Multilevel Transmon
In this example we will look at a multilevel transmon qubit with a Hamiltonian given by
\[\hat{H}(t) = -\frac{\delta}{2} \hat{n}(\hat{n} - 1) + u_1(t) (\hat{a} + \hat{a}^\dagger) + u_2(t) i (\hat{a} - \hat{a}^\dagger)\]
where $\hat{n} = \hat{a}^\dagger \hat{a}$ is the number operator, $\hat{a}$ is the annihilation operator, $\delta$ is the anharmonicity, and $u_1(t)$ and $u_2(t)$ are control fields.
We will use the following parameter values:
\[\begin{aligned} \delta &= 0.2 \text{ GHz}\\ \abs{u_i(t)} &\leq 0.2 \text{ GHz}\\ T_0 &= 10 \text{ ns}\\ \end{aligned}\]
For convenience, we have defined the TransmonSystem function in the QuantumSystemTemplates module, which returns a QuantumSystem object for a transmon qubit. We will use this function to define the system.
Setting up the problem
To begin, let's load the necessary packages, define the system parameters, and create a a QuantumSystem object using the TransmonSystem function.
using QuantumCollocation
using PiccoloQuantumObjects
using NamedTrajectories
using LinearAlgebra
using SparseArrays
using Random; Random.seed!(123)
using PiccoloPlots
using CairoMakie
# define the time parameters
T₀ = 10 # total time in ns
T = 50 # number of time steps
Δt = T₀ / T # time step
# define the system parameters
levels = 5
δ = 0.2
# add a bound to the controls
a_bound = 0.2
# create the system
sys = TransmonSystem(levels=levels, δ=δ)
# let's look at the parameters of the system
sys.paramsDict{Symbol, Any} with 8 entries:
:lab_frame_type => :duffing
:ω => 4.0
:lab_frame => false
:δ => 0.2
:mutiply_by_2π => true
:drives => true
:levels => 5
:frame_ω => 4.0Since this is a multilevel transmon and we want to implement an, let's say, $X$ gate on the qubit subspace, i.e., the first two levels we can utilize the EmbeddedOperator type to define the target operator.
# define the target operator
op = EmbeddedOperator(:X, sys)
# show the full operator
op.operator |> sparse5×5 SparseArrays.SparseMatrixCSC{ComplexF64, Int64} with 2 stored entries:
⋅ 1.0+0.0im ⋅ ⋅ ⋅
1.0+0.0im ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ In this formulation, we also use a subspace identity as the initial state, which looks like
function get_subspace_identity(op::EmbeddedOperator)
return embed(
Matrix{ComplexF64}(I(length(op.subspace))),
op.subspace,
size(op)[1]
)
end
get_subspace_identity(op) |> sparse5×5 SparseArrays.SparseMatrixCSC{ComplexF64, Int64} with 2 stored entries:
1.0+0.0im ⋅ ⋅ ⋅ ⋅
⋅ 1.0+0.0im ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ We can then pass this embedded operator to the UnitarySmoothPulseProblem template to create the problem
# create the problem
prob = UnitarySmoothPulseProblem(sys, op, T, Δt; a_bound=a_bound)
# solve the problemDirectTrajOptProblem
timesteps = 50
duration = 9.799999999999997
variable names = (:Ũ⃗, :a, :da, :dda, :Δt)
knot point dimension = 57
solve!(prob; max_iter=50) initializing optimizer...
applying constraint: timesteps all equal constraint
applying constraint: initial value of Ũ⃗
applying constraint: initial value of a
applying constraint: final value of a
applying constraint: bounds on a
applying constraint: bounds on da
applying constraint: bounds on dda
applying constraint: bounds on Δt
******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit https://github.com/coin-or/Ipopt
******************************************************************************
This is Ipopt version 3.14.19, running with linear solver MUMPS 5.8.1.
Number of nonzeros in equality constraint Jacobian...: 130578
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 11223
Total number of variables............................: 2796
variables with only lower bounds: 0
variables with lower and upper bounds: 246
variables with only upper bounds: 0
Total number of equality constraints.................: 2695
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 6.3299435e-04 9.98e-01 1.21e+01 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 1.7461331e+01 4.87e-01 3.66e+03 -0.6 1.02e+00 2.0 6.32e-01 5.00e-01h 2
2 1.1690187e+01 1.94e-01 6.11e+03 0.0 9.75e-01 2.4 1.00e+00 6.00e-01h 1
3 1.0956380e+00 1.36e-01 4.05e+03 -0.3 6.45e-01 2.9 1.00e+00 3.00e-01f 1
4 3.9110348e+00 1.13e-01 3.98e+03 -1.0 5.07e-01 3.3 1.00e+00 1.68e-01h 1
5 1.8650893e+01 4.46e-02 4.75e+03 -1.4 4.88e-01 2.8 1.00e+00 6.04e-01h 1
6 2.1587340e+01 3.10e-02 3.39e+03 -2.5 1.91e-01 3.2 1.00e+00 3.05e-01h 1
7 2.3916251e+01 2.00e-02 2.39e+03 -3.6 1.32e-01 2.7 1.00e+00 3.54e-01h 1
8 2.5059257e+01 1.40e-02 1.70e+03 -3.5 9.07e-02 3.2 1.00e+00 2.99e-01h 1
9 2.7401103e+01 4.99e-04 9.84e+02 -4.0 6.26e-02 2.7 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.6662020e+01 2.47e-05 8.42e+00 -1.9 1.25e-02 2.2 9.92e-01 1.00e+00f 1
