Manuscript Oai290-A@1 · Oai290-A.tex · section · 7c6e104a

A complete-record qubit confidence construction

A complete-record qubit confidence construction · lines 1030–1060

This section supplies one way to instantiate Theorem thm:certificate; it does not report an experiment. The construction follows the same declared-channel discipline as Oai265-B and Cheung's bounded complete-record interfaces Oai265B,CheungEn01C.

For a qubit,

P_{2} = \frac{I + X \otimes X - Y \otimes Y + Z \otimes Z}{4} .

Let $s_{x} = 1, s_{y} = - 1, s_{z} = 1$ . Every attempted trial in setting $j$ has a predeclared score $Z_{j i} \in [- 1, 1]$ , including failure records.

Conditional on training and calibration data, assume independent scores within each setting, fixed counts $n_{j}$ , means $m_{j}$ , and a common pre-analyzer channel $E_{0}$ . Set

F_{obs} = \frac{1 + m _{x} - m _{y} + m _{z}}{4} .

On a calibration event $G$ , assume

∣ F_{obs} - F_{e} ∣ \leq b_{cal}, d_{⋄} (E_{⋆}, E_{0}) \leq b, Pr (G) \geq 1 - β .

Displayed formulas in this passage

unlabeled · line 1039
$P_{2} = \frac{I + X \otimes X - Y \otimes Y + Z \otimes Z}{4} .$
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$F_{obs} = \frac{1 + m _{x} - m _{y} + m _{z}}{4} .$
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$∣ F_{obs} - F_{e} ∣ \leq b_{cal}, d_{⋄} (E_{⋆}, E_{0}) \leq b, Pr (G) \geq 1 - β .$

A complete-record qubit confidence construction

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