Abstract
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons on the toric code model. By encoding the model in the multi-partite entangled state of polarized photons, we are able to demonstrate various manipulations of anyonic states and, in particular, their characteristic fractional statistics.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. In three spatial dimensions, only two types of statistical behaviour have been observed dividing particles into two groups: bosons and fermions. If one is restricted to two-dimensional systems the situation changes drastically. There, anyons can appear which exhibit fractional statistics ranging continuously from bosonic to fermionic.
Main results. Anyons can be realized as quasiparticles in highly entangled many-body systems and are responsible for the fractional quantum Hall effect. However, the continuing presence of interactions in the latter system makes the observation of anyons quite elusive. Here, as an alternative approach, we encode the relevant many-body state of an anyonic model—the toric code—in the multi-partite entangled state of polarized photons. This quantum system enables easy manipulation and detection of abelian anyons, allows for the demonstration of their fusion rules and facilitates the unambiguous determination of their quantum statistical properties in a minimal instance of the toric code.
Wider implications. Our experiment conclusively demonstrates the presence of fractional statistics by the manipulation of entangled quantum states. One would like to employ anyons and their properties to perform error free quantum computation. This is the first in-principle demonstration for the implementation of such anyonic quantum processing.