11 2.4573360e+01 1.87e-04 1.95e+00 -3.1 3.51e-02 1.7 1.00e+00 1.00e+00f 1
12 1.9710930e+01 1.13e-03 1.57e+00 -3.5 8.47e-02 1.3 1.00e+00 1.00e+00f 1
13 1.3214702e+01 3.33e-03 2.21e+00 -2.8 1.36e-01 0.8 1.00e+00 1.00e+00f 1
14 8.9713575e+00 5.27e-03 3.39e+00 -2.4 1.44e-01 0.3 1.00e+00 1.00e+00f 1
15 5.6268437e+00 9.48e-02 1.50e+01 -1.1 2.43e+00 -0.2 6.20e-01 2.66e-01f 1
16 2.8332166e+00 8.38e-03 8.30e+00 -1.7 1.95e-01 0.3 9.97e-01 1.00e+00h 1
17 2.3173027e+00 1.07e-02 2.03e+02 -2.2 2.13e-01 -0.2 1.00e+00 1.00e+00h 1
18 3.5518904e+00 3.98e-03 1.95e+02 -1.9 1.73e-01 0.2 1.00e+00 1.00e+00h 1
19 2.8780348e+00 7.54e-05 1.50e+01 -3.3 2.12e-02 1.5 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 2.8000721e+00 1.94e-05 1.26e-01 -4.0 1.09e-02 1.1 1.00e+00 1.00e+00h 1
21 2.4804159e+00 1.27e-04 1.66e-01 -4.0 2.97e-02 0.6 1.00e+00 1.00e+00f 1
22 1.6341968e+00 8.22e-04 1.25e+00 -4.0 7.05e-02 0.1 1.00e+00 1.00e+00f 1
23 1.6390439e+00 6.27e-05 1.40e-01 -4.0 2.16e-02 0.5 1.00e+00 1.00e+00h 1
24 8.8490886e-01 8.76e-04 1.83e+00 -4.0 5.89e-02 0.1 1.00e+00 1.00e+00f 1
25 1.0781093e+00 6.37e-05 9.24e-02 -4.0 2.09e-02 0.5 1.00e+00 1.00e+00h 1
26 1.0394450e+00 8.22e-06 6.02e-02 -4.0 7.43e-03 0.9 1.00e+00 1.00e+00h 1
27 9.1719824e-01 6.75e-05 1.43e-01 -4.0 2.07e-02 0.4 1.00e+00 1.00e+00f 1
28 8.8207275e-01 9.13e-06 5.61e-02 -4.0 7.78e-03 0.9 1.00e+00 1.00e+00h 1
29 7.6943296e-01 7.46e-05 1.76e-01 -4.0 2.16e-02 0.4 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 7.3872292e-01 9.90e-06 5.17e-02 -4.0 8.08e-03 0.8 1.00e+00 1.00e+00h 1
31 6.3617857e-01 8.02e-05 2.02e-01 -4.0 2.24e-02 0.3 1.00e+00 1.00e+00f 1
32 6.1009072e-01 1.04e-05 4.71e-02 -4.0 8.27e-03 0.8 1.00e+00 1.00e+00h 1
33 5.1753483e-01 8.38e-05 2.35e-01 -4.0 2.28e-02 0.3 1.00e+00 1.00e+00f 1
34 4.9659870e-01 1.06e-05 4.21e-02 -4.0 8.31e-03 0.7 1.00e+00 1.00e+00h 1
35 4.1286956e-01 8.49e-05 2.86e-01 -4.0 2.30e-02 0.2 1.00e+00 1.00e+00f 1
36 3.9824804e-01 1.03e-05 3.92e-02 -4.0 8.19e-03 0.7 1.00e+00 1.00e+00h 1
37 3.1915370e-01 8.79e-05 3.87e-01 -4.0 2.28e-02 0.2 1.00e+00 1.00e+00f 1
38 3.1446190e-01 9.70e-06 3.30e-02 -4.0 7.88e-03 0.6 1.00e+00 1.00e+00h 1
39 2.1762752e-01 1.13e-04 6.66e-01 -4.0 2.31e-02 0.1 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 2.4363453e-01 9.72e-06 2.96e-02 -4.0 7.55e-03 0.6 1.00e+00 1.00e+00h 1
41 2.1604015e-01 6.65e-04 1.88e+02 -4.0 4.17e-01 0.1 1.00e+00 1.61e-01h 1
42 3.6597306e-01 1.29e-04 1.88e+02 -2.7 7.52e-02 -0.4 1.00e+00 1.00e+00H 1
43 3.5647971e-01 1.17e-06 1.64e+00 -2.8 2.13e-03 1.8 1.00e+00 1.00e+00h 1
44 3.4753360e-01 1.58e-06 6.64e-02 -4.0 2.95e-03 1.4 1.00e+00 1.00e+00h 1
45 3.3045607e-01 3.45e-06 9.48e-02 -4.0 4.85e-03 0.9 1.00e+00 1.00e+00f 1
46 2.9815119e-01 2.50e-05 8.55e-02 -4.0 1.35e-02 0.4 1.00e+00 1.00e+00h 1
47 2.8948071e-01 3.32e-06 3.25e-02 -4.1 4.88e-03 0.8 1.00e+00 1.00e+00h 1
48 2.5998426e-01 2.55e-05 6.31e-02 -4.0 1.35e-02 0.3 1.00e+00 1.00e+00h 1
49 2.5126499e-01 3.58e-06 2.93e-02 -4.1 4.94e-03 0.8 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 2.2337171e-01 2.87e-05 8.86e-02 -4.0 1.34e-02 0.3 1.00e+00 1.00e+00h 1
Number of Iterations....: 50
(scaled) (unscaled)
Objective...............: 2.2337171204275508e-01 2.2337171204275508e-01
Dual infeasibility......: 8.8610846418504252e-02 8.8610846418504252e-02
Constraint violation....: 2.8712906816219519e-05 2.8712906816219519e-05
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 1.0048178594192366e-04 1.0048178594192366e-04
Overall NLP error.......: 8.8610846418504252e-02 8.8610846418504252e-02
Number of objective function evaluations = 55
Number of objective gradient evaluations = 51
Number of equality constraint evaluations = 55
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 51
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 50
Total seconds in IPOPT = 293.520
EXIT: Maximum Number of Iterations Exceeded.
Let's look at the fidelity in the subspace
fid = unitary_rollout_fidelity(prob.trajectory, sys; subspace=op.subspace, drive_name=:a)
println("Fidelity: ", fid)
@assert fid > 0.99Fidelity: 0.9985904929446057and plot the result using the plot_unitary_populations function.
plot_unitary_populations(prob.trajectory; fig_size=(900, 700), control_name=:a)
Leakage suppresion
As can be seen from the above plot, there is a substantial amount of leakage into the higher levels during the evolution. To mitigate this, we have implemented a constraint to avoid populating the leakage levels, which should ideally drive those leakage populations down to zero. To implement this, pass leakage_constraint=true and set leakage_constraint_value={value} and leakage_cost={value} to the PiccoloOptions instance passed to the UnitarySmoothPulseProblem template.
