Periodic Reporting for period 3 - MajoranasAreReal (Search for mechanisms to control chiral Majorana modes in superconductors)
Período documentado: 2022-11-01 hasta 2024-04-30
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.
Our objective is to design 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 aim for 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 impact of this project is that it will provide the basic building blocks for the integration of localized and flying Majorana qubits in the architecture of a topological quantum computer. The key high-risk/high-reward deliverable is a method to exploit the chiral motion of flying Majorana qubits to facilitate braiding operations, as a demonstration of non-Abelian exchange statistics.
Our objective is to design 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 aim for 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 impact of this project is that it will provide the basic building blocks for the integration of localized and flying Majorana qubits in the architecture of a topological quantum computer. The key high-risk/high-reward deliverable is a method to exploit the chiral motion of flying Majorana qubits to facilitate braiding operations, as a demonstration of non-Abelian exchange statistics.
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.
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 a "split operator" discretisation technique. This development could well have implications beyond the context of quantum information processing for which it has been developed.