Graduate Quantum computers and Annular Josephson junctions

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Annular Josephson junctions are not currently used as qubits in mainstream quantum computers, as early superconducting qubit technologies have largely been replaced by modern designs like transmons. Vortices and fluxons are related but distinct concepts; vortices are physical entities representing quantized magnetic flux, while fluxons refer to quantized flux in circuits. Modern qubit designs, such as Fluxonium and heavy fluxonium, utilize these concepts, with quantized variables in annular Josephson junctions being flux. The original idea behind using vortices in annular junctions as qubits highlights the connection between these two terms, but they are not synonymous. Overall, advancements in qubit technology continue to evolve, moving beyond earlier designs.
LagrangeEuler
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Are annular Josephson junctions qubits in some quantum computer right now?
https://www.nature.com/articles/425133aI found this article from 2003. What is the progress right now?

Also are vortices and fluxons same thing?
 
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No, I believe it is fair to say that it was a bit of a dead end. None of the early superconducting qubit technologies are in much use anymore; they haven been superseded by more modern topologies (usually based on transmons)

A vortex is "physical thing", it is a "ring" (with a core) of quantised magnetic flux (google "image of Abricosov vortices") which can be imaged if you use the right type of microscope.

"Fluxons" is a more abstract term which typically refers to some form of quantised flux in a circuit.
There is a range of different types of qubits with charge qubits (tunnelling Cooper pairs) at one end and flux qubits at the other (tunnelling flux). Modern qubits sit somewhere closer to the middle of this range.
The "Fluxonium" is is an example of a modern flux-based design which looks promising, there are also more complicated versions such as the "heavy fluxonium" which is quite recent.
 
Is there any chance that in annular Josephson junctions fluxons and vortex are the same thing? Or are in any case those two are synonyms?
 
The basic idea of the annular JJ was -as far as I remember- to use vortices in one of two states as the qubit. Because of the design the quantised variable in this type of qubit is flux, which means that the "abstract things" which tunnels are fluxons.
So, at least using the terminology I am used to, the two are related but they are not the the same; you can have fluxons in qubits without vortices.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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