# create the a leakage suppression problem, initializing with the previous solution
prob_leakage = UnitarySmoothPulseProblem(sys, op, T, Δt;
a_bound=a_bound,
a_guess=prob.trajectory.a[:, :],
piccolo_options=PiccoloOptions(
leakage_constraint=true,
leakage_constraint_value=1e-2,
leakage_cost=1e-2,
),
)
# solve the problem constructing UnitarySmoothPulseProblem...
using integrator: typeof(UnitaryIntegrator)
control derivative names: [:da, :dda]
applying leakage suppression: Ũ⃗ < 0.01
applying timesteps_all_equal constraint: Δtsolve!(prob_leakage; max_iter=250) initializing optimizer...
applying constraint: timesteps all equal constraint
applying constraint: initial value of Ũ⃗
applying constraint: initial value of a
applying constraint: final value of a
applying constraint: bounds on a
applying constraint: bounds on da
applying constraint: bounds on dda
applying constraint: bounds on Δt
This is Ipopt version 3.14.19, running with linear solver MUMPS 5.8.1.
Number of nonzeros in equality constraint Jacobian...: 130578
Number of nonzeros in inequality constraint Jacobian.: 58800
Number of nonzeros in Lagrangian Hessian.............: 196198
Total number of variables............................: 2796
variables with only lower bounds: 0
variables with lower and upper bounds: 246
variables with only upper bounds: 0
Total number of equality constraints.................: 2695
Total number of inequality constraints...............: 1200
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 1200
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 2.2434810e-01 1.80e-01 2.30e-01 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 5.1360583e-01 1.65e-01 1.95e+02 -1.4 7.80e-01 0.0 3.96e-01 1.19e-01h 1
2 3.3978388e-01 1.50e-01 1.74e+02 -2.6 9.24e-01 - 1.15e-01 1.04e-01h 1
3 1.5298834e-01 1.41e-01 1.63e+02 -1.4 1.88e+00 - 1.06e-01 6.31e-02f 1
4 1.7494458e-01 1.29e-01 4.47e+01 -2.1 1.72e+00 - 9.03e-02 8.41e-02h 1
5 3.5467772e-01 1.24e-01 4.26e+01 -4.0 2.44e+00 - 3.22e-02 4.34e-02h 1
6 6.4298267e-01 1.18e-01 4.07e+01 -2.7 3.39e+00 - 5.09e-02 4.23e-02h 1
7 1.0024286e+00 1.14e-01 3.91e+01 -4.0 5.49e+00 - 1.37e-02 3.81e-02h 2
8 1.0670467e+00 1.14e-01 3.90e+01 -2.0 2.79e+01 - 1.34e-02 2.36e-03h 4
9 2.1279853e+00 1.06e-01 3.66e+01 -0.8 2.04e+00 -0.5 4.67e-02 6.21e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.9482553e+00 9.76e-02 3.39e+01 -1.5 2.87e+00 - 1.14e-01 7.71e-02h 1
11 3.6354733e+00 8.55e-02 2.98e+01 -1.6 3.21e+00 - 1.45e-01 1.27e-01h 1
12 3.9542845e+00 8.22e-02 3.53e+01 -3.2 1.25e+00 -1.0 1.51e-01 3.99e-02h 1
13 4.6058365e+00 7.25e-02 2.53e+01 -2.9 2.91e+00 -1.4 7.32e-02 1.23e-01h 1
14 4.4192139e+00 7.13e-02 2.48e+01 -4.0 2.34e+01 -1.9 1.58e-02 1.65e-02h 1
15 4.4716125e+00 7.06e-02 2.92e+01 -1.6 1.25e+01 -1.5 4.57e-02 9.32e-03h 2
16 5.2029137e+00 6.41e-02 2.31e+01 -4.0 1.27e+00 -1.1 4.50e-02 9.55e-02h 1
17 5.8079661e+00 5.89e-02 2.10e+01 -2.3 4.45e+00 -1.5 6.89e-02 8.31e-02h 1
18 6.0649488e+00 5.68e-02 2.00e+01 -4.0 1.51e+00 -1.1 7.23e-02 3.56e-02h 1
19 6.1470389e+00 5.50e-02 1.94e+01 -1.9 1.01e+01 -1.6 3.33e-02 3.11e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 7.3900831e+00 4.73e-02 9.26e+01 -1.5 2.16e+00 -1.2 8.51e-03 1.41e-01h 1
21 7.3175120e+00 4.64e-02 9.28e+01 -4.0 7.91e+00 -1.6 3.53e-02 1.89e-02h 1
22 7.2518493e+00 4.47e-02 8.74e+01 -2.4 2.67e+00 -1.2 5.36e-02 3.74e-02f 1
23 7.4999269e+00 4.22e-02 8.11e+01 -4.0 2.69e+00 -1.7 1.01e-01 5.58e-02h 1
24 9.3286084e+00 3.55e-02 6.99e+01 -1.2 3.01e+00 -1.3 5.23e-02 1.51e-01f 1
25 9.2556248e+00 3.47e-02 7.09e+01 -1.6 1.19e+01 -1.7 3.77e-02 2.28e-02h 2
26 1.0820117e+01 2.59e-02 6.61e+01 -1.6 1.64e+00 -1.3 1.64e-01 2.65e-01h 1
27 1.1406085e+01 2.23e-02 5.64e+01 -2.4 7.21e-01 -0.9 2.58e-01 1.44e-01h 1
28 1.1873495e+01 1.98e-02 4.85e+01 -2.8 1.25e+00 -1.4 2.25e-01 1.40e-01h 1
