. D. Kent, G. L. Fatin, B. Scharf, I. Zutic, “Tunable Magnetic Textures: From Majorana Bound States to Braiding”, Solid State Communications 262, 1 (2017).

**Superconducting qubits based on Josephson transistors: Gatemons**

Over the last 20 years, superconducting circuits based on Al/AlOx/Al Josephson tunnel junctions have clearly became a leading platform for implementing a functional quantum computer. Many factors contributed to this leadership. Conventional classical transistors have their own merits: fast manipulation, low-power consumption and a more direct path toward scalability. Recent studies show that hybrid superconductor and semiconductor devices could have advantages of both systems.

Read more:

- Z. Qi, H. Xie, J. Shabani, V. E. Manucharyan, A. Levchenko and M. G. Vavilov, “Controlled-Z gate for transmon qubits coupled by semiconductor junctions”, submitted for publication. Available online at arXiv:1801.04291.
- Y.P. Shim, C. Tahan, “Semiconductor-inspired design principles for superconducting quantum computing”, Nature Communication,
**7**, 11059 (2016)

**Low Power Josephson Transistor Circuitry**

Reducing the operating temperature of a logic or memory element can lead to gradual changes of various metrics, such as an increase in mobility or a decrease in series resistance at low temperature. Josephson transistors (superconductor-semiconductor-superconductor junction) are the basic building block of power efficient logics and circuits.

Read more:

- J. Shabani, M. Kjaergaard, H. J. Suominen, Younghyun Kim, F. Nichele, K. Pakrouski, T. Stankevic, R. M. Lutchyn, P. Krogstrup, R. Feidenhansl, S. Kraemer, C. Nayak, M. Troyer, C. M. Marcus, and C. J. Palmstrom, “Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks”, Phys. Rev. B
**93**, 155402 (2016).

**Andreev Bound States in Epitaxial Semiconductor-Superconductor Junctions **

**Quantum Hall Physics With Superconducting Contacts**

Anyons, quasiparticles with exotic statistics, are one of the most intriguing possibilities that exist in condensed matter and atomic systems. Their novelty from the fundamental physics point of view notwithstanding, much recent attention has been drawn to their potential applications for quantum information processing. More specifically, anyons of non-Abelian kind are associated with a multidimensional Hilbert space where quantum information can be stored, while their braiding allows for its manipulation. While anyons are undoubtedly exist e.g. in fractional quantum Hall systems, they are mostly of the Abelian kind. Non-Abelian anyons are theoretically expected to be found only in a few special fractional quantum Hall states such as v = 5/2 (and possibly 12/5), yet no unambiguous experimental confirmation exists so far. The main stumbling block in this direction is the fragility of these fractional quantum Hall states and, as result, very stringent material and experimental requirements.

In an exciting development, it was realized recently that engineering an effective Hamiltonian at the interface of a superconductor-two-dimensional electron gas (2DEG) in the quantum Hall regime could lead to creation of non-Abelian quasiparticles, Majorana and Parafermion zero-modes. The main idea behind these theoretical predictions stem from the earlier proposal for creating Majorana zero modes at a helical edge of a 2D topological insulator. An energy gap can be induced in such a helical edge by one of two means: either by (i) violating time-reversal symmetry with the aid of a magnetic field (or, equivalently, by proximity to a ferromagnet) or by (ii) violating charge conservation via the superconducting proximity effect. If one creates a sequence of such alternating gapped domains, the domain walls will bind Majorana zero modes. A crucial step required for practical implementation of these ideas is being able to induce the superconducting proximity effect in the quantum Hall regime.

Read more:

- C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma, “Non-Abelian anyons and topological quantum computation”, Rev. Mod. Phys.,
**80**, 1083 (2008). - D. J. Clarke, J. Alicea and K. Shtengel, “Exotic non-Abelian anyons from conventional fractional quantum Hall states”, Nature Communications,
**5**, 1348 (2013). - L. Fu and C. L. Kane, “Superconducting proximity effect and Majorana fermions at the surface of a topological insulator”, Phys. Rev. Lett,
**100**, 096407 (2008).