Manuscript Hawk02-E@1 · Hawk02-E.tex · section · 4841592b

Parity-preserving qubit diary

Pure preparation and coherent diary loading › Parity-preserving qubit diary · lines 630–659

Hawk02-E@1#eq:diary-code, Hawk02-E@1#eq:W

Introduce a carrier $D$ containing two fermionic modes. Encode the logical qubit by

J_{D} ∣ 0 ⟩ = ∣ 00 ⟩_{D}, J_{D} ∣ 1 ⟩ = ∣ 11 ⟩_{D} .

Both logical basis vectors have even parity. The logical reference $Q$ is an abstract quantum register.

Choose two source modes $T$ before studying recovery. Let $U_{sw}$ be the second quantization of the one-particle unitary exchanging those source modes with the carrier modes. It is number conserving and parity preserving.

Define the insertion isometry

W ∣ ψ ⟩ = U_{sw} (J_{D} ∣ ψ ⟩ \otimes ∣ Ω_{S} ⟩), W : C ⟶ H_{S} \otimes H_{D} .

Fix the fermionic occupation ordering once and for all.

Displayed formulas in this passage

Hawk02-E@1#eq:diary-code · line 634
$J_{D} ∣ 0 ⟩ = ∣ 00 ⟩_{D}, J_{D} ∣ 1 ⟩ = ∣ 11 ⟩_{D} .$
Hawk02-E@1#eq:W · line 649
$W ∣ ψ ⟩ = U_{sw} (J_{D} ∣ ψ ⟩ \otimes ∣ Ω_{S} ⟩), W : C ⟶ H_{S} \otimes H_{D} .$

Parity-preserving qubit diary

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