Manuscript X-I-ST@1 · X-I-ST.tex · section · 9745fd40

The complete task-clock instrument

Complete destructive instruments and their composition › The complete task-clock instrument · lines 1749–1768

X-I-ST@1#eq:instrument

Let $C ≅ C^{2^{q}}$ , $q \geq 1$ , have a calibrated orthonormal basis ${∣ τ_{j} ⟩}$ . Let $A_{fin}$ contain every surviving finite quantum register. An untouched reference is denoted $E$ .

For installed finite words $w_{j}$ , put

D_{j} = ⟨ τ_{j} ∣_{C} \otimes I_{A_{fin}},

M (Z) = j \sum ∣ j, w_{j} ⟩ ⟨ j, w_{j} ∣_{R} \otimes D_{j} Z D_{j}^{†} .

If fewer than $2^{q}$ task entries are used, the remaining codes report a retained invalid-task status.

Displayed formulas in this passage

X-I-ST@1#eq:instrument · line 1761
$M (Z) = j \sum ∣ j, w_{j} ⟩ ⟨ j, w_{j} ∣_{R} \otimes D_{j} Z D_{j}^{†} .$
unlabeled · line 1758
$D_{j} = ⟨ τ_{j} ∣_{C} \otimes I_{A_{fin}},$

Nearby in this section

theorem: Theorem: Complete residual-report instrument
section: The complete task-clock instrument