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 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...............: 2.2337171204369502e-01 2.2337171204369502e-01
Dual infeasibility......: 8.8610846417012112e-02 8.8610846417012112e-02
Constraint violation....: 2.8712906816774630e-05 2.8712906816774630e-05
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 1.0048178594190573e-04 1.0048178594190573e-04
Overall NLP error.......: 8.8610846417012112e-02 8.8610846417012112e-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 = 457.401
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: 0.997779151119143and 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 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 5.8079662e+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 7.3900832e+00 4.73e-02 9.26e+01 -1.5 2.16e+00 -1.2 8.51e-03 1.41e-01h 1
21 7.3175121e+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 7.4999270e+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 9.2556249e+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 1.6584320e+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 1.6715807e+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 1.6387643e+01 1.43e-02 1.96e+01 -4.0 5.65e+00 -1.7 2.87e-02 3.86e-02f 1
41 1.6176015e+01 1.19e-02 2.87e+01 -2.4 6.66e-01 -1.2 5.17e-01 2.27e-01h 1
42 1.5766440e+01 4.69e-03 9.78e+00 -2.8 2.38e-01 -0.8 1.00e+00 6.89e-01h 1
43 1.5502061e+01 5.75e-03 7.89e+00 -4.0 1.50e+00 -1.3 1.27e-01 2.65e-01h 1
44 1.5464772e+01 5.67e-03 6.62e+00 -3.6 4.26e+00 -1.8 5.48e-02 1.95e-02h 1
45 1.5363978e+01 4.82e-03 2.08e+01 -3.7 9.38e-01 -1.3 4.76e-01 1.70e-01h 1
46 1.5272266e+01 7.92e-03 2.18e+01 -2.5 4.89e+00 -1.8 1.16e-01 9.52e-02f 1
47 1.5200604e+01 6.91e-03 1.79e+01 -4.0 5.59e-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 1.5130170e+01 3.73e-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 1.4961266e+01 2.34e-03 2.16e-01 -3.0 2.32e-01 -1.0 1.00e+00 1.00e+00h 1
51 1.4901420e+01 3.82e-03 2.50e+00 -4.0 2.05e+01 -1.5 1.78e-02 2.70e-02f 1
52 1.4820033e+01 3.34e-03 1.34e+01 -3.2 5.63e-01 -1.1 4.46e-01 2.65e-01h 1
53 1.4695331e+01 1.04e-03 2.87e+00 -3.2 1.98e-01 -0.6 1.00e+00 8.87e-01h 1
54 1.4710827e+01 1.40e-03 2.75e+01 -2.1 1.22e+00 -1.1 2.90e-01 1.37e-01f 1
