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 problem
solve!(prob; max_iter=50) constructing UnitarySmoothPulseProblem...
using integrator: typeof(UnitaryIntegrator)
control derivative names: [:da, :dda]
applying timesteps_all_equal constraint: Δt
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 3.14.17, running with linear solver MUMPS 5.8.0.
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 2.0497214e+01 4.88e-01 3.61e+03 -0.6 1.02e+00 2.0 6.37e-01 5.00e-01h 2
2 1.3491779e+01 1.94e-01 6.08e+03 0.0 9.85e-01 2.4 1.00e+00 5.99e-01h 1
3 2.9422241e+00 1.38e-01 3.99e+03 -0.3 6.38e-01 2.9 1.00e+00 2.89e-01f 1
4 3.0923996e+00 1.11e-01 4.06e+03 -1.0 5.09e-01 3.3 1.00e+00 1.96e-01h 1
5 1.2619020e+01 7.22e-02 2.13e+03 -1.5 4.84e-01 2.8 1.00e+00 3.49e-01h 1
6 2.0738356e+01 3.25e-02 1.77e+03 -2.4 3.03e-01 3.2 1.00e+00 5.49e-01h 1
7 2.3369234e+01 2.01e-02 1.86e+03 -3.3 1.62e-01 2.7 1.00e+00 3.82e-01h 1
8 2.3952415e+01 1.71e-02 1.59e+03 -4.0 9.06e-02 3.2 1.00e+00 1.50e-01h 1
9 2.6857125e+01 7.48e-04 2.13e+03 -4.0 7.25e-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 2.6127823e+01 2.30e-05 1.13e+01 -1.8 1.24e-02 2.2 9.89e-01 1.00e+00f 1
11 2.4112236e+01 1.81e-04 1.92e+00 -3.0 3.46e-02 1.7 1.00e+00 1.00e+00f 1
12 1.9434757e+01 1.10e-03 1.53e+00 -3.5 8.29e-02 1.3 1.00e+00 1.00e+00f 1
13 1.3140688e+01 3.22e-03 2.15e+00 -2.8 1.33e-01 0.8 1.00e+00 1.00e+00f 1
14 8.8917963e+00 5.23e-03 3.35e+00 -2.4 1.41e-01 0.3 9.93e-01 1.00e+00f 1
15 4.9743382e+00 1.02e-01 1.65e+01 -1.1 1.87e+00 -0.2 6.52e-01 3.53e-01f 1
16 2.4462880e+00 8.51e-03 8.80e+00 -1.7 2.06e-01 0.3 1.00e+00 1.00e+00h 1
17 2.3411292e+00 9.99e-03 2.02e+02 -2.1 2.12e-01 -0.2 1.00e+00 1.00e+00h 1
18 3.4427509e+00 3.89e-03 1.94e+02 -1.9 1.71e-01 0.2 1.00e+00 1.00e+00h 1
19 2.7849793e+00 7.23e-05 1.49e+01 -3.3 2.13e-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 2.7136927e+00 1.83e-05 1.22e-01 -4.0 1.06e-02 1.1 1.00e+00 1.00e+00h 1
21 2.4136342e+00 1.23e-04 1.70e-01 -4.0 2.87e-02 0.6 1.00e+00 1.00e+00f 1
22 1.6071670e+00 8.06e-04 1.25e+00 -4.0 6.87e-02 0.1 1.00e+00 1.00e+00f 1
23 1.6204685e+00 6.56e-05 1.33e-01 -4.0 2.15e-02 0.5 1.00e+00 1.00e+00h 1
24 8.4793547e-01 9.10e-04 1.93e+00 -4.0 5.98e-02 0.1 1.00e+00 1.00e+00f 1
25 1.0833586e+00 5.82e-05 8.47e-02 -4.0 1.99e-02 0.5 1.00e+00 1.00e+00h 1
26 1.0463530e+00 7.56e-06 5.74e-02 -4.0 7.08e-03 0.9 1.00e+00 1.00e+00h 1
27 9.2878482e-01 6.25e-05 1.39e-01 -4.0 1.98e-02 0.4 1.00e+00 1.00e+00f 1
28 8.9482594e-01 8.44e-06 5.36e-02 -4.0 7.44e-03 0.9 1.00e+00 1.00e+00h 1
29 7.8556955e-01 6.96e-05 1.76e-01 -4.0 2.08e-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 7.5566667e-01 9.24e-06 4.98e-02 -4.0 7.77e-03 0.8 1.00e+00 1.00e+00h 1
31 6.5518011e-01 7.59e-05 2.03e-01 -4.0 2.16e-02 0.3 1.00e+00 1.00e+00f 1
32 6.2953661e-01 9.87e-06 4.56e-02 -4.0 8.01e-03 0.8 1.00e+00 1.00e+00h 1
33 5.3771420e-01 8.06e-05 2.37e-01 -4.0 2.23e-02 0.3 1.00e+00 1.00e+00f 1
34 5.1689444e-01 1.02e-05 4.12e-02 -4.0 8.15e-03 0.7 1.00e+00 1.00e+00h 1
35 4.3260003e-01 8.35e-05 2.91e-01 -4.0 2.27e-02 0.2 1.00e+00 1.00e+00f 1
36 4.1787263e-01 1.02e-05 3.79e-02 -4.0 8.14e-03 0.7 1.00e+00 1.00e+00h 1
37 3.3681225e-01 8.78e-05 3.95e-01 -4.0 2.29e-02 0.2 1.00e+00 1.00e+00f 1
38 3.3214144e-01 9.79e-06 3.20e-02 -4.0 8.01e-03 0.6 1.00e+00 1.00e+00h 1
