paper

Permutation-invariant constant-excitation quantum codes for amplitude damping

arXiv:1809.09801 · doi:10.1109/TIT.2019.2956142

Abstract

The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors which model photon loss. Although considerable research has been devoted to quantum error correcting codes for amplitude damping, not so much attention has been paid to having these codes simultaneously lie within the decoherence free subspace of their underlying physical system. One common physical system comprises of quantum harmonic oscillators, and constant-excitation quantum codes can be naturally stabilized within them. The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes. To construct such quantum codes, we use the nullspace of a specially constructed matrix based on integer partitions.

arXiv comment19 pages, 1 figure, 1 table. More examples, including a code for 5 AD errors using 30 excitations. An unproven claim in Corollary 5 is also removed, which slightly changes Equation (1.2)

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