Anyons, simulation, and "real" systems

 Quanta magazine this week published an article about two very recent papers, in which different groups performed quantum simulations of anyons, objects that do not follow Bose-Einstein or Fermi-Dirac statistics when they are exchanged.  For so-called Abelian anyons (which I wrote about in the link above), the wavefunction picks up a phase factor \(\exp(i\alpha)\), where \(\alpha\) is not \(\pi\) (as is the case for Fermi-Dirac statistics), nor is it 0 or an integer multiple of \(2\pi\) (which is the case for Bose-Einstein statistics).  Moreover, in both of the new papers (here and here), the scientists used quantum simulators (based on trapped ions in the former, and superconducting qubits in the latter) to create objects that act like nonAbelian anyons.  For nonAbelian anyons, you shouldn't even think in terms of phase factors under exchange - the actual quantum state of the system is changed by the exchange process in a nontrivial way.  That means that the system has a memory of particle exchanges, a property that has led to a lot of interest in trying to encode and manipulate information that way, called braiding, because swapping objects that "remember" their past locations is a bit like braiding yarn - the braided lengths of the yarn strands keep a record of how the yarn ends have been twisted around each other.

Hat tip to Pierre-Luc Dallaire-Demers for the meme.

I haven't read these papers in depth, but the technical achievements seem pretty neat.  The discussion of these papers has also been interesting - see the meme to the right.  Condensed matter physicists have been trying for a long time to look at nonAbelian objects, specifically quasiparticle excitations in certain 2D systems, including particular fractional quantum Hall states, to demonstrate conclusively that these objects exist in nature.  (Full disclosure, my former postdoctoral mentor has done very impressive work on this.)  So, the question arises, does the quantum simulation of nonAbelian anyons "count"?  This issue, the role of quantum simulation, is something that I wrote about last year in the media tizzy about wormholes.  The related issue, are quasiparticles "real", I also wrote about last year. The meme pokes fun at peoples' reactions (and is so narrow in its appeal that the general public truly won't get it).  

Analog simulation goes back a long way.  It is possible to build electronic circuits using op-amps and basic components so that the output voltage obeys desired differential equations, effectively solving some desired problem.  In some sense, the present situation is a bit like this.  Using (somewhat noise, intermediate-scale) quantum computing hardware, the investigators have set up a system that obeys the math of nonAbelian anyons, and they report that they have demonstrated braiding.  Assuming that the technical side holds up, this is impressive and shows that it is possible to implement some version of the math behind this idea of topologically encoding information.  That is not the same, however, as showing that some many-body system's spontaneously occurring excitations obey that math, which is the key scientific question of interest to CM physicists.

(Obligatory nerdy joke:  What is purple and commutes?  An Abelian grape.)