39 2.2896514e-01 1.18e-04 6.96e-01 -4.0 2.36e-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 2.5836915e-01 9.08e-06 2.82e-02 -4.0 7.92e-03 0.6 1.00e+00 1.00e+00h 1
41 2.5270638e-01 1.22e-06 2.76e-02 -4.0 2.91e-03 1.0 1.00e+00 1.00e+00h 1
42 2.3463229e-01 1.04e-05 4.34e-02 -4.0 8.23e-03 0.5 1.00e+00 1.00e+00h 1
43 2.2893134e-01 1.47e-06 2.57e-02 -4.0 3.05e-03 0.9 1.00e+00 1.00e+00h 1
44 2.1089191e-01 1.23e-05 5.95e-02 -4.0 8.57e-03 0.4 1.00e+00 1.00e+00h 1
45 2.0548478e-01 1.77e-06 2.39e-02 -4.0 3.19e-03 0.9 1.00e+00 1.00e+00h 1
46 1.8762248e-01 1.46e-05 7.53e-02 -4.0 8.84e-03 0.4 1.00e+00 1.00e+00h 1
47 1.8261332e-01 2.10e-06 2.20e-02 -4.0 3.30e-03 0.8 1.00e+00 1.00e+00h 1
48 1.6500170e-01 1.70e-05 9.38e-02 -4.0 9.03e-03 0.3 1.00e+00 1.00e+00h 1
49 1.6056173e-01 2.46e-06 2.00e-02 -4.0 3.38e-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 1.4312848e-01 1.93e-05 1.19e-01 -4.0 9.10e-03 0.3 1.00e+00 1.00e+00h 1
Number of Iterations....: 50
(scaled) (unscaled)
Objective...............: 1.4312847869185594e-01 1.4312847869185594e-01
Dual infeasibility......: 1.1926413598918373e-01 1.1926413598918373e-01
Constraint violation....: 1.9342550412471127e-05 1.9342550412471127e-05
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 9.9999999971021029e-05 9.9999999971021029e-05
Overall NLP error.......: 1.1926413598918373e-01 1.1926413598918373e-01
Number of objective function evaluations = 54
Number of objective gradient evaluations = 51
Number of equality constraint evaluations = 54
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 = 441.304
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)
println("Fidelity: ", fid)
@assert fid > 0.99Fidelity: 0.9985904929446043and plot the result using the plot_unitary_populations function.
plot_unitary_populations(prob.trajectory; fig_size=(900, 700))
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
solve!(prob_leakage; max_iter=250) constructing UnitarySmoothPulseProblem...
using integrator: typeof(UnitaryIntegrator)
control derivative names: [:da, :dda]
applying leakage suppression: Ũ⃗ < 0.01
applying timesteps_all_equal constraint: Δt
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 3.14.17, running with linear solver MUMPS 5.8.0.
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 1.4950134e-01 1.85e-01 2.29e-01 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 5.0824652e-01 1.69e-01 1.96e+02 -1.4 7.25e-01 0.0 3.87e-01 1.23e-01h 1
2 3.5258495e-01 1.54e-01 1.78e+02 -2.6 9.20e-01 - 1.15e-01 9.37e-02h 1
3 2.4017237e-01 1.47e-01 1.70e+02 -4.0 1.52e+00 - 8.65e-02 4.27e-02h 1
4 5.0460395e-02 1.34e-01 4.00e+01 -2.4 1.81e+00 - 9.54e-02 8.65e-02h 1
5 1.7890116e-01 1.29e-01 3.82e+01 -1.8 3.37e+00 - 3.46e-02 4.02e-02h 1
6 4.0032329e-01 1.24e-01 3.70e+01 -1.7 4.63e+00 - 3.89e-02 2.77e-02h 1
7 7.2440848e-01 1.20e-01 3.60e+01 -1.5 1.73e+01 - 1.70e-02 2.38e-02f 1
8 9.8420024e-01 1.19e-01 3.56e+01 -1.2 2.43e+01 - 1.14e-02 1.04e-02f 1
9 1.4377510e+00 1.13e-01 3.40e+01 -1.2 5.32e+00 - 1.96e-02 4.60e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.1041138e+00 1.06e-01 3.46e+01 -1.2 2.30e+00 - 3.22e-02 6.45e-02f 1
11 2.6999909e+00 1.00e-01 3.24e+01 -1.2 1.84e+00 - 6.19e-02 5.01e-02h 1
12 3.8962937e+00 9.04e-02 3.59e+01 -1.1 1.82e+00 - 5.51e-02 9.60e-02h 1
13 4.5923397e+00 8.07e-02 3.88e+01 -1.2 4.06e+00 - 1.24e-01 1.06e-01h 1
14 7.0404696e+00 7.37e-02 4.82e+01 -0.3 3.21e+00 - 3.20e-02 5.40e-02f 1
