Fabian Hassler, RWTH Aachen

Universal quantum computation with Majorana fermions

co-authors: A.R. Akhmerov, M. Burrello, B. van Heck, C.-Y. Hou, C.W.J. Beenakker, all (2)

(1) Institute for Quantum Information, RWTH Aachen University, Germany
(2) Instituut-Lorentz, Universiteit Leiden, The Netherlands

Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform universal quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system---irrespective of any quasiparticle excitations. We propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. By controlling the Coulomb interaction of the superconducting islands, we moreover show how to exchange (braid) Majorana fermions in a network of superconducting nanowires. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor.