Manuscript En10-B@1 · En10-B.tex · section · a1105bad

Named generators

The frozen finite source and generator model › Named generators · lines 327–371

En10-B@1#eq:kick-H, En10-B@1#eq:CZ-H, En10-B@1#eq:exchange-H

Let $X, Y, Z$ be the Pauli matrices in the graph basis and set

K_{n} = n_{x} X + n_{y} Y + n_{z} Z .

The $X, Y$ terms are edge couplings; the $Z$ term is an on-site contrast. The vector $n$ is an effective generator axis until a physical correspondence is supplied.

Freeze positive externally scheduled durations $T_{k}, T_{c}, T_{e}$ , and $ℏ > 0$ . For label $k$ , prescribe

H_{k, k} = \frac{ℏ ( ϕ + ξ _{k} )}{T _{k}} (K_{n} \otimes I - I \otimes K_{n}) .

Its normal and antiqubit factors have opposite signs.

The interaction stage has generator

H_{c} = \frac{π ℏ}{T _{c}} ∣ 11 ⟩ ⟨ 11 ∣ .

For relaxation, allocate $E$ in $∣ 0 ⟩$ . On $A \otimes E$ , define the self-adjoint exchange generator

K_{e} = i (∣ 01 ⟩ ⟨ 10 ∣ - ∣ 10 ⟩ ⟨ 01 ∣), χ_{γ} = arcsin γ,

and prescribe

H_{e} = \frac{ℏ χ _{γ}}{T _{e}} K_{e} .

These are finite, piecewise scheduled generator data. They are not derived from an unprovided Galactic action.

Displayed formulas in this passage

En10-B@1#eq:kick-H · line 340
$H_{k, k} = \frac{ℏ ( ϕ + ξ _{k} )}{T _{k}} (K_{n} \otimes I - I \otimes K_{n}) .$
En10-B@1#eq:CZ-H · line 350
$H_{c} = \frac{π ℏ}{T _{c}} ∣ 11 ⟩ ⟨ 11 ∣ .$
En10-B@1#eq:exchange-H · line 365
$H_{e} = \frac{ℏ χ _{γ}}{T _{e}} K_{e} .$
unlabeled · line 330
$K_{n} = n_{x} X + n_{y} Y + n_{z} Z .$
unlabeled · line 357
$K_{e} = i (∣ 01 ⟩ ⟨ 10 ∣ - ∣ 10 ⟩ ⟨ 01 ∣), χ_{γ} = arcsin γ,$

Nearby in this section

remark: Remark: Meaning of antiqubit