55 1.4638807e+01 1.31e-03 3.05e-01 -2.7 2.01e-01 -0.7 9.87e-01 9.76e-01h 1
56 1.4546595e+01 1.63e-03 2.35e+01 -2.8 5.84e-01 -1.2 6.52e-01 2.55e-01f 1
57 1.4388272e+01 1.11e-03 1.58e-01 -2.9 1.74e-01 -0.8 1.00e+00 1.00e+00h 1
58 1.4242355e+01 2.38e-03 2.04e-01 -2.9 8.04e-01 -1.2 3.22e-01 3.28e-01h 1
59 1.4172905e+01 1.83e-03 2.73e+01 -3.5 2.43e-01 -0.8 1.00e+00 2.68e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 1.4055939e+01 1.07e-02 1.53e+01 -2.5 8.02e-01 -1.3 1.00e+00 7.28e-01f 1
61 1.4044108e+01 2.44e-02 1.78e+01 -2.0 2.89e+00 -1.8 1.31e-01 2.47e-01f 1
62 1.3933915e+01 2.05e-02 1.14e+01 -2.0 1.45e+00 -1.3 4.07e-01 3.32e-01f 1
63 1.3615248e+01 1.21e-02 1.50e+01 -3.3 3.10e-01 -0.9 7.46e-01 4.31e-01h 1
64 1.3465368e+01 1.15e-02 1.38e+01 -3.0 2.73e+00 -1.4 1.49e-01 1.03e-01h 1
65 1.3260366e+01 6.18e-03 3.14e+00 -2.4 4.62e-01 -1.0 9.12e-01 1.00e+00f 1
66 1.3217326e+01 6.81e-03 3.67e+00 -1.8 3.54e+00 -1.4 1.37e-01 1.02e-01f 1
67 1.3299395e+01 8.59e-03 8.89e+00 -1.7 3.42e+00 -1.9 2.32e-01 1.87e-01f 1
68 1.3098262e+01 1.42e-02 7.76e+00 -2.2 1.32e+01 -2.4 1.59e-02 3.97e-02f 1
69 1.3780887e+01 1.23e-02 2.33e+01 -1.2 2.40e+00 -2.0 2.07e-01 1.33e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
70 1.3452914e+01 4.12e-02 2.98e+01 -1.8 6.63e+00 - 4.61e-02 1.23e-01f 1
71 1.3203138e+01 3.51e-02 3.14e+01 -1.8 1.75e+00 -1.5 1.71e-01 2.66e-01f 1
72 1.3005919e+01 9.25e-03 7.47e+00 -1.8 4.24e-01 -1.1 1.00e+00 7.88e-01h 1
73 1.2840830e+01 1.10e-02 1.59e+01 -4.0 4.11e+01 - 1.41e-02 6.36e-03f 1
74 1.4063072e+01 5.81e-02 9.13e+00 -1.3 2.18e+00 -1.6 4.67e-01 4.45e-01f 1
75 1.2905266e+01 1.79e-02 2.25e+00 -1.6 8.13e-01 -1.2 1.00e+00 1.00e+00f 1
76 1.2495253e+01 1.78e-02 9.59e+00 -1.6 3.37e+00 - 2.29e-01 1.51e-01f 1
77 1.1698663e+01 1.56e-02 3.54e+01 -2.0 9.73e-01 -1.6 8.85e-01 4.41e-01f 1
78 1.0745079e+01 8.08e-03 5.32e+00 -2.1 4.59e-01 -1.2 1.00e+00 8.09e-01h 1
79 1.0470890e+01 1.31e-02 4.04e+00 -2.4 1.69e+00 -1.7 2.34e-01 2.40e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
80 1.0359829e+01 2.79e-02 1.04e+01 -1.9 1.07e+00 -1.3 1.00e+00 5.13e-01f 1
81 9.9471423e+00 3.19e-02 1.08e+01 -2.4 1.95e+00 -1.7 1.90e-01 1.63e-01h 1
82 9.6175434e+00 2.17e-02 1.16e+01 -2.4 9.15e-01 -1.3 4.81e-01 3.43e-01h 1
83 9.3639825e+00 1.94e-02 1.58e+01 -2.3 3.99e+00 -1.8 1.46e-01 9.89e-02h 1