15 1.0716498e+01 5.84e-02 4.80e+01 -1.2 8.41e-01 -0.5 1.39e-01 2.37e-01h 1
16 1.0796271e+01 5.75e-02 5.33e+01 -4.0 1.30e+00 -1.0 1.32e-01 1.61e-02h 1
17 1.0758077e+01 5.00e-02 3.96e+01 -2.4 2.89e+00 -1.4 1.15e-01 1.31e-01h 1
18 1.0750479e+01 4.74e-02 4.62e+01 -1.6 2.13e+00 -1.0 1.07e-01 4.75e-02h 1
19 9.8188360e+00 4.66e-02 4.56e+01 -0.7 6.34e+01 -1.5 1.07e-02 1.07e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 9.8655313e+00 4.56e-02 6.89e+01 -4.0 2.38e+00 -1.1 2.79e-01 2.26e-02h 1
21 1.5262766e+01 2.97e-02 1.26e+02 -1.4 1.38e+00 -0.6 2.32e-01 5.11e-01h 1
22 1.5345194e+01 2.79e-02 1.20e+02 -4.0 7.86e-01 -1.1 2.67e-01 7.06e-02h 1
23 1.5098998e+01 2.70e-02 1.24e+02 -1.9 4.61e+00 -1.6 2.68e-01 9.91e-02f 1
24 1.5661951e+01 1.98e-02 9.29e+01 -4.0 7.13e-01 -1.2 5.67e-01 2.96e-01h 1
25 1.8642805e+01 1.01e-02 5.04e+01 -1.6 3.78e-01 -0.7 8.45e-01 5.51e-01h 1
26 2.1623972e+01 1.18e-02 1.00e+01 -1.4 4.91e-01 -1.2 6.85e-01 8.37e-01h 1
27 2.0701492e+01 2.84e-02 4.29e+00 -1.7 1.62e+00 -1.7 5.92e-01 5.66e-01f 1
28 2.0358386e+01 9.81e-03 8.29e+00 -1.7 6.52e-01 -1.3 6.64e-01 7.50e-01h 1
29 1.9575393e+01 1.29e-02 5.86e+00 -4.0 1.39e+00 -1.7 3.13e-01 3.01e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 2.0949644e+01 3.60e-02 1.38e+01 -1.5 9.70e-01 -1.3 7.82e-01 1.00e+00f 1
31 1.9665655e+01 5.46e-03 1.42e+00 -1.6 5.44e-01 -0.9 1.00e+00 1.00e+00h 1
32 1.8921625e+01 2.05e-02 5.66e+00 -1.7 2.78e+00 - 3.09e-01 2.38e-01f 1
33 1.9869663e+01 4.95e-02 5.19e+00 -1.4 9.77e-01 -1.4 9.48e-01 1.00e+00f 1
34 1.8782254e+01 8.33e-02 4.54e+00 -1.5 1.13e+01 -1.8 1.06e-01 8.81e-02f 1
35 1.8006443e+01 5.99e-02 1.12e+01 -1.5 1.90e+00 -1.4 5.89e-01 4.05e-01f 1
36 1.6376032e+01 1.10e-02 1.28e+00 -1.7 6.36e-01 -1.0 9.98e-01 1.00e+00h 1
37 1.6483636e+01 4.20e-02 1.44e+00 -1.5 1.69e+00 - 4.60e-01 4.64e-01f 1
38 1.5397169e+01 3.19e-02 2.70e+00 -1.7 1.09e+00 -1.5 7.27e-01 8.50e-01f 1
39 1.5084121e+01 3.54e-02 2.95e+01 -4.0 7.02e+00 -1.9 1.17e-01 4.19e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 1.4056991e+01 7.26e-02 1.53e+01 -1.9 2.39e+00 -1.5 4.40e-01 4.61e-01f 1
41 1.6270302e+01 5.23e-02 2.84e+01 -1.0 2.21e+00 -2.0 2.21e-01 2.76e-01f 1
42 1.4885369e+01 6.97e-02 2.56e+01 -1.5 1.83e+00 -1.6 1.61e-01 6.30e-01f 1
43 1.4891578e+01 3.02e-02 1.76e+02 -1.5 8.85e-01 -1.1 1.41e-01 1.00e+00f 1
44 1.3989350e+01 1.03e-02 4.48e+01 -1.6 5.00e-01 -1.6 1.00e+00 7.49e-01h 1
45 1.7030209e+01 5.35e-02 3.22e+01 -0.8 4.08e+00 -2.1 2.74e-01 2.54e-01f 1
46 1.4661824e+01 1.59e-01 1.52e+01 -1.3 4.11e+00 -1.7 4.25e-01 6.61e-01f 1
47 1.5001915e+01 4.47e-02 3.99e+00 -1.3 1.33e+00 -1.2 1.00e+00 1.00e+00h 1
48 1.4407039e+01 1.61e-02 5.43e+00 -1.3 1.04e+00 - 1.00e+00 1.00e+00h 1
49 1.3304531e+01 9.98e-02 2.02e+01 -1.3 1.95e+00 -1.7 7.36e-01 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 1.3259109e+01 3.59e-02 1.67e+00 -1.3 1.37e+00 -1.3 1.00e+00 1.00e+00h 1
51 1.0893769e+01 2.08e-02 1.46e+01 -1.8 1.01e+00 - 9.70e-01 6.04e-01f 1
52 1.1281470e+01 1.35e-01 5.04e+00 -1.4 2.10e+00 -1.8 5.60e-01 6.97e-01f 1
53 9.5853066e+00 4.06e-02 1.95e+00 -1.6 1.26e+00 -1.3 1.00e+00 1.00e+00h 1
54 9.2755609e+00 4.44e-02 2.85e+00 -1.6 1.46e+00 - 5.53e-01 5.97e-01h 1
55 9.1343245e+00 7.28e-02 1.57e+01 -1.3 5.97e+00 -1.8 3.09e-01 1.53e-01f 1
56 8.0379252e+00 3.71e-02 1.90e+01 -2.1 8.82e-01 -1.4 1.00e+00 5.52e-01h 1
