Concepts from algebraic topology (such as homology and cohomology groups, chain complexes, etc.) can then be used to understand and analyze those codes. While we will only consider surface codes defined on a 2D square lattice here, they can actually be generalized to the cellulation of any manifold in any dimension (including hyperbolic!). While this post will be mainly concerned with the quantum error correction properties of the surface code, my friend Dominik Kufel wrote an excellent complementary post which describes the condensed matter perspective.įinally, the surface code is the simplest example to illustrate the more general concept of topological quantum error-correction. For instance, in condensed matter theory, the surface code (more often called toric code in this context 1) is used as a prime example of topological phase of matter and is related to the more general family of spin liquids. And indeed, the surface code has deep connections to many areas of maths and physics. Inspired by the condensed matter concepts of topological order and anyonic particle, it was discovered by Alexei Kitaev in 1997, in a paper in which he also introduces the idea of topological quantum computing. And Google is far from the only company considering the surface code (or some of its variants) as part of their their fault-tolerant architecture!Īpart from its experimental relevance, the surface code is also one of the most beautiful ideas of quantum computing, and if you ask me, of all physics. And how did they achieve such a milestone? You guessed it, by using the surface code to protect their qubits! The reasons they chose this code are plentiful: it can be layed down on a 2D lattice, it has a very high threshold compared to other codes, it doesn’t require too many qubits in its smallest instances, etc. What this means is that their experiment reached noise levels that are low enough such that by increasing the size of their code, they progressively reduced the number of errors in the encoded qubit. Last July, the quantum team at Google released a milestone paper, in which they show the first experimental demonstration of quantum error correction below threshold.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |