A family of permutationally invariant quantum codes

We construct a new family of permutationally invariant codes that correct t Pauli errors for any t≥1. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new ((4,2,2)) optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t, these conditions can be used to construct new examples of codes by computer.

我们构建了一个新的置换式代码，该代码纠正了任何t≥1的pauli错误。量子代码是特定的情况，在许多情况下，新家庭中的代码比以前最佳的明确说明要短对Pauli错误和删除的置换代码。 T = 1的t = 1到任何数量的误差，这些条件可用于构造计算机的新示例。