57 7.8238494e+00 2.58e-02 1.43e+01 -1.8 2.12e+00 -1.9 2.49e-01 2.48e-01h 1
58 6.8031434e+00 2.60e-02 1.40e+00 -2.0 7.42e-01 -1.4 1.00e+00 9.98e-01h 1
59 6.7288304e+00 2.58e-02 9.97e+00 -4.0 5.01e+01 - 6.99e-03 3.14e-03f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 6.5232725e+00 3.57e-02 7.19e+00 -2.0 2.54e+00 -1.9 1.73e-01 2.10e-01f 1
61 6.4633212e+00 3.51e-02 9.22e+00 -4.0 1.18e+01 -2.4 2.44e-02 1.30e-02h 1
62 6.3179312e+00 3.14e-03 5.00e-01 -2.1 3.13e-01 -1.1 1.00e+00 1.00e+00f 1
63 6.0699047e+00 1.62e-02 2.78e+00 -3.1 4.25e+00 - 1.40e-01 1.19e-01f 1
64 5.8741139e+00 1.32e-02 8.47e+00 -2.2 7.74e-01 -1.6 8.53e-01 4.92e-01h 1
65 5.5109805e+00 1.01e-02 5.32e-01 -2.3 3.45e-01 -1.1 1.00e+00 1.00e+00h 1
66 5.3509922e+00 1.39e-02 6.58e+00 -2.6 1.99e+00 -1.6 3.77e-01 1.53e-01h 1
67 5.2378728e+00 1.61e-02 1.11e+01 -3.6 3.66e+00 -2.1 7.94e-02 5.40e-02h 1
68 5.1471254e+00 1.66e-02 9.69e+00 -4.0 1.26e+01 -2.6 1.31e-02 2.13e-02h 1
69 4.9640603e+00 1.57e-02 7.26e+00 -2.4 1.72e+00 -2.1 2.15e-01 2.70e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
70 4.8989747e+00 1.36e-02 1.18e+01 -3.5 8.13e-01 -1.7 3.80e-01 1.35e-01h 1
71 4.9100539e+00 8.05e-03 6.43e-01 -2.4 3.13e-01 -1.3 1.00e+00 1.00e+00f 1
72 4.8495883e+00 8.13e-03 1.10e+01 -4.0 2.15e+00 - 1.28e-01 6.56e-02h 1
73 4.6522537e+00 9.48e-03 2.36e+00 -4.0 7.39e-01 -1.8 2.03e-01 3.97e-01h 1
74 4.5977947e+00 1.00e-02 1.69e+00 -2.5 3.91e-01 -1.3 9.34e-01 1.00e+00h 1
75 4.7721142e+00 3.72e-02 5.06e+00 -1.9 2.21e+00 -1.8 4.54e-01 3.69e-01f 1
76 4.6068687e+00 4.41e-02 4.99e+00 -2.2 9.65e+00 -2.3 3.58e-02 4.05e-02h 1
77 4.5169088e+00 4.26e-02 4.43e+00 -2.2 7.74e+00 -1.9 4.92e-02 5.11e-02h 1
78 4.2885147e+00 3.19e-02 6.32e+00 -3.4 7.24e-01 -1.4 4.94e-01 2.55e-01h 1
79 4.2695034e+00 3.18e-02 1.75e+01 -1.3 2.59e+01 -1.9 1.76e-02 5.04e-03f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
80 4.4234736e+00 5.52e-02 6.21e+00 -2.0 1.33e+00 -1.5 6.46e-01 6.22e-01f 1
81 4.2321418e+00 4.62e-02 9.23e+00 -2.1 2.34e+00 -2.0 3.11e-01 1.56e-01h 1
82 4.4310439e+00 2.13e-02 6.38e+00 -1.8 8.16e-01 -1.5 9.22e-01 7.25e-01f 1
83 3.9441575e+00 3.72e-02 8.42e+00 -2.0 1.88e+00 -2.0 3.68e-01 5.46e-01h 1
84 3.7903641e+00 2.69e-02 5.02e+00 -2.0 9.25e-01 -1.6 8.91e-01 7.10e-01h 1
85 3.6199185e+00 2.19e-02 1.12e+01 -3.1 1.21e+00 -2.1 2.91e-01 1.61e-01h 1
86 3.0550876e+00 2.75e-02 1.68e+00 -2.4 8.12e-01 -1.6 1.00e+00 9.13e-01f 1
87 3.2138793e+00 2.95e-02 5.34e+00 -1.7 2.11e+00 -2.1 2.39e-01 1.80e-01f 1
88 3.0041918e+00 3.14e-02 7.67e+00 -2.2 8.64e-01 -1.7 3.64e-01 7.31e-01h 1
89 2.8216146e+00 2.93e-02 7.47e+00 -3.2 2.52e+00 -2.2 2.66e-01 1.45e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
90 2.7783060e+00 2.87e-02 1.15e+01 -2.0 8.14e+00 -2.6 7.26e-02 3.89e-02f 1
91 2.4695149e+00 3.92e-03 3.50e-01 -2.8 3.04e-01 -1.3 1.00e+00 9.63e-01h 1
92 2.5184992e+00 1.31e-02 2.62e+00 -2.5 3.93e-01 -1.8 7.80e-01 1.00e+00h 1
93 2.4004000e+00 4.65e-03 1.15e-01 -2.6 2.52e-01 -1.4 1.00e+00 1.00e+00h 1
94 2.3143415e+00 1.06e-02 8.26e-01 -2.8 1.77e+00 -1.8 1.99e-01 1.62e-01h 1
95 2.2356040e+00 7.63e-03 5.32e+00 -2.9 3.85e-01 -1.4 1.00e+00 3.66e-01h 1
96 2.2200264e+00 1.06e-02 1.37e+01 -2.0 5.49e+00 -1.9 1.98e-01 7.73e-02f 1
97 2.0287158e+00 1.04e-02 4.10e-01 -2.7 3.85e-01 -1.5 1.00e+00 1.00e+00h 1
98 1.9852866e+00 1.08e-02 2.12e+00 -4.0 1.46e+01 - 2.60e-02 1.94e-02h 1