29 1.2962332e+01 1.60e-02 4.00e+01 -1.9 5.99e-01 -0.9 4.93e-01 1.93e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 1.3655030e+01 1.29e-02 2.97e+01 -3.5 1.14e+00 -1.4 3.82e-01 2.48e-01h 1
31 1.4246526e+01 1.02e-02 4.19e+01 -3.1 7.10e-01 -1.0 5.61e-01 2.10e-01h 1
32 1.4273160e+01 1.03e-02 3.94e+01 -4.0 2.86e+00 -1.5 9.80e-02 7.56e-02h 1
33 1.6584319e+01 9.17e-03 4.71e+01 -1.6 9.30e-01 -1.0 3.37e-01 4.96e-01h 1
34 1.6353390e+01 9.01e-03 3.80e+01 -4.0 1.16e+00 -1.5 3.17e-01 1.81e-01h 1
35 1.7121024e+01 1.11e-02 2.29e+01 -1.8 8.51e-01 -1.1 5.44e-01 4.72e-01h 1
36 1.7000596e+01 1.03e-02 2.89e+01 -2.1 1.52e+00 -1.6 4.17e-01 1.66e-01h 1
37 1.7009235e+01 1.13e-02 8.85e+00 -2.2 5.82e-01 -1.1 1.00e+00 7.66e-01h 1
38 1.6715808e+01 1.14e-02 8.39e+00 -4.0 4.85e+00 -1.6 8.01e-02 7.52e-02f 1
39 1.6583232e+01 1.31e-02 2.10e+01 -2.0 1.08e+00 -1.2 5.96e-01 2.87e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 1.6387644e+01 1.43e-02 1.96e+01 -4.0 5.65e+00 -1.7 2.87e-02 3.86e-02f 1
41 1.6176023e+01 1.19e-02 2.87e+01 -2.4 6.66e-01 -1.2 5.17e-01 2.27e-01h 1
42 1.5766434e+01 4.69e-03 9.78e+00 -2.8 2.38e-01 -0.8 1.00e+00 6.89e-01h 1
43 1.5502056e+01 5.75e-03 7.89e+00 -4.0 1.50e+00 -1.3 1.27e-01 2.65e-01h 1
44 1.5464768e+01 5.67e-03 6.62e+00 -3.6 4.26e+00 -1.8 5.48e-02 1.95e-02h 1
45 1.5363973e+01 4.82e-03 2.08e+01 -3.7 9.38e-01 -1.3 4.76e-01 1.70e-01h 1
46 1.5272261e+01 7.92e-03 2.18e+01 -2.5 4.89e+00 -1.8 1.16e-01 9.52e-02f 1
47 1.5200598e+01 6.91e-03 1.79e+01 -4.0 5.60e-01 -1.4 1.63e-01 1.67e-01h 1
48 1.5101997e+01 3.17e-03 9.84e+00 -3.3 1.68e-01 -1.0 1.00e+00 5.43e-01h 1
49 1.5130171e+01 3.72e-03 6.11e+00 -2.4 1.19e+00 -1.4 2.86e-01 3.25e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 1.4961267e+01 2.34e-03 2.16e-01 -3.0 2.31e-01 -1.0 1.00e+00 1.00e+00h 1
51 1.4901294e+01 3.83e-03 2.50e+00 -4.0 2.03e+01 -1.5 1.79e-02 2.72e-02f 1
52 1.4820034e+01 3.34e-03 1.34e+01 -3.2 5.62e-01 -1.1 4.46e-01 2.65e-01h 1
53 1.4695608e+01 1.05e-03 3.00e+00 -3.2 1.98e-01 -0.6 1.00e+00 8.82e-01h 1
54 1.4710425e+01 1.41e-03 2.73e+01 -2.1 1.23e+00 -1.1 2.91e-01 1.37e-01f 1
55 1.4637563e+01 1.31e-03 2.29e-01 -2.7 2.02e-01 -0.7 9.89e-01 9.84e-01h 1
56 1.4544992e+01 1.64e-03 2.38e+01 -2.8 5.81e-01 -1.2 6.51e-01 2.61e-01f 1
57 1.4354862e+01 1.08e-03 1.34e+00 -3.1 1.71e-01 -0.8 1.00e+00 9.56e-01h 1
58 1.4218876e+01 2.07e-03 2.49e+00 -3.1 9.92e-01 -1.2 2.14e-01 2.82e-01f 1
59 1.4178814e+01 1.72e-03 3.84e+01 -3.3 2.49e-01 -0.8 1.00e+00 1.96e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 1.4128541e+01 1.64e-03 2.86e+01 -3.0 6.05e-01 -1.3 5.48e-01 1.44e-01h 1
61 1.4062175e+01 2.04e-03 2.79e+01 -4.0 5.98e+01 -1.8 5.80e-03 3.90e-03f 1
62 1.3989562e+01 2.56e-03 2.77e+01 -3.2 1.12e+00 -1.3 4.45e-01 1.47e-01h 1
63 1.3957837e+01 2.92e-03 2.60e+01 -4.0 1.02e+01 -1.8 8.19e-03 1.73e-02h 1
64 1.3963036e+01 4.31e-03 2.34e+01 -2.3 1.53e+00 -1.4 2.62e-01 1.84e-01f 1
65 1.3795483e+01 3.47e-03 1.88e+00 -2.8 3.49e-01 -1.0 9.47e-01 9.17e-01h 1
66 1.3821989e+01 1.09e-02 4.66e+00 -2.1 1.31e+00 -1.4 2.16e-01 3.34e-01f 1
67 1.3513501e+01 6.60e-03 3.23e+00 -2.6 2.97e-01 -1.0 7.31e-01 1.00e+00h 1
68 1.3615375e+01 7.56e-03 2.41e+01 -1.6 3.11e+00 -1.5 1.78e-01 7.96e-02f 1
69 1.3458542e+01 7.89e-03 5.66e+00 -2.3 5.76e-01 -1.1 1.00e+00 8.38e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
70 1.3209032e+01 8.36e-03 5.46e+00 -4.0 2.52e+00 -1.5 9.78e-02 1.74e-01f 1
71 1.3633791e+01 5.45e-03 9.66e+00 -1.8 6.13e-01 -1.1 5.58e-01 4.43e-01f 1
72 1.3361759e+01 9.05e-03 5.53e+00 -2.0 1.44e+00 -1.6 3.92e-01 3.56e-01f 1
73 1.3238282e+01 9.07e-03 1.45e+01 -2.0 5.20e+00 -2.1 8.91e-02 5.42e-02f 1
74 1.2955181e+01 2.46e-02 5.02e+00 -2.0 1.41e+00 -1.6 5.40e-01 5.52e-01f 1
75 1.2574793e+01 1.40e-02 6.90e-01 -2.1 4.31e-01 -1.2 9.98e-01 1.00e+00f 1
76 1.3377424e+01 2.95e-02 2.93e+01 -1.5 1.35e+00 -1.7 2.77e-01 5.21e-01f 1
