Hybrid optimization schemes for quantum control

EPJ Quantum Technology

Table 2 Optimization success for different optimization schemes

	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.