Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

Conventions and the explicit five-qubit encoding

Conventions and the explicit five-qubit encoding · lines 246–261

Equation (eq:Vmatrix) specifies all $64$ matrix entries, including zeros and phases; it is not a definition only up to logical basis or local Clifford equivalence.

Let $H$ be the Hadamard gate and $S = diag (1, i)$ . Define

U_{G} = CZ_{12} CZ_{23} CZ_{34} CZ_{45} CZ_{51}, U_{par} = CX_{2 \to 1} CX_{3 \to 1} CX_{4 \to 1} CX_{5 \to 1} .

Products act on vectors from right to left.

Displayed formulas in this passage

unlabeled · line 254
$U_{G} = CZ_{12} CZ_{23} CZ_{34} CZ_{45} CZ_{51}, U_{par} = CX_{2 \to 1} CX_{3 \to 1} CX_{4 \to 1} CX_{5 \to 1} .$

Nearby in this section

section: Conventions and the explicit five-qubit encoding
definition: Definition: Printed encoding matrix
proposition: Proposition: Encoding circuit and isometry
section: Conventions and the explicit five-qubit encoding