84 9.2283067e+00 1.80e-02 9.57e+00 -4.0 1.57e+01 -2.3 1.44e-02 2.71e-02h 1
85 9.0613062e+00 3.94e-03 5.28e-01 -2.2 2.39e-01 -0.9 1.00e+00 1.00e+00h 1
86 9.2253653e+00 1.88e-02 4.18e+00 -2.0 5.04e-01 -1.4 8.46e-01 1.00e+00f 1
87 9.0268998e+00 2.41e-02 4.69e+00 -2.1 7.11e+00 -1.9 6.14e-02 5.36e-02h 1
88 8.6275632e+00 2.21e-02 1.02e+01 -4.0 9.11e-01 -1.5 4.55e-01 2.59e-01h 1
89 8.5260991e+00 3.10e-02 1.16e+01 -1.7 5.87e+00 -1.9 7.65e-02 1.31e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
90 8.3488203e+00 3.06e-02 9.13e+00 -1.9 1.48e+00 -1.5 4.29e-01 3.31e-01f 1
91 8.1810916e+00 2.95e-02 8.59e+00 -4.0 3.58e+00 -2.0 6.30e-02 7.11e-02h 1
92 8.0188750e+00 2.75e-02 5.42e+00 -2.1 1.62e+00 -1.6 3.78e-01 3.68e-01f 1
93 7.4577245e+00 9.96e-03 5.39e-01 -2.4 3.50e-01 -1.1 9.51e-01 9.73e-01h 1
94 7.2737975e+00 1.42e-02 4.18e-01 -2.6 1.53e+00 -1.6 2.24e-01 2.24e-01h 1
95 7.2063198e+00 1.53e-02 2.54e+01 -1.7 9.17e+01 -2.1 1.01e-02 2.36e-03f 1
96 7.2412085e+00 1.21e-02 1.93e+01 -2.1 1.10e+00 -1.7 2.76e-01 1.93e-01f 1
97 7.0026225e+00 5.15e-03 3.48e+00 -2.5 2.77e-01 -1.2 1.00e+00 8.68e-01h 1
98 7.1189860e+00 4.56e-02 5.52e+00 -1.7 3.37e+00 -1.7 2.85e-01 2.33e-01f 1
99 6.9630233e+00 4.38e-02 7.74e+00 -2.2 6.67e+00 -2.2 5.20e-02 4.18e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
100 6.7431755e+00 3.53e-02 1.88e+01 -2.6 1.25e+00 -1.8 2.99e-01 1.92e-01h 1
101 6.4648467e+00 9.10e-03 2.08e+00 -2.3 4.37e-01 -1.3 8.78e-01 8.97e-01h 1
102 6.4457630e+00 2.49e-02 2.11e+00 -2.1 1.50e+00 -1.8 3.43e-01 3.27e-01f 1
103 6.3123507e+00 3.23e-02 2.03e+00 -4.0 1.79e+01 -2.3 1.43e-02 1.53e-02f 1
104 6.2464306e+00 2.91e-02 2.47e+01 -2.5 9.86e-01 -1.9 3.63e-01 9.73e-02f 1
105 6.0788120e+00 1.46e-02 1.20e+01 -2.4 5.63e-01 -1.4 1.00e+00 4.96e-01h 1
106 5.8880884e+00 1.45e-02 6.26e+00 -4.0 1.68e+00 -1.9 1.38e-01 2.16e-01h 1
107 6.0767328e+00 1.84e-02 4.66e+00 -1.9 1.18e+00 -1.5 4.61e-01 3.99e-01f 1
108 5.8326608e+00 5.23e-03 6.27e-01 -2.2 3.36e-01 -1.1 1.00e+00 1.00e+00h 1
109 5.3388134e+00 2.69e-02 6.02e-01 -2.8 1.10e+00 -1.6 5.51e-01 5.19e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
110 5.2148964e+00 2.02e-02 1.25e+01 -2.9 3.75e-01 -1.1 8.46e-01 2.82e-01h 1
111 5.0192896e+00 2.00e-02 1.21e+01 -3.0 1.10e+00 -1.6 3.14e-01 2.58e-01h 1
