The surfaces codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but they differ in their boundary conditions.

Source: https://quantumcomputing.stackexchange.com/a/2107 (by @JamesWootton)

The surfaces codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but they differ in their boundary conditions.

The members of the surface code family are sometimes also described by more specific names: The toric code is a surface code with periodic boundary conditions, the planar code is one defined on a plane, etc. The term ‘surface code’ is sometimes also used interchangeably with ‘planar code’, since this is the most realistic example of the surface code family.

The surface codes are currently a large research area, so I’ll just point you towards some good entry points (in addition to the Wikipedia article linked to above).

The surface codes can also be generalized to qudits. For more on that, see here.

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