Julien B.
Group Meeting, October 11th 2024
Zoology of Honeycomb Floquet codes
Depths & Logical operations
Ideas leading to the Floquet codes
Stabilizer codes
\text {For a stabilizer code }\llbracket n,k,d \rrbracket
\forall s \in \mathcal{S},s\bar{\ket{\psi}} = {\color{red}+} \bar{\ket{\psi}}
k = n-rank(\mathcal{S})
\set{\forall s_i,s_j \in \mathcal{S} \subsetneq\mathcal{P}^n,[s_i,s_j]=0}
The toric code
Subsystem codes
\text {For a subsystem code }\llbracket n,k,d \rrbracket
\text{Add checks s.t. }[c,\mathcal{S}]=0
\forall s \in \mathcal{S},\exists I,\prod_{i\in I}c_i = s
Kitaev inspired version
Kitaev model
With a bunch of local unitaries
Any tricolored lattice
Process
'Free' gates
'Free' gates
'Free' gates
'Free' gates
Equivalent codes
Colour code inspired version
Colour code
CSS code
Decoding comparison
Going Planar
Going Planar
- Surface code approach
- Colour code approach
Surface code
Gidney & Newman
Kesselring & Magdalena de la F.
Colour code
Kesselring & Magdalena de la F.
'Exotic idea' code
Vuillot