99 2.0735543e+00 3.11e-02 1.46e+00 -2.2 1.36e+00 -1.9 4.14e-01 4.33e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
100 2.0483624e+00 2.78e-02 2.86e+00 -2.5 5.06e+00 -2.4 6.82e-02 8.91e-02h 1
101 1.9990778e+00 1.67e-02 3.04e+00 -2.5 6.56e-01 -2.0 2.59e-01 2.92e-01h 1
102 1.8995871e+00 1.71e-02 2.73e+00 -2.5 3.81e-01 -1.6 8.61e-01 1.00e+00h 1
103 1.8297115e+00 1.81e-02 2.49e+00 -4.0 3.25e+00 - 7.41e-02 7.73e-02h 1
104 1.7406630e+00 1.04e-02 3.35e+00 -2.7 7.40e-01 -2.0 3.53e-01 4.97e-01h 1
105 1.7032249e+00 1.26e-02 3.71e+00 -3.2 2.40e+00 -2.5 1.39e-01 7.37e-02h 1
106 1.6420597e+00 1.38e-02 2.62e+00 -4.0 1.51e+00 -2.1 7.93e-02 1.67e-01h 1
107 1.8949922e+00 4.26e-02 2.43e+00 -2.1 1.32e+00 -1.7 7.20e-01 6.21e-01f 1
108 1.7090533e+00 4.75e-02 5.55e+00 -2.3 2.39e+00 -2.1 4.02e-01 2.41e-01h 1
109 1.6600077e+00 3.01e-02 9.75e+00 -2.3 6.26e-01 -1.7 8.49e-01 3.63e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
110 1.5821127e+00 3.55e-02 7.40e+00 -2.3 2.35e+00 -2.2 2.40e-01 2.27e-01h 1
111 1.4694270e+00 3.24e-02 6.42e+00 -4.0 5.36e+00 -2.7 6.43e-02 1.16e-01h 1
112 1.3604158e+00 3.95e-02 5.61e+00 -4.0 5.46e+00 -2.3 8.75e-02 1.26e-01h 1
113 1.6176224e+00 7.17e-02 3.24e+00 -2.1 9.18e-01 -1.8 7.52e-01 1.00e+00f 1
114 1.5149564e+00 8.22e-02 4.34e+00 -2.2 2.81e+01 -2.3 2.56e-02 1.73e-02h 1
115 1.2972966e+00 3.22e-02 2.80e+00 -2.2 7.78e-01 -1.9 7.15e-01 6.15e-01h 1
116 1.2132160e+00 2.26e-02 2.94e+00 -2.2 2.03e+00 -2.4 3.83e-01 2.95e-01h 1
117 1.0346906e+00 1.90e-02 1.41e+00 -2.4 7.80e-01 -1.9 9.98e-01 8.23e-01h 1
118 9.0747084e-01 2.58e-02 2.78e+00 -2.9 2.25e+00 -2.4 3.86e-01 2.49e-01h 1
119 9.6398456e-01 9.89e-02 1.31e+00 -2.2 1.14e+00 -2.0 9.01e-01 9.15e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
120 8.7446464e-01 9.37e-02 4.09e+00 -2.3 5.30e+00 -2.5 1.61e-01 8.99e-02h 1
121 1.2036974e+00 6.43e-02 1.02e+01 -1.9 1.08e+00 -2.0 5.48e-01 1.00e+00f 1
122 1.0601402e+00 8.44e-02 8.70e+00 -2.1 7.50e+00 -2.5 1.50e-01 1.48e-01h 1
123 7.0735812e-01 1.98e-01 3.61e+00 -2.1 1.83e+00 -2.1 6.40e-01 9.27e-01f 1
124 6.0671237e-01 1.81e-01 4.11e+00 -2.4 5.98e+00 -2.6 2.03e-01 1.34e-01h 1
125 5.3036749e-01 6.41e-02 3.30e+00 -2.2 1.21e+00 -2.1 9.97e-01 6.64e-01h 1
126 2.9923788e-01 5.34e-03 2.27e-01 -2.7 3.16e-01 -1.7 9.98e-01 1.00e+00h 1
127 2.9492150e-01 4.09e-03 2.76e+00 -2.7 3.53e-01 -2.2 9.73e-01 2.43e-01h 3
128 1.7308825e-01 1.44e-03 1.80e-01 -3.3 1.63e-01 -1.8 1.00e+00 1.00e+00h 1
129 1.6628159e-01 1.77e-03 8.36e-01 -3.3 2.74e-01 -2.2 6.88e-01 5.30e-01H 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
130 1.5897832e-01 4.62e-03 6.05e-01 -3.4 5.08e-01 -2.7 5.03e-01 3.90e-01h 1
131 1.3628352e-01 1.94e-03 4.01e-01 -3.9 1.53e-01 -2.3 1.00e+00 7.41e-01h 1
132 1.2814693e-01 3.68e-04 4.55e-02 -4.0 6.28e-02 -1.9 1.00e+00 1.00e+00h 1
133 1.2876462e-01 6.89e-04 2.35e+00 -3.7 3.55e-01 -2.3 1.00e+00 3.28e-01h 1
134 1.2492838e-01 5.95e-03 5.48e+00 -3.8 7.70e-01 - 7.21e-02 2.84e-01h 1
135 1.6095936e-01 1.04e-02 4.67e+00 -2.2 1.19e+01 -2.8 4.71e-02 5.71e-02f 1
136 1.6039164e-01 9.93e-03 4.04e+00 -3.4 4.59e+00 -3.3 5.80e-02 4.74e-02h 2
137 1.4623346e-01 2.96e-03 8.08e-01 -3.4 2.37e-01 -2.0 1.00e+00 8.37e-01h 1
138 1.3957533e-01 5.61e-03 5.16e-01 -3.4 4.56e-01 -2.4 4.24e-01 6.30e-01f 1
139 1.3510262e-01 5.62e-03 2.98e+00 -3.4 1.73e+00 -2.9 2.97e-01 7.11e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
