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I am trying to understand fault tolerance for gate gadgets a bit better. Here Gottesman provides the following definition: I generally understand this definition but I have two questions. (1) Why is …

Background: There is a single qubit quantum gate of the form $$ \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & -i \\ 1 & i \end{pmatrix}. $$ As far as I know, this was originally introduced as the $T$ gate in …

This is Eric (other author). If $\lambda = \chi_3$ then $\lambda^* = \chi_3$ (not $\chi_2$). You check this explicitly in GAP using $$\texttt{ComplexConjugate(\lambda)=\lambda;}$$ which evaluates to $ …

Suppose I have a single block $n$-qubit stabilizer code that can correct a weight 1 error (so the distance is $d=3$). If I apply a $1$-transversal gate of the form $U = U_1 \otimes U_2 \otimes \cdots …

The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In practice w …

Suppose I have a quantum error correcting code $|\psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$, say the $[[7,1,3]]$ Steane code for concreteness. Suppose there is a black box that either impl …