Permutation-invariant codes encoding more than one qubit

Abstract

A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous decay errors. To prove the result, we use elementary number theory with prior theory on permutation invariant codes and quantum error correction.

4 pages, minor changes

References in corpus (4)

• Entanglement and permutational symmetry
• Perfect quantum state transfer with randomly coupled quantum chains
• Permutationally invariant state reconstruction
• Quantum communication via a continuously monitored dual spin chain

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