Also called a checkerboard code. CSS variant of the surface code defined on a square lattice that has been rotated 45 degrees such that qubits are on vertices, and both \(X\)- and \(Z\)-type check operators occupy plaquettes in an alternating checkerboard pattern.
The \([[L^2,1,L]]\) variant of this family includes the \([[9,1,3]]\) surface-17 code, named as such because 8 ancilla qubits are used for check operator measurements alongside the 9 physical qubits.
Local neural-network using 3D convolutions, combined with a separate global decoder .
A particular choice of CNOT gates during syndrome extraction is required to be fault-tolerant to syndrome qubit errors .
- Kitaev surface code — Rotated surface codes can be obtained using the same procedure as for the original surface codes but considering slightly different combinatorial surfaces  than those considered in the original proposal.
- Quantum Tanner code — Specializing the quantum Tanner construction to the surface code yields the rotated surface code .
- Hierarchical code — Hierarchical code is a concatenation of a constant-rate QLDPC code with a rotated surface code.
- Hypergraph product code — Rotated code can be obtained from hypergraph product of two cyclic binary cyclic codes with palindromic generator polynomial (, Ex. 7).
- Heavy-hexagon code — A rotated surface code can be mapped onto a heavy square lattice, resulting in a code similar to the heavy-hexagon code .
- \([[4,2,2]]\) CSS code — Various \([[4,1,2]]\) subcodes are small rotated planar codes .
- Subsystem rotated surface code
- XZZX surface code — XZZX code is obtained from the rotated surface code by applying Hadamard gates on a subset of qubits such that \(XXXX\) and \(ZZZZ\) generators are both mapped to \(XZXZ\).
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Page edit log
- Marcus P da Silva (2023-03-20) — most recent
- Victor V. Albert (2022-07-30)
“Rotated surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/rotated_surface