| |
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
|
|
Pre-opt. s.m.
|
185
|
518
|
5.07 × 10−5
|
1.11 × 10−5
|
3.36 × 10−5
|
|
Pre-opt. 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 ‘pre-opt. s.m.’ and ‘pre-opt. geo.’ include both the 116 propagations of the first stage simplex optimization and the propagations from the second-stage 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 wall-clock time required to obtain the result starting from the original guess pulse.