112 5.1541815e+00 5.72e-03 4.03e+00 -2.2 3.54e-01 -1.2 7.04e-01 7.34e-01f 1
113 5.0029938e+00 1.51e-02 1.02e+01 -4.0 1.27e+01 - 1.06e-02 2.67e-02f 1
114 4.9696001e+00 1.48e-02 7.18e+00 -4.0 4.11e+00 - 6.28e-02 2.03e-02h 1
115 4.9658473e+00 1.08e-02 1.83e+01 -2.1 1.01e+00 -1.7 5.52e-01 2.68e-01f 1
116 4.7380721e+00 4.71e-02 1.26e+01 -4.0 5.02e+00 -2.1 4.11e-02 1.76e-01h 1
117 4.6109574e+00 3.50e-02 7.98e+00 -2.5 1.02e+00 -1.7 4.28e-01 2.54e-01h 1
118 4.2469478e+00 5.91e-03 3.83e-01 -2.8 3.23e-01 -1.3 1.00e+00 1.00e+00h 1
119 4.1613474e+00 7.53e-03 7.05e+00 -2.8 1.18e+00 -1.8 4.39e-01 2.22e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
120 4.1656938e+00 6.97e-03 8.65e+00 -2.0 2.80e+00 -2.2 1.01e-01 6.36e-02f 1
121 4.0987005e+00 5.69e-03 6.36e+00 -2.7 8.42e-01 -1.8 2.68e-01 2.53e-01h 1
122 4.0647900e+00 4.41e-03 9.30e+00 -2.7 2.72e-01 -1.4 9.73e-01 3.93e-01h 1
123 3.8982308e+00 7.11e-04 1.12e-01 -3.4 8.47e-02 -1.0 1.00e+00 1.00e+00h 1
124 4.0882464e+00 1.20e-02 7.22e+00 -2.4 5.90e-01 -1.4 4.64e-01 7.89e-01f 1
125 4.0163103e+00 7.31e-03 1.45e+01 -2.8 1.26e-01 -1.0 7.76e-01 3.87e-01h 1
126 3.8891402e+00 1.21e-02 9.03e+00 -2.8 1.09e+00 -1.5 3.84e-01 3.47e-01f 1
127 3.8642572e+00 6.11e-03 5.27e+00 -2.5 2.00e-01 -1.1 1.00e+00 5.61e-01f 1
128 3.9622154e+00 9.47e-03 8.49e+00 -2.1 5.40e-01 -1.5 1.00e+00 5.67e-01f 1
129 3.8882506e+00 1.71e-02 7.96e+00 -2.2 8.29e+00 - 6.85e-02 6.76e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
130 3.7952046e+00 2.10e-02 6.52e+00 -2.2 2.04e+00 -2.0 1.61e-01 1.66e-01f 1
131 3.6709818e+00 1.58e-02 5.59e+00 -2.2 7.10e-01 -1.6 1.00e+00 7.54e-01f 1
132 3.5684130e+00 2.17e-02 5.56e+00 -2.3 8.33e+00 -2.1 5.40e-02 3.80e-02h 1
133 3.6915863e+00 2.65e-02 2.49e+00 -2.0 8.09e-01 -1.6 5.85e-01 6.03e-01f 1
134 3.5313636e+00 2.51e-02 5.26e+00 -2.1 2.45e+00 -2.1 1.77e-01 2.15e-01h 1
135 3.1036174e+00 2.88e-02 2.77e+00 -2.5 1.18e+00 -1.7 5.19e-01 4.98e-01h 1
136 3.0760896e+00 2.82e-02 1.87e+01 -4.0 5.16e+00 - 8.28e-02 2.04e-02h 1
137 2.8415770e+00 6.44e-03 3.24e+00 -2.6 3.48e-01 -1.3 1.00e+00 8.35e-01h 1
138 2.8400769e+00 1.44e-02 2.83e+00 -2.3 8.20e-01 -1.7 5.43e-01 5.05e-01f 1
139 2.7949017e+00 3.97e-02 3.54e+00 -2.0 2.80e+00 -2.2 2.88e-01 2.19e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
