Manuscript En01-A@1 · En01-A.tex · example · 558b972b

Example: Five-qubit phase family

Exact operator cancellation with unchanged scalar data · lines 1913–1940

En01-A@1#ex:cancellation, En01-A@1#eq:phasefamily

Use qubits $s_{1}, a_{1}, s_{2}, a_{2}, A$ , initially zero. Apply:

H_{s_{1}}, CNOT_{s_{1} \to a_{1}}, H_{s_{2}}, CNOT_{s_{2} \to a_{2}},

then $X$ on $A$ controlled by $s_{2} = 1$ , and $diag (1, e^{i θ})$ on $A$ controlled by $s_{1} = s_{2} = 1$ . These are legal compiled events. The classes are

K_{1} = {s_{1}, a_{1}}, K_{2} = {s_{2}, a_{2}},

and the final state is

∣ Ψ_{θ} ⟩ = \frac{1}{2} a, b \in {0, 1} \sum e^{i θ ab} ∣ aa ⟩_{K_{1}} ∣ bb ⟩_{K_{2}} ∣ b ⟩_{A} .

Let $J = {1}$ , $S = K_{1}$ , and $S^{'} = K_{1} \cup {A}$ .

Displayed formulas in this passage

En01-A@1#eq:phasefamily · line 1933
$∣ Ψ_{θ} ⟩ = \frac{1}{2} a, b \in {0, 1} \sum e^{i θ ab} ∣ aa ⟩_{K_{1}} ∣ bb ⟩_{K_{2}} ∣ b ⟩_{A} .$
unlabeled · line 1916
$H_{s_{1}}, CNOT_{s_{1} \to a_{1}}, H_{s_{2}}, CNOT_{s_{2} \to a_{2}},$
unlabeled · line 1927
$K_{1} = {s_{1}, a_{1}}, K_{2} = {s_{2}, a_{2}},$

Example: Five-qubit phase family

Displayed formulas in this passage

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