Majorana Zero Modes

An operator P might be a particle-hole symmetry of the matrix H if P is ...

• unitary

  and

  maps H -> H

• antiunitary

  and

  maps H -> H

• unitary

  and

  maps H -> -H

• antiunitary

  and

  maps H -> -H

What is the functional dependence of the Majorana gap on the length N of the Kitaev chain?

Which setup does NOT host Majorana Zero Modes?

• half-infinite disordered topological Kitaev chain

• finite non-dimerized topological Kitaev chain

• finite topological Kitaev chain in fully dimerized limit

• half-infinite clean topological Kitaev chain

The Fock-space excitation operators of a Majorana Zero Mode follow the commutator relations of ...

• fermions

• bosons

• neither

• both

Which is a defining property of a Majorana Zero Mode?

• it is a zero-energy eigenvector of the BdG Hamiltonian

• it is its own time-reversal-symmetric partner

• neither

• both

A topological fully dimerized Kitaev chain has .... ground state.

• a Majorana Zero Mode

• a particle-hole symmetric

• topologically protected

• a twofold degenerate

Adiabatic back-and-forth domain wall motion is ... on the Majorana qubit.

• a braiding

• a zero mode

• an idle gate

• a pi/2 gate

... exchange of trivial-topological domain walls results in a pi/2 gate on the Majorana qubit.

• Rapid...

• Adiabatic...

• Heisenberg ...

• Stock ...