Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

Exact coherent transfer

E5: constructed coherent access and decoder implementation › Exact coherent transfer · lines 1446–1462

For each physical cell choose its all-vacuum vector $∣ g ⟩$ . For every other physical basis label $u$ , swap the disjoint pairs

A_{u} = ∣ u ⟩_{cell} ∣ 0 ⟩_{Q_{acc}}, B_{u} = ∣ g ⟩_{cell} ∣ code (u) ⟩_{Q_{acc}} .

The all-vacuum input is fixed. Define

R_{u} = \frac{1}{2} ∣ A_{u} - B_{u} ⟩ ⟨ A_{u} - B_{u} ∣ .

The rank-one projections are orthogonal. A pulse of area $π$ on $\sum_{u} R_{u}$ gives all swaps exactly, because $e^{- i π R_{u}} = I - 2 R_{u}$ .

Displayed formulas in this passage

unlabeled · line 1450
$A_{u} = ∣ u ⟩_{cell} ∣ 0 ⟩_{Q_{acc}}, B_{u} = ∣ g ⟩_{cell} ∣ code (u) ⟩_{Q_{acc}} .$
unlabeled · line 1456
$R_{u} = \frac{1}{2} ∣ A_{u} - B_{u} ⟩ ⟨ A_{u} - B_{u} ∣ .$