77 1.2848595e+01 1.63e-02 1.98e+01 -1.9 5.63e-01 -1.3 8.93e-01 4.79e-01h 1
78 1.2442586e+01 2.64e-02 2.03e+01 -1.9 2.21e+00 -1.7 1.28e-01 2.76e-01f 1
79 1.2939107e+01 7.17e-02 1.01e+01 -1.6 9.80e-01 -1.3 7.02e-01 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
80 1.2540492e+01 6.64e-02 2.88e+01 -1.7 2.47e+00 -1.8 3.46e-01 1.20e-01h 1
81 1.1850553e+01 2.24e-02 1.66e+01 -1.7 8.38e-01 -1.4 1.00e+00 6.85e-01h 1
82 1.1643625e+01 6.17e-02 7.86e+00 -1.5 4.52e+00 -1.8 2.34e-01 2.82e-01f 1
83 1.0693663e+01 8.69e-02 2.03e+01 -1.8 1.80e+00 -1.4 3.59e-01 5.56e-01h 1
84 1.0121059e+01 4.34e-02 1.27e+01 -2.0 5.38e-01 -1.0 1.00e+00 5.24e-01h 1
85 9.9079535e+00 3.43e-02 3.91e+01 -2.0 9.18e-01 -1.5 8.55e-01 2.13e-01h 1
86 9.3270814e+00 2.37e-02 1.29e+01 -3.2 2.75e+00 -1.9 6.93e-02 2.71e-01f 1
87 9.7550231e+00 2.76e-02 2.21e+01 -1.6 1.09e+00 -1.5 7.90e-01 3.85e-01f 1
88 9.3161893e+00 5.83e-02 2.05e+01 -1.8 6.81e+00 -2.0 7.14e-02 1.27e-01f 1
89 8.8970316e+00 4.98e-02 1.67e+01 -2.1 2.16e+00 -1.6 5.22e-01 2.35e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
90 8.3140819e+00 1.15e-02 8.69e-01 -2.1 5.05e-01 -1.1 1.00e+00 1.00e+00h 1
91 7.9603342e+00 1.49e-02 1.21e+00 -4.0 2.12e+00 - 1.61e-01 1.80e-01f 1
92 7.9082637e+00 2.14e-02 9.53e+00 -1.6 8.79e+00 - 8.96e-02 4.88e-02f 1
93 7.4312193e+00 2.57e-02 2.44e+00 -2.5 8.29e-01 -1.6 5.08e-01 6.15e-01h 1
94 7.5632963e+00 1.43e-02 5.65e+00 -2.0 4.45e-01 -1.2 1.00e+00 6.54e-01f 1
95 7.3716256e+00 1.38e-02 9.73e+00 -4.0 2.16e+00 - 1.39e-01 1.06e-01h 1
96 7.4338637e+00 3.44e-02 5.69e+00 -1.8 1.70e+00 -1.7 4.15e-01 4.16e-01f 1
97 7.1910678e+00 3.69e-02 2.01e+01 -2.0 3.52e+00 -2.1 1.54e-01 1.09e-01h 1
98 6.8160733e+00 2.75e-02 1.30e+01 -2.4 1.25e+00 -1.7 3.27e-01 3.39e-01h 1
99 8.2506540e+00 3.23e-02 1.68e+01 -1.6 7.74e-01 -1.3 6.37e-01 9.30e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
100 7.3157431e+00 4.03e-02 1.02e+01 -1.8 1.57e+00 -1.8 2.78e-01 6.61e-01f 1
101 7.1076817e+00 2.28e-02 9.53e+00 -1.8 7.72e-01 -1.3 7.04e-01 4.74e-01h 1
102 6.7105604e+00 4.00e-02 1.03e+01 -1.8 1.97e+00 -1.8 3.03e-01 4.58e-01h 1
103 5.9436852e+00 3.67e-02 7.93e+00 -2.0 9.57e-01 -1.4 1.00e+00 7.26e-01h 1
104 5.4304167e+00 4.09e-02 6.88e+00 -2.8 3.21e+00 -1.9 1.91e-01 1.82e-01f 1
105 5.2876386e+00 3.81e-02 1.44e+01 -4.0 3.32e+00 -2.4 1.25e-01 6.85e-02h 1
106 5.0522132e+00 3.31e-02 8.28e+00 -4.0 3.83e+00 -1.9 4.37e-02 1.28e-01h 1
107 4.8183441e+00 2.26e-02 7.66e+00 -3.1 6.15e-01 -1.5 5.09e-01 3.19e-01h 1
108 4.5165257e+00 3.72e-03 3.23e-01 -2.7 2.61e-01 -1.1 1.00e+00 1.00e+00h 1
109 4.5291198e+00 1.18e-02 2.75e+00 -2.3 6.54e-01 -1.6 8.79e-01 7.24e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
110 4.3926958e+00 1.77e-02 6.37e+00 -2.4 2.59e+00 -2.0 2.04e-01 1.37e-01h 1
111 4.2375398e+00 1.07e-02 7.22e+00 -2.9 4.28e-01 -1.6 5.63e-01 3.78e-01h 1
112 4.0537762e+00 3.74e-03 5.91e+00 -3.4 1.58e-01 -1.2 1.00e+00 6.45e-01h 1
113 4.1155608e+00 5.63e-03 8.62e+00 -2.1 1.53e+00 -1.7 2.38e-01 1.67e-01f 1
114 4.0155551e+00 2.88e-03 2.16e+00 -2.8 1.63e-01 -1.2 1.00e+00 9.19e-01h 1
115 3.9067802e+00 9.49e-04 2.21e+00 -3.5 9.75e-02 -0.8 9.99e-01 7.61e-01h 1
116 3.9938137e+00 1.98e-03 2.49e+00 -2.5 3.74e-01 -1.3 6.02e-01 4.51e-01f 1
117 3.9460827e+00 5.23e-04 6.51e-02 -2.7 7.95e-02 -0.9 1.00e+00 9.98e-01h 1
118 3.8128176e+00 1.25e-03 2.15e+01 -3.3 2.15e-01 -1.3 4.48e-01 8.99e-01h 1
119 3.7482636e+00 5.57e-04 8.14e-01 -3.5 9.63e-02 -0.9 1.00e+00 9.64e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
120 3.7800814e+00 5.58e-03 3.09e+00 -2.4 1.05e+00 -1.4 4.69e-01 3.13e-01f 1
121 3.7400411e+00 6.72e-03 3.06e+00 -2.8 1.71e+01 -1.9 7.91e-03 7.94e-03f 1
122 3.8745681e+00 6.14e-03 1.25e+01 -1.4 7.48e+00 -2.3 1.12e-01 3.36e-02f 1
123 3.7898720e+00 1.16e-02 9.87e+00 -2.3 1.95e+00 -1.9 2.99e-01 2.10e-01h 1
124 3.7294414e+00 1.86e-02 7.93e+00 -2.3 5.37e+00 - 6.24e-02 9.37e-02h 1