140 1.2970661e-01 1.78e-02 5.01e-01 -3.4 6.49e-01 -2.5 2.60e-01 5.67e-01h 1
141 1.1250205e-01 4.50e-02 2.75e+00 -3.4 2.67e+00 -3.0 1.01e-01 2.44e-01h 1
142 9.5042512e-02 2.88e-02 1.80e+00 -3.9 9.29e-01 -2.5 4.27e-01 3.51e-01h 1
143 6.8617611e-02 7.44e-03 9.96e-02 -3.8 3.23e-01 -2.1 1.00e+00 1.00e+00h 1
144 6.0973707e-02 7.23e-03 1.08e-01 -4.0 9.24e-01 -2.6 2.53e-01 2.11e-01h 1
145 5.5453064e-02 5.14e-03 1.08e+00 -4.0 2.68e-01 -2.2 8.61e-01 3.67e-01h 1
146 5.1114097e-02 4.75e-03 9.14e-01 -4.0 8.46e-01 -2.6 1.72e-01 1.68e-01h 1
147 5.2096437e-02 3.81e-03 3.64e-01 -3.6 3.45e-01 -2.2 6.40e-01 6.26e-01h 1
148 4.7763780e-02 9.24e-03 4.16e-01 -3.4 3.12e+01 - 6.50e-03 1.12e-02h 1
149 3.7560987e-02 1.69e-02 5.90e-01 -4.0 5.04e+00 - 4.97e-02 7.34e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
150 2.7702473e-02 1.94e-02 9.49e-01 -4.0 6.30e+00 - 4.60e-02 7.79e-02h 1
151 2.7702847e-02 1.85e-02 1.23e+00 -3.5 1.38e+00 - 2.52e-01 1.02e-01h 1
152 1.5090687e-02 1.64e-02 1.67e-01 -3.9 3.98e-01 -2.7 8.97e-01 1.00e+00h 1
153 1.2286637e-02 1.43e-02 3.94e-01 -4.0 8.07e-01 -3.2 2.95e-01 4.68e-01h 1
154 1.3531181e-02 1.31e-02 3.80e-01 -3.9 1.90e+00 - 1.94e-02 1.69e-02H 1
155 1.3328682e-02 1.19e-02 6.25e-01 -4.0 3.06e+00 - 7.65e-02 1.29e-01h 1
156 1.0380614e-02 2.72e-02 9.78e-01 -4.0 1.69e+00 -3.6 1.51e-01 3.65e-01h 1
157 9.3581176e-03 2.51e-02 9.14e-01 -4.0 3.59e+00 - 7.38e-02 1.30e-01h 1
158 8.1922292e-03 2.61e-02 8.03e-01 -4.0 3.25e+00 -4.1 1.20e-01 1.45e-01h 1
159 7.5155979e-03 3.73e-02 6.38e-01 -4.0 1.65e+00 -3.7 2.09e-01 4.28e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
160 8.6915717e-03 3.73e-02 4.90e-01 -4.0 4.69e+00 - 8.87e-02 2.71e-02h 2
161 3.1459932e-03 1.63e-02 1.98e+02 -4.0 4.60e-01 -3.3 8.36e-01 1.00e+00h 1
162 3.4874475e-03 1.54e-02 7.57e+00 -4.0 3.86e+00 - 5.04e-02 3.81e-02h 2
163 2.7353094e-03 2.07e-04 3.19e-01 -4.1 4.05e-02 -1.9 1.00e+00 1.00e+00h 1
164 2.7086497e-03 7.70e-04 1.99e+02 -4.0 2.09e-01 -2.4 7.69e-01 4.85e-01h 2
165 3.9566269e-03 9.81e-03 9.26e+01 -4.0 1.01e+00 - 5.91e-01 4.66e-01h 1
166 7.8489046e-03 5.28e-03 1.49e+02 -4.1 1.10e-01 0.7 9.27e-01 4.63e-01h 1
167 4.1552213e-02 2.98e-04 1.98e+02 -4.1 5.90e-02 0.2 7.41e-01 1.00e+00h 1
168 3.5381914e-02 2.31e-04 4.15e+01 -4.0 6.87e-02 1.6 1.44e-01 2.09e-01F 1
169 2.9133550e-02 2.14e-04 3.83e+01 -3.4 2.76e-02 1.1 1.00e+00 7.54e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
170 2.3855719e-02 8.23e-06 1.98e+02 -3.4 6.72e-03 1.5 1.00e+00 1.00e+00f 1
171 1.5417848e-02 9.16e-06 6.91e+00 -2.6 6.45e-03 1.9 1.00e+00 1.00e+00f 1
172 1.3048443e-02 2.97e-06 9.94e-02 -4.0 3.42e-03 1.5 1.00e+00 1.00e+00h 1
173 5.2702429e-03 5.88e-06 4.66e-02 -4.0 4.82e-03 1.0 1.00e+00 1.00e+00h 1
174 3.1724232e-03 5.24e-06 2.39e-02 -4.0 4.64e-03 0.5 1.00e+00 1.00e+00h 1
175 3.3664824e-03 2.87e-06 9.37e-03 -4.0 3.69e-03 0.0 1.00e+00 1.00e+00h 1
176 3.3154760e-03 7.29e-09 5.31e-03 -4.0 3.54e-03 -0.4 1.00e+00 1.00e+00H 1
177 3.2185539e-03 1.78e-06 3.22e-03 -4.0 3.81e-03 -0.9 1.00e+00 1.00e+00h 1
178 2.9622517e-03 6.77e-06 5.04e-03 -4.1 5.53e-03 -1.4 1.00e+00 1.00e+00h 1
179 3.1231354e-03 3.18e-05 8.00e-03 -4.0 1.52e-02 -1.9 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
180 2.8498124e-03 1.01e-04 1.82e-03 -4.1 3.12e-02 -2.4 1.00e+00 1.00e+00h 1
181 3.0424271e-03 1.71e-05 1.00e-02 -4.0 1.35e-02 -1.9 1.00e+00 1.00e+00h 1
