4

I understand the basic quantum mechanics definition of anyons through the very nice answer of "user1271772 No more free time" here. I guess (?!) it requires to use non-trivial anyons (i.e. that are neither Fermions or Boson), but I'm not sure. See the related question here.

My questions:

  • I would like to understand in the simplest manner why it can lead to quantum computer more noise resilient than if they use traditionnal qubit. Note that I do not understand what "braid" are.
  • I would like to know if there is a connection with surface or toric code (because they are sometimes called topological codes). I understand how such codes work in order to apply a quantum memory (i.e. I know how the X and Z stabilisers are formed in this code, and how logical X and Z are defined).

Importantly, I would like an answer that makes minimal assumption about the required knowledge: I am familiar with stabilizer codes but I'm not an expert of the specific case of surface code (if we leave the quantum memory case, I have a basic understanding of lattice surgery but I'm clearly not an expert there)

Sachin Valera
  • 123
  • 5
Marco Fellous-Asiani
  • 2,220
  • 2
  • 15
  • 42

1 Answers1

3

The simplest way that explains the noise resilience is the non-local component of topological qubits. As discussed in the post by Simon Burton that you linked. Topological states like ones involving non-Abelian canyons or Majorana zero modes are designed to encode their quantum information in a global way because they are defined by topological order. This means that small errors or noise cannot as easily change the global topological state since they occur locally.

The link between topological codes and topological qubits besides the namesake is that topological codes like ones on a square or torus also store the information non-locally making it more difficult for noise to disturb the logically encoded qubit which is why they are used to aid fault-tolerance. This is in contrast to codes like the 5-qubit code that are defined algebraically and lack a topological structure.

Hope this was simple enough but still helpful!

broncosaurus
  • 341
  • 5