Permutation-invariant quantum codes

Understand

A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded.

• Ideally, the quantum code lies within the ground space of the physical system.
• When the physical model is the Heisenberg ferromagnet in the absence of an external magnetic field, the corresponding ground-space contains all permutation-invariant states.
• We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes.