
T [ns]

prop.

\(\varepsilon _{C}\)

\(\varepsilon _{\mathrm {pop}}\)

\(\varepsilon _{\mathrm {avg}}\)


Guess

200

0

1.92 × 10^{−1}

5.94 × 10^{−3}

8.25 × 10^{−2}

Direct s.m.

200

20,000

2.23 × 10^{−2}

4.13 × 10^{−3}

1.45 × 10^{−2}

Direct geo.

200

11,032

1.83 × 10^{−6}

1.42 × 10^{−4}

1.43 × 10^{−4}

Simplex

185

116

1.95 × 10^{−5}

1.40 × 10^{−2}

1.40 × 10^{−2}

Preopt. s.m.

185

518

5.07 × 10^{−5}

1.11 × 10^{−5}

3.36 × 10^{−5}

Preopt. geo.

185

300

5.24 × 10^{−5}

1.40 × 10^{−5}

3.50 × 10^{−5}

 For each scheme, we give the gate duration T, the total number of propagations, the concurrence error \(\varepsilon _{C}\equiv1  C\) by which the gate differs from a perfect entangler, the loss of population \(\varepsilon _{\mathrm {pop}}\) from the logical subspace, and the gate error \(\varepsilon _{\mathrm {avg}}\equiv1  F_{\mathrm {avg}}\) with respect to a geometric phase gate. The number of propagations for ‘preopt. s.m.’ and ‘preopt. geo.’ include both the 116 propagations of the first stage simplex optimization and the propagations from the secondstage optimization using Krotov’s method, with 201 respectively 92 iterations, and two propagations per iteration. The reported number of propagations is thus proportional to the total CPU and wallclock time required to obtain the result starting from the original guess pulse.