182 2.8065670e-03 8.09e-05 1.46e-03 -4.1 3.37e-02 -2.4 1.00e+00 1.00e+00h 1
183 2.9976045e-03 1.72e-05 1.03e-02 -4.0 1.44e-02 -2.0 1.00e+00 1.00e+00h 1
184 2.7772861e-03 8.28e-05 1.77e-03 -4.1 3.65e-02 -2.5 1.00e+00 1.00e+00h 1
185 2.9648388e-03 2.31e-05 1.14e-02 -4.0 1.55e-02 -2.0 1.00e+00 1.00e+00h 1
186 2.7513160e-03 8.11e-05 4.63e-03 -4.1 3.94e-02 -2.5 1.00e+00 1.00e+00h 1
187 2.9338856e-03 3.49e-05 1.35e-02 -4.0 1.66e-02 -2.1 1.00e+00 1.00e+00h 1
188 2.9526508e-03 1.54e-04 8.43e-03 -4.0 4.97e-02 -2.6 1.00e+00 1.00e+00h 1
189 2.7448661e-03 3.27e-05 9.61e-03 -4.1 1.57e-02 -2.1 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
190 2.5131248e-03 3.68e-04 9.39e-02 -4.0 1.66e-01 -2.6 1.00e+00 5.00e-01h 2
191 2.4853428e-03 4.16e-04 1.99e+02 -3.7 5.87e-01 -3.1 1.00e+00 1.18e-01h 3
192 3.8837096e-03 6.47e-02 1.99e+02 -4.0 1.20e+00 - 5.52e-01 1.00e+00h 1
193 2.4951940e-03 4.66e-02 5.74e+01 -4.0 5.68e-01 1.9 1.38e-01 2.89e-01h 1
194 5.7258184e-03 3.32e-02 1.58e+02 -4.0 4.39e-01 1.4 3.26e-01 2.88e-01h 1
195 6.6289370e-03 3.04e-02 1.44e+02 -4.0 3.12e-01 1.8 1.00e+00 8.59e-02h 1
196 1.0290864e-02 1.26e-02 6.02e+01 -4.0 2.93e-01 1.3 8.17e-01 5.83e-01h 1
197 1.5054004e-02 1.48e-03 1.90e+02 -4.0 1.28e-01 0.8 1.00e+00 8.63e-01h 1
198 8.0999700e-03 3.27e-05 1.99e+02 -4.0 1.73e-02 0.4 1.00e+00 1.00e+00f 1
199 5.1544991e-03 6.78e-06 5.06e+00 -4.0 4.19e-03 1.7 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
200 5.3202850e-03 8.79e-07 2.29e-02 -4.0 1.37e-03 1.2 1.00e+00 1.00e+00h 1
201 4.0697432e-03 1.69e-06 1.12e-02 -4.0 2.01e-03 0.7 1.00e+00 1.00e+00h 1
202 3.3133522e-03 1.52e-06 6.98e-03 -4.0 2.96e-03 0.3 1.00e+00 1.00e+00h 1
203 2.9817989e-03 1.90e-06 9.59e-03 -4.0 5.47e-03 -0.2 1.00e+00 1.00e+00h 1
204 2.8419797e-03 7.23e-06 1.50e-02 -4.0 1.17e-02 -0.7 1.00e+00 1.00e+00h 1
205 2.7246297e-03 1.40e-05 1.88e-02 -4.0 2.15e-02 -1.2 1.00e+00 1.00e+00h 1
206 2.6862402e-03 1.72e-05 5.10e-03 -4.0 2.27e-02 -1.6 1.00e+00 1.00e+00h 1
207 2.6006229e-03 6.49e-05 9.75e-03 -4.0 3.03e-02 -2.1 1.00e+00 1.00e+00h 1
208 2.3127690e-03 3.57e-04 4.93e-02 -4.0 5.23e-02 -2.6 1.00e+00 1.00e+00h 1
209 2.3192757e-03 1.30e-04 3.36e-02 -4.0 4.20e-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
210 2.1848880e-03 1.89e-04 1.99e+02 -4.0 4.88e-01 -2.6 5.61e-01 1.21e-01h 4
211 2.4311487e-03 4.81e-02 1.04e+02 -4.0 2.92e+00 - 3.90e-01 5.25e-01h 1
212 4.3257023e-03 3.72e-02 1.20e+02 -4.1 7.38e-01 1.4 1.52e-01 2.42e-01h 1
213 3.2829071e-03 2.78e-02 8.88e+01 -4.1 5.96e-01 0.9 1.71e-01 2.57e-01h 1
214 8.4219014e-03 1.48e-02 1.51e+02 -4.1 4.88e-01 0.4 1.64e-01 4.58e-01h 1
215 9.6179551e-03 1.31e-02 1.33e+02 -4.1 2.41e-01 1.8 1.00e+00 1.15e-01h 1
216 1.1961050e-02 4.83e-03 4.77e+01 -4.1 2.19e-01 1.3 1.00e+00 6.42e-01h 1
217 7.8591657e-03 7.74e-04 1.92e+02 -4.1 8.50e-02 0.8 9.52e-01 8.51e-01h 1
218 8.5921918e-03 2.58e-05 1.99e+02 -4.1 2.04e-02 0.3 5.28e-01 1.00e+00f 1
219 6.9845901e-03 3.03e-06 2.92e+00 -4.1 3.28e-03 1.7 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
220 4.9710759e-03 1.34e-06 2.87e-02 -4.1 1.85e-03 1.2 1.00e+00 1.00e+00h 1
221 3.4357255e-03 2.68e-06 1.40e-02 -4.1 2.65e-03 0.7 1.00e+00 1.00e+00h 1
222 2.4720001e-03 2.14e-06 2.08e-02 -4.1 3.01e-03 0.2 1.00e+00 1.00e+00h 1
223 2.4272352e-03 3.75e-06 1.91e-02 -4.0 6.83e-03 -0.2 1.00e+00 1.00e+00h 1
224 2.3476937e-03 8.33e-06 1.97e-02 -4.0 1.30e-02 -0.7 1.00e+00 1.00e+00h 1