125 3.6624469e+00 8.21e-03 8.88e-01 -2.3 4.72e-01 -1.5 9.54e-01 9.63e-01h 1
126 3.4770994e+00 2.40e-02 7.83e-01 -2.3 2.78e+00 -2.0 2.21e-01 2.06e-01h 1
127 3.2724867e+00 1.71e-02 1.41e+01 -2.9 5.74e-01 -1.5 8.81e-01 3.84e-01h 1
128 3.7215344e+00 2.46e-02 3.42e+00 -2.1 5.70e-01 -1.1 9.09e-01 1.00e+00f 1
129 3.6754401e+00 2.39e-02 8.81e+00 -2.2 4.07e+00 - 1.24e-01 2.48e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
130 3.4989042e+00 2.54e-02 5.43e+00 -2.2 4.64e+00 - 9.56e-02 1.33e-01f 1
131 3.2315579e+00 1.65e-02 5.75e+00 -2.2 7.09e-01 -1.6 9.71e-01 6.15e-01h 1
132 3.1257008e+00 1.70e-02 8.10e+00 -4.0 1.88e+00 - 1.43e-01 9.81e-02h 1
133 2.8849951e+00 2.72e-02 4.97e+00 -2.6 1.94e+00 -2.1 2.00e-01 3.03e-01f 1
134 3.0253615e+00 3.41e-02 4.62e+00 -2.0 1.11e+00 -1.6 7.17e-01 5.34e-01f 1
135 2.9480268e+00 2.82e-02 5.49e+00 -2.1 1.54e+00 -2.1 2.96e-01 2.25e-01h 1
136 3.4284208e+00 6.64e-02 1.66e+00 -1.8 1.03e+00 -1.7 1.00e+00 1.00e+00f 1
137 3.0555677e+00 9.96e-02 2.35e+00 -1.9 1.08e+01 -2.2 9.12e-02 1.10e-01h 1
138 2.6721864e+00 5.49e-02 3.68e+00 -1.9 1.34e+00 -1.7 7.39e-01 8.67e-01h 1
139 2.5816079e+00 5.25e-02 2.97e+00 -1.9 2.46e+00 -2.2 3.44e-01 2.50e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
140 3.2016552e+00 6.92e-02 6.96e+00 -1.6 1.25e+00 -1.8 7.22e-01 1.00e+00f 1
141 2.8670661e+00 1.23e-01 1.11e+01 -1.8 2.23e+01 -2.3 4.66e-02 6.59e-02h 1
142 2.2296733e+00 1.46e-01 5.13e+00 -1.8 3.41e+00 -1.8 5.11e-01 5.22e-01h 1
143 1.9719741e+00 5.35e-02 6.03e+00 -2.0 7.19e-01 -2.3 8.23e-01 1.00e+00h 1
144 1.8488817e+00 3.33e-02 3.54e+00 -2.0 1.36e+00 - 8.45e-01 6.73e-01h 1
145 1.5934637e+00 4.64e-02 4.15e+00 -4.0 2.84e+00 -2.8 1.72e-01 2.78e-01h 1
146 1.4649895e+00 5.72e-02 4.14e+00 -4.0 1.03e+01 -2.4 5.52e-02 6.73e-02h 1
147 1.5944640e+00 5.23e-02 3.72e+00 -1.8 1.38e+00 -1.9 8.25e-01 5.81e-01f 1
148 1.4816354e+00 4.55e-02 1.04e+01 -4.0 1.87e+00 - 2.53e-01 1.17e-01h 1
149 1.1724953e+00 3.02e-02 6.50e+00 -3.1 1.84e+00 -2.4 3.94e-01 3.77e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
150 1.4361504e+00 6.78e-02 1.00e+00 -1.9 1.26e+00 -2.0 9.16e-01 1.00e+00f 1
151 1.2787540e+00 1.45e-01 1.96e+00 -2.1 1.66e+02 -2.5 9.47e-03 8.42e-03f 1
152 1.1133893e+00 1.01e-01 8.22e+00 -2.1 2.57e+00 -2.0 7.56e-01 3.45e-01h 1
153 7.1877856e-01 1.03e-02 4.86e-01 -2.4 5.52e-01 -1.6 1.00e+00 1.00e+00h 1
154 5.5133410e-01 1.74e-02 1.09e+00 -2.7 6.52e-01 - 9.96e-01 8.01e-01h 1
155 4.7307732e-01 2.26e-02 9.28e-01 -4.0 1.93e+00 - 1.91e-01 2.48e-01h 1
156 5.1588511e-01 2.78e-02 2.07e+00 -2.5 7.01e-01 -2.1 1.00e+00 7.02e-01h 1
157 4.3312655e-01 2.03e-02 1.98e+00 -3.3 5.22e-01 -2.6 5.09e-01 4.01e-01h 1
158 4.0894430e-01 7.56e-02 1.43e+00 -2.8 7.99e-01 -2.1 6.93e-01 9.36e-01h 1
159 3.6136357e-01 4.55e-02 2.80e+00 -3.0 3.31e-01 -1.7 1.00e+00 4.12e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
160 5.3620960e-01 4.67e-02 6.79e+00 -1.8 4.43e+00 -2.2 3.35e-01 1.70e-01f 1
161 4.6413185e-01 5.25e-02 5.00e+00 -2.3 4.42e+00 - 2.23e-01 1.55e-01h 1
162 4.1983466e-01 4.75e-02 3.71e+00 -2.3 3.83e+00 -2.7 2.16e-01 2.57e-01h 1
163 4.2918854e-01 5.22e-02 3.31e+00 -2.3 1.15e+00 -2.3 5.31e-01 7.78e-01h 1
164 4.0017389e-01 8.62e-02 6.62e+00 -2.3 2.79e+00 -2.7 2.01e-01 3.54e-01h 1
165 3.6484128e-01 3.95e-02 2.53e+00 -2.3 9.69e-01 -2.3 6.88e-01 6.38e-01h 1
166 3.2481979e-01 4.88e-02 1.77e+00 -2.3 2.71e+00 -2.8 4.23e-01 2.87e-01h 1
167 4.8744457e-01 1.18e-01 8.58e-01 -2.1 1.41e+00 -2.4 1.00e+00 1.00e+00f 1
168 3.5853645e-01 2.35e-02 1.91e-01 -2.1 7.20e-01 -1.9 1.00e+00 1.00e+00h 1
169 1.5396381e-01 3.96e-02 9.27e-01 -2.5 8.14e-01 - 9.90e-01 9.50e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
170 6.6503664e-02 2.29e-02 4.12e-01 -2.8 6.83e-01 -2.4 1.00e+00 1.00e+00h 1
171 4.4384277e-02 5.68e-02 6.06e-01 -4.0 7.09e+00 - 9.70e-02 1.18e-01h 1
