Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

Exact example endpoints

Supplied script execution report and its interpretation › Exact example endpoints · lines 1251–1326

The following fractions are transcribed from the supplied report. Here $L$ and $U_{rat}$ are the returned rational error endpoints. The square-root bracketing makes $U_{rat}$ at least the ideal mathematical upper expression, so it is conservative.

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Case	$F_{L}$	$F_{U}$	$L$	$U_{rat}$
Identity	$\frac{3568244821}{4294967296}$	$1$	$0$	$\frac{28267292255}{34359738368}$
Pure replacement	$0$	$\frac{4132899669}{8589934592}$	$\frac{4457034923}{8589934592}$	$1$
Mixed replacement	$0$	$\frac{150211823}{268435456}$	$\frac{118223633}{268435456}$	$1$
Dephasing	$\frac{2829358859}{4294967296}$	$\frac{8367722945}{8589934592}$	$\frac{222211647}{8589934592}$	$1$
Rotation	$\frac{2982894065}{8589934592}$	$\frac{831958049}{1073741824}$	$\frac{241783775}{1073741824}$	$1$
Amplitude damping	$\frac{753268147}{2147483648}$	$\frac{7214677977}{8589934592}$	$\frac{1375256615}{8589934592}$	$1$
Completed loss	$\frac{4280188763}{8589934592}$	$\frac{1961035205}{2147483648}$	$\frac{186448443}{2147483648}$	$1$

The exact fractions, rather than rounded decimal displays, define the recorded numerical certificates ExecutionReport. Their illustrative decimal values are:

identity pure replacement mixed replacement dephasing rotation amplitude damping completed loss F_{L} 0.830797 00 0.658761 0.347255 0.350768 0.498280 F_{U} 1 0.481133 0.559583 0.974131 0.774821 0.839899 0.913178 L 0 0.518867 0.440417 0.025869 0.225179 0.160101 0.086822 U_{rat} 0.822686 111111

These rounded numbers are not substituted into the acceptance test.

Displayed formulas in this passage

unlabeled · line 1313
$identity pure replacement mixed replacement dephasing rotation amplitude damping completed loss F_{L} 0.830797 00 0.658761 0.347255 0.350768 0.498280 F_{U} 1 0.481133 0.559583 0.974131 0.774821 0.839899 0.913178 L 0 0.518867 0.440417 0.025869 0.225179 0.160101 0.086822 U_{rat} 0.822686 111111$