225 2.2014042e-03 2.96e-05 2.91e-02 -4.0 2.46e-02 -1.2 1.00e+00 1.00e+00h 1
226 2.1018367e-03 5.84e-05 3.01e-02 -4.0 2.91e-02 -1.7 1.00e+00 1.00e+00h 1
227 2.0043886e-03 7.32e-05 3.45e-02 -4.0 3.14e-02 -2.2 1.00e+00 1.00e+00h 1
228 1.9662234e-03 1.53e-04 1.99e+02 -4.0 2.15e-01 -2.6 1.00e+00 2.50e-01h 3
229 1.9146539e-03 5.12e-02 1.28e+02 -4.0 2.45e+00 - 5.40e-01 6.44e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
230 5.5990383e-03 3.22e-02 1.20e+02 -3.2 7.69e-01 1.4 1.00e+00 3.88e-01h 1
231 3.8252607e-03 1.62e-02 1.40e+02 -3.3 5.63e-01 0.9 3.69e-01 5.10e-01h 1
232 9.5170278e-03 8.01e-03 6.78e+01 -3.3 2.78e-01 1.4 8.49e-01 5.15e-01h 1
233 1.4138807e-02 8.31e-04 1.99e+02 -3.3 1.51e-01 0.9 1.00e+00 1.00e+00h 1
234 1.5065282e-02 2.28e-05 1.99e+02 -3.3 8.18e-03 0.4 1.00e+00 1.00e+00h 1
235 8.1229967e-03 1.57e-05 7.92e+00 -3.3 6.19e-03 1.7 1.00e+00 1.00e+00h 1
236 9.0265699e-03 1.54e-06 3.91e-02 -3.3 2.16e-03 1.3 1.00e+00 1.00e+00h 1
237 6.3741779e-03 1.98e-06 1.75e-02 -3.3 2.03e-03 0.8 1.00e+00 1.00e+00h 1
238 5.1515374e-03 1.79e-06 2.08e-02 -3.3 4.31e-03 0.3 1.00e+00 1.00e+00h 1
239 4.5319488e-03 8.86e-06 1.94e-02 -3.3 1.13e-02 -0.2 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
240 4.1163000e-03 3.38e-05 1.91e-02 -3.3 2.40e-02 -0.7 1.00e+00 1.00e+00h 1
241 3.9178475e-03 6.86e-05 1.49e-02 -3.3 3.34e-02 -1.1 1.00e+00 1.00e+00h 1
242 3.9944114e-03 3.85e-05 1.40e-02 -3.3 2.17e-02 -1.6 1.00e+00 1.00e+00h 1
243 4.0191126e-03 1.48e-04 2.42e-02 -3.3 3.95e-02 -2.1 1.00e+00 1.00e+00h 1
244 3.9534385e-03 7.02e-04 4.51e-02 -3.3 6.84e-02 -2.6 1.00e+00 1.00e+00h 1
245 3.7635703e-03 3.57e-03 6.87e-02 -3.3 2.13e-01 -3.0 1.00e+00 1.00e+00h 1
246 4.0641571e-03 1.49e-02 1.00e-01 -3.3 6.81e-01 -3.5 1.00e+00 1.00e+00h 1
247 5.8986121e-03 3.27e-02 1.96e-01 -3.3 2.39e+00 -4.0 6.91e-01 4.65e-01h 2
248 6.1762943e-03 2.89e-02 5.66e-02 -3.3 1.07e+00 -3.6 1.00e+00 1.00e+00h 1
249 4.8094205e-03 2.21e-02 1.90e-01 -3.3 2.94e+00 - 3.74e-01 2.78e-01h 2
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
250 7.4370825e-03 2.51e-02 2.48e-01 -3.3 2.55e+00 -4.0 8.76e-01 2.50e-01h 3
Number of Iterations....: 250
(scaled) (unscaled)
Objective...............: 7.4370825250493038e-03 7.4370825250493038e-03
Dual infeasibility......: 2.4800875221182228e-01 2.4800875221182228e-01
Constraint violation....: 2.5078637923391316e-02 2.5078637923391316e-02
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 7.1147782375965659e-04 7.1147782375965659e-04
Overall NLP error.......: 2.4800875221182228e-01 2.4800875221182228e-01
Number of objective function evaluations = 298
Number of objective gradient evaluations = 251
Number of equality constraint evaluations = 298
Number of inequality constraint evaluations = 298
Number of equality constraint Jacobian evaluations = 251
Number of inequality constraint Jacobian evaluations = 251
Number of Lagrangian Hessian evaluations = 250
Total seconds in IPOPT = 2345.067
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)
println("Fidelity: ", fid_leakage)
@assert fid_leakage > 0.99Fidelity: 0.9999830241360017and plot the result using the plot_unitary_populations function.
plot_unitary_populations(prob_leakage.trajectory; fig_size=(900, 700))
Here we can see that the leakage populations have been driven substantially down.
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