172 1.5349234e-02 3.24e-02 3.78e-01 -4.0 7.35e-01 -2.9 5.34e-01 4.75e-01h 1
173 7.4965966e-03 1.82e-02 1.53e+00 -4.0 9.07e-01 -3.4 3.28e-01 6.35e-01h 1
174 6.9626552e-03 1.65e-02 1.99e+02 -3.6 4.40e-01 -2.9 9.37e-01 1.00e+00h 1
175 1.2976435e-02 6.05e-02 4.57e+01 -2.9 3.57e+00 -3.4 9.61e-01 2.30e-01h 1
176 9.9430069e-03 5.59e-02 4.04e+01 -3.0 4.67e+00 -3.9 5.32e-02 1.16e-01h 1
177 2.0724336e-02 3.30e-02 1.99e+02 -3.0 5.76e-01 -2.6 6.97e-01 1.00e+00h 1
178 2.5641423e-02 5.24e-02 6.32e+01 -3.0 2.50e+00 - 1.64e-01 3.18e-01h 1
179 9.6886814e-03 4.63e-02 1.43e+02 -3.0 4.39e-01 -1.2 3.96e-01 1.23e-01f 2
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
180 3.9528584e-02 3.37e-02 9.58e+01 -3.0 3.97e-01 -1.7 4.93e-01 2.82e-01h 2
181 4.6505271e-02 2.30e-04 5.51e+00 -3.0 1.11e-01 1.4 1.00e+00 1.00e+00h 1
182 2.8594169e-02 2.76e-04 1.99e+02 -3.7 5.92e-02 - 1.00e+00 1.00e+00h 1
183 1.1357325e-02 3.20e-06 1.99e+02 -3.4 3.38e-03 1.0 1.00e+00 1.00e+00h 1
184 1.1942377e-02 2.07e-08 2.79e-01 -4.0 3.55e-04 2.3 1.00e+00 1.00e+00h 1
185 1.0738335e-02 1.03e-07 5.19e-02 -4.0 8.16e-04 1.8 1.00e+00 1.00e+00h 1
186 8.5569293e-03 5.20e-07 3.35e-02 -4.0 1.58e-03 1.3 1.00e+00 1.00e+00h 1
187 6.6983517e-03 1.50e-06 1.55e-02 -4.0 1.97e-03 0.8 1.00e+00 1.00e+00h 1
188 5.6878659e-03 2.33e-06 1.60e-02 -4.0 2.25e-03 0.4 1.00e+00 1.00e+00h 1
189 5.1115152e-03 4.07e-06 1.09e-02 -4.0 2.88e-03 -0.1 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
190 4.7593272e-03 1.66e-05 4.02e-03 -4.0 5.29e-03 -0.6 1.00e+00 1.00e+00h 1
191 4.3579530e-03 7.11e-05 5.56e-03 -4.0 1.45e-02 -1.1 1.00e+00 1.00e+00h 1
192 3.8785754e-03 1.89e-04 8.20e-03 -4.0 3.52e-02 -1.5 1.00e+00 1.00e+00h 1
193 3.5277161e-03 1.90e-04 6.74e-03 -4.0 7.68e-02 -2.0 1.00e+00 1.00e+00h 1
194 3.2061392e-03 5.08e-04 2.37e-02 -4.0 1.32e-01 -2.5 1.00e+00 1.00e+00h 1
195 3.1816034e-03 5.76e-05 3.86e-03 -4.0 4.15e-02 -2.1 1.00e+00 1.00e+00h 1
196 3.0190506e-03 2.87e-04 7.90e-03 -4.0 7.62e-02 -2.5 1.00e+00 1.00e+00h 1
197 2.9927482e-03 3.17e-05 3.36e-03 -4.0 2.32e-02 -2.1 1.00e+00 1.00e+00h 1
198 2.9115675e-03 1.74e-04 6.63e-03 -4.0 4.11e-02 -2.6 1.00e+00 1.00e+00h 1
199 2.8993710e-03 2.13e-05 3.80e-03 -4.0 1.49e-02 -2.2 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
200 2.8387760e-03 1.26e-04 8.95e-03 -4.0 4.44e-02 -2.6 1.00e+00 1.00e+00h 1
201 2.8347380e-03 3.51e-05 6.44e-03 -4.0 1.65e-02 -2.2 1.00e+00 1.00e+00h 1
202 2.7619576e-03 1.92e-04 1.59e-02 -4.0 4.95e-02 -2.7 1.00e+00 1.00e+00h 1
203 2.7648427e-03 8.33e-05 1.45e-02 -4.0 2.03e-02 -2.3 1.00e+00 1.00e+00h 1
204 2.5920076e-03 5.44e-04 3.67e-02 -4.0 5.49e-02 -2.7 1.00e+00 1.00e+00h 1
205 2.5455650e-03 2.41e-04 4.38e-02 -4.0 5.54e-02 -2.3 1.00e+00 1.00e+00h 1
206 2.3979241e-03 2.69e-04 1.99e+02 -4.0 1.17e-01 -2.8 1.00e+00 5.00e-01h 2
207 2.5314040e-03 6.84e-02 7.27e+01 -4.0 3.91e+00 - 2.12e-01 3.66e-01h 1
208 7.0306846e-03 5.09e-02 1.46e+02 -4.1 6.76e-01 0.3 1.19e-01 2.72e-01h 1
209 4.6038412e-03 1.58e-02 1.53e+02 -4.1 5.41e-01 -0.1 3.53e-01 6.89e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
210 5.9407063e-03 1.18e-02 1.15e+02 -4.1 1.78e-01 2.1 1.00e+00 2.51e-01h 1
211 6.9597881e-03 8.05e-03 7.80e+01 -4.1 1.39e-01 1.6 1.00e+00 3.21e-01h 1
212 2.5875054e-03 2.29e-04 1.99e+02 -4.1 9.99e-02 1.1 1.00e+00 1.00e+00h 1
213 8.3993369e-03 4.97e-06 1.99e+02 -3.7 4.12e-03 0.7 1.00e+00 1.00e+00h 1
214 8.7259576e-03 1.77e-07 4.52e-01 -3.8 8.98e-04 2.0 1.00e+00 1.00e+00h 1
215 6.8485782e-03 5.94e-07 4.93e-02 -4.0 1.51e-03 1.5 1.00e+00 1.00e+00h 1
216 4.8365983e-03 1.31e-06 7.56e-02 -4.0 2.13e-03 1.0 1.00e+00 8.64e-01h 1
217 3.4448013e-03 3.00e-06 1.10e-02 -4.0 3.04e-03 0.6 1.00e+00 1.00e+00h 1
218 2.8205650e-03 1.76e-06 1.12e-02 -4.0 3.88e-03 0.1 1.00e+00 1.00e+00h 1
219 2.6563934e-03 3.61e-06 1.39e-02 -4.0 8.51e-03 -0.4 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
