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Table 2 Optimization success for different optimization schemes

From: Hybrid optimization schemes for quantum control

  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
  1. 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.