What barriers have prevented us from using Landau levels to make qubits? Landau levels allow us to jam all electrons into nearly identical quantum states - these states share the same quantum numbers (e.g. orbital and spin) except for the guiding center. Furthermore, the energies of each Landau level can be tuned by modulating applied electric or magnetic fields, and electrons can be excited between states with cyclotron resonance. It's also known how to prepare certain superposition states with applied electric and magnetic fields, e.g. the canted antiferromagnet of bilayer graphene. Because of this, a Landau level seems like a viable setup for a qubit, yet I've never heard of Landau levels being used to make qubits. Why is that?
I don't see why cryogenic temperatures would be any more of a problem for Landau levels than they are for superoconducting qubits and trapped cold atom qubits. Likewise, I would expect edge states not to be an issue since qubit manipulation is typically done by photon not by wire.
On the other hand, I am not sure whether it would be difficult to isolate a specific qubit, or whether the small size of energy gaps (radio rather than visible) or the required high magnetic fields would be a problem. If I had to make an educated guess, I would think that isolating a specific qubit among the many degenerate electrons is the main problem. Can anyone answer this?
 A: My initial reaction was the same as your guess, that isolating particular qubits is very difficult, if even possible. Another limiting factor could be the gate set that can be realized for such qubits.
Requiring high magnetic fields is fine, that happens in the cavity QED and other AMO contexts. I don't think that often about Quantum Hall / Landau Levels, so I'm not sure where the qubit lives in this idea...is it just the occupation of different states in the LLL or something?
Generally speaking, I would think that having lots of particles that share a nearly indistinguishable state would be very bad for making qubits if you want to manipulate and measure specific ones. A more typical setting is the excited/ground states of particular orbitals of an atom or ion.
Perhaps you could explain a little more what the 0 and 1 states would correspond to in terms of degrees of freedom in the QHE fluid? This would also give an idea of what gates could be applied. At minimum you'd want to be able to apply Clifford gates (all Paulis, Hadamard gates, CNOT, and CZ gates).
