Search for mechanisms to control chiral Majorana modes in superconductors

Project Information

MajoranasAreReal

Grant agreement ID: 832256

DOI

10.3030/832256

Project closed

EC signature date 16 April 2019

Start date 1 November 2019

End date 30 April 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 952 759,00

EU contribution

€ 1 952 759,00

Coordinated by

UNIVERSITEIT LEIDEN
Netherlands

Periodic Reporting for period 4 - MajoranasAreReal (Search for mechanisms to control chiral Majorana modes in superconductors)

Reporting period: 2024-05-01 to 2025-04-30

Summary of the context and overall objectives of the project

Quantum mechanics teaches that electrons have a complex wave function, characterized by an amplitude and a phase. As first theorized by Majorana, it is possible in principle for a charge-neutral particle to have a real wave function. Such real fermions, or Majorana fermions, could be robust carriers of quantum information, insensitive to charge noise and other sources of dephasing. With recent experimental developments in topological superconductivity this idea is becoming a reality.

In this project we have designed methods to control the flow of quantum information encoded in “flying” qubits based on Majorana fermions propagating unidirectionally (chirally) in the edge modes of a topological superconductor. We have developed tools to control the phase, charge, and fermion parity of the chiral Majorana modes, on both two-dimensional and three-dimensional platforms, to enable the computational applications of entanglement, braiding, and quantum state transfer.

The main deliverable of the project is a method to exploit the chiral motion of flying Majorana qubits to facilitate braiding operations, as a demonstration of non-Abelian exchange statistics. This provides the basic building blocks for the integration of localized and flying Majorana qubits in the architecture of a topological quantum computer.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Two-dimensional superconductors with broken time-reversal symmetry have been predicted to support topologically protected chiral edge states, providing a superconducting counterpart to the quantum Hall effect in semiconductors. The edge states carry charge-neutral quasiparticles, coherent superpositions of electrons and holes referred to as 'Majorana fermions'. We have developed electrical and thermal probes of the superconducting edge states, focusing on unique signatures of their Majorana nature and on applications for topological quantum computation. In particular, we have shown how topological qubits can be braided by injecting them into the conducting edge of a superconductor. The injection is accomplished by a so-called Josephson junction, which injects the topological qubits in vortices that propagate unidirectionally (chirally) along the superconducting edge. When opposite edges meet or "fuse", they transport a charge equal to plus or minus one half the electron charge. This enables a way to detect the topological qubits in purely electrical way. The sign of the fused charge is a qubit degree of freedom, which is protected from sources of decoherence because it is stored non locally on the opposite edges. A major effort in this project has been to develop methods that allow an efficient and reliable computer simulation of the processes. This is of particular importance in view of the lack of reliable experiments to date.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The research into the dynamics of the massless excitations (Majorana fermions or Dirac fermions) has compelled us to develop a novel methodology to simulate this dynamics on a lattice. A lattice artefact known as "fermion doubling" has plagued these simulations for decades, and we have hit on a method to avoid that artefact by the "tangent fermion" discretisation technique. This development is expected to have implications beyond the context of quantum information processing for which it has been developed.

Intensity profile of the deconfined phase of a Majorana zero mode in a vortex lattice.