A model that exhibits excitations of this type can be solved by decomposing the spin-one-half degrees of freedom into four Majorana fermions that are paired by x, y, and z-link nearest neighbor interactions. For 10 points each:
[10h] Give this property of excitations in the gapped phase of the Kitaev honeycomb model. Google researchers verified the experimental production of a system with this property in 2023 by checking “fusion rules.”
ANSWER: anyonic (“any-on-ic”) [reject “anion” or “anionic” (“AN-eye-on-ic”); accept abelian anyons or non-abelian anyons]
[10e] Anyons are identical particles that behave more generally than fermions or bosons under this process. For fermions, the wavefunction picks up a minus sign under this process.
ANSWER: particle exchange
[10m] Anyons appear in many models designed for this task needed for fault tolerant quantum computing, such as one studied by Kitaev on a torus. On that model, syndromes can be found by measuring star and plaquette operators.
ANSWER: quantum error correction [accept word forms like correcting errors in quantum computers]
<Eric Bobrow, Physics>