Color code defined on a two-dimensional planar graph. Each face hosts two stabilizer generators, a Pauli- X and a Pauli- Z string acting on all the qubits of the face. Most translation-invariant …

focus on 2D topological color codes (without boundaries) and relax the assumption of translation invariance. We show local equivalence between arbitrary 2D color codes and copies of …

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically …

Apr 3, 2018 · In this paper we focus on 2D topological color codes and relax the assumption of translation invariance. Using a linear algebraic framework we show that any 2D color code …

In this thesis, we focus on color codes and relax the constraint on translation invariance. We show that any color code can be mapped to exactly two copies of a related surface code. The …

2D color code — The 2D color code is equivalent to multiple decoupled copies of the 2D surface code via a local constant-depth Clifford circuit [196–198] and has the same topological …

The 2D color code is equivalent to multiple decoupled copies of the 2D surface code via a local constant-depth Clifford circuit [1–3] and has the same topological entanglement entropy . The …

Any 2D color code (on a 2-colex Γ without parallel edges) is equivalent to a pair of surface codes τ(Γ) under the map π. Mapping can be done locally for each c00-colored face Stabilizers on …

Jul 10, 2009 · The colour code of (PRL 97:180501, 2006) is a related scheme partially solving the problem, providing a means to perform all Clifford group gates transversally. We review the …

May 13, 2023 · The surface code is also a stepping stone to understand more complicated codes, from the color code (the second most famous family of 2D codes) to hypergraph product …