220 2.5089040e-03 1.41e-05 2.25e-02 -4.0 1.68e-02 -0.9 1.00e+00 1.00e+00h 1
221 2.3732645e-03 3.41e-05 2.89e-02 -4.0 2.44e-02 -1.3 1.00e+00 1.00e+00h 1
222 2.3637758e-03 2.54e-05 1.72e-03 -4.0 1.98e-02 -1.8 1.00e+00 1.00e+00h 1
223 2.1029461e-03 1.57e-04 4.26e-02 -4.0 4.46e-02 -2.3 1.00e+00 1.00e+00h 1
224 2.0875193e-03 2.38e-04 1.99e+02 -3.5 1.43e+00 -2.8 7.60e-01 3.05e-02h 4
225 2.4858676e-03 2.39e-02 1.66e+02 -3.9 1.30e+00 - 8.51e-01 8.36e-01h 1
226 2.3758097e-03 4.63e-03 4.60e+02 -3.9 5.06e-01 2.2 4.78e-01 8.45e-01h 1
227 9.0031537e-03 1.67e-04 1.99e+02 -3.9 9.47e-02 1.7 4.38e-01 1.00e+00h 1
228 8.9035157e-03 3.59e-07 1.37e+00 -3.9 1.27e-03 2.1 1.00e+00 1.00e+00h 1
229 6.5831658e-03 6.34e-07 8.07e-02 -3.9 1.88e-03 1.6 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
230 3.4751776e-03 1.29e-06 4.11e-02 -4.0 2.88e-03 1.2 1.00e+00 1.00e+00h 1
231 2.2304574e-03 1.29e-06 1.49e-02 -4.0 2.39e-03 0.7 1.00e+00 1.00e+00h 1
232 2.1636089e-03 7.28e-07 1.15e-02 -4.0 1.99e-03 0.2 1.00e+00 1.00e+00h 1
233 2.0982790e-03 1.12e-06 9.63e-03 -4.0 3.70e-03 -0.3 1.00e+00 1.00e+00h 1
234 2.0733464e-03 2.59e-06 6.42e-03 -4.0 7.75e-03 -0.8 1.00e+00 1.00e+00h 1
235 2.0265419e-03 7.64e-06 6.06e-03 -4.0 1.26e-02 -1.2 1.00e+00 1.00e+00h 1
236 1.9679894e-03 7.81e-06 2.87e-03 -4.0 1.37e-02 -1.7 1.00e+00 1.00e+00h 1
237 1.8796167e-03 2.80e-05 1.39e-02 -4.0 2.95e-02 -2.2 1.00e+00 1.00e+00h 1
238 1.8625501e-03 4.14e-06 7.39e-03 -4.0 9.70e-03 -1.8 1.00e+00 1.00e+00h 1
239 1.8161312e-03 1.94e-05 1.48e-02 -4.0 2.03e-02 -2.2 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
240 1.8079284e-03 5.34e-06 8.15e-03 -4.0 6.77e-03 -1.8 1.00e+00 1.00e+00h 1
241 1.7822434e-03 1.60e-05 1.37e-02 -4.0 1.36e-02 -2.3 1.00e+00 1.00e+00h 1
242 1.7767597e-03 6.20e-06 8.05e-03 -4.0 7.06e-03 -1.9 1.00e+00 1.00e+00h 1
243 1.7590995e-03 1.97e-05 1.42e-02 -4.0 1.23e-02 -2.3 1.00e+00 1.00e+00h 1
244 1.7551865e-03 8.03e-06 8.98e-03 -4.0 8.33e-03 -1.9 1.00e+00 1.00e+00h 1
245 1.7381917e-03 3.01e-05 1.70e-02 -4.0 1.37e-02 -2.4 1.00e+00 1.00e+00h 1
246 1.7355438e-03 1.21e-05 1.17e-02 -4.0 1.11e-02 -2.0 1.00e+00 1.00e+00h 1
247 1.7084108e-03 5.16e-05 2.32e-02 -4.0 1.95e-02 -2.4 1.00e+00 1.00e+00h 1
248 1.7080428e-03 2.11e-05 1.73e-02 -4.0 1.68e-02 -2.0 1.00e+00 1.00e+00h 1
249 1.6359863e-03 1.07e-04 3.64e-02 -4.0 3.43e-02 -2.5 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
250 1.6487637e-03 4.14e-05 2.81e-02 -4.0 2.77e-02 -2.1 1.00e+00 1.00e+00h 1
Number of Iterations....: 250
(scaled) (unscaled)
Objective...............: 1.6487637480209457e-03 1.6487637480209457e-03
Dual infeasibility......: 2.8069428563796350e-02 2.8069428563796350e-02
Constraint violation....: 4.1350575226820063e-05 4.1350575226820063e-05
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 1.0000000000000002e-04 1.0000000000000002e-04
Overall NLP error.......: 2.8069428563796350e-02 2.8069428563796350e-02
Number of objective function evaluations = 270
Number of objective gradient evaluations = 251
Number of equality constraint evaluations = 270
Number of inequality constraint evaluations = 270
Number of equality constraint Jacobian evaluations = 251
Number of inequality constraint Jacobian evaluations = 251
Number of Lagrangian Hessian evaluations = 250
Total seconds in IPOPT = 1605.362
EXIT: Maximum Number of Iterations Exceeded.
Let's look at the fidelity in the subspace
fid_leakage = unitary_rollout_fidelity(prob_leakage.trajectory, sys; subspace=op.subspace, drive_name=:a)
println("Fidelity: ", fid_leakage)
@assert fid_leakage > 0.99Fidelity: 0.9999415712652364and plot the result using the plot_unitary_populations function.
plot_unitary_populations(prob_leakage.trajectory; fig_size=(900, 700), control_name=:a)
Here we can see that the leakage populations have been driven substantially down.
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