140 2.7304637e+00 3.60e-02 1.07e+01 -3.8 1.41e+00 - 2.13e-01 9.22e-02h 1
141 2.8805768e+00 4.66e-02 8.96e+00 -2.1 9.94e-01 -1.8 5.54e-01 1.00e+00f 1
142 2.6585759e+00 1.88e-02 6.14e+00 -2.3 5.15e-01 -1.4 1.00e+00 6.33e-01h 1
143 3.3455577e+00 5.42e-02 1.17e+01 -1.7 1.29e+00 -1.8 4.21e-01 6.97e-01f 1
144 3.0767662e+00 6.73e-02 1.14e+01 -2.0 1.95e+01 -2.3 5.11e-02 3.33e-02h 1
145 2.7528424e+00 4.85e-02 7.33e+00 -2.0 1.82e+00 -1.9 2.75e-01 3.24e-01h 1
146 2.5427397e+00 5.94e-02 6.15e+00 -2.0 9.09e+00 -2.4 7.22e-02 1.04e-01h 1
147 2.2370102e+00 4.16e-02 4.19e+00 -2.5 1.67e+00 -1.9 3.38e-01 3.21e-01h 1
148 2.6385292e+00 4.86e-02 7.10e-01 -1.8 8.76e-01 -1.5 1.00e+00 1.00e+00f 1
149 2.2018396e+00 7.09e-02 1.45e+00 -4.0 6.07e+00 - 1.71e-01 1.67e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
150 1.7615556e+00 5.90e-02 5.46e+00 -3.2 1.91e+00 -2.0 5.25e-01 3.25e-01h 1
151 3.1307050e+00 5.11e-02 6.87e+00 -1.5 9.24e-01 -1.6 7.18e-01 8.65e-01f 1
152 2.4006929e+00 3.05e-02 5.13e+00 -1.7 1.32e+00 -2.0 9.74e-01 7.78e-01h 1
153 3.4908891e+00 4.43e-02 9.75e-01 -1.4 8.97e-01 -1.6 1.00e+00 1.00e+00f 1
154 2.6996582e+00 1.96e-01 1.15e+01 -1.5 7.30e+00 - 3.08e-01 3.79e-01h 1
155 2.7697532e+00 1.08e-01 8.09e+00 -1.5 1.25e+00 -2.1 1.00e+00 5.00e-01h 2
156 2.5738993e+00 8.54e-02 8.98e+00 -1.5 6.47e+00 -2.6 4.14e-01 2.08e-01h 1
157 2.4062377e+00 2.08e-01 1.62e+00 -1.5 2.60e+00 -2.1 1.00e+00 1.00e+00f 1
158 1.9647763e+00 2.80e-01 8.33e+00 -1.5 1.59e+01 -2.6 1.70e-01 1.84e-01h 1
159 2.1442814e+00 5.56e-02 7.08e+00 -1.5 1.46e+00 -1.3 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
160 2.2489535e+00 2.34e-02 2.96e+00 -1.5 1.01e+00 - 1.00e+00 1.00e+00h 1
161 1.5484583e+00 1.21e-01 4.58e+00 -4.0 1.10e+01 - 1.77e-01 2.11e-01f 1
162 1.4466123e+00 2.36e-02 1.18e+00 -1.7 1.37e+00 -1.8 1.00e+00 1.00e+00h 1
163 8.6378982e-01 1.72e-02 9.39e-01 -2.0 8.89e-01 - 9.95e-01 1.00e+00h 1
164 6.7298093e-01 8.70e-02 2.17e+00 -4.0 1.76e+01 - 7.12e-02 8.63e-02h 1
165 6.9834815e-01 5.69e-02 6.63e-01 -2.0 1.37e+00 -2.3 9.13e-01 1.00e+00h 1
166 4.8850197e-01 6.66e-02 7.89e-01 -4.0 2.47e+00 - 3.13e-01 3.02e-01h 1
167 3.7116047e-01 8.13e-02 1.38e+00 -2.9 3.71e+00 -2.7 2.92e-01 2.39e-01h 1
168 2.6880903e-01 3.97e-02 3.47e+00 -2.6 1.16e+00 -2.3 1.00e+00 5.60e-01h 1
169 9.1763010e-02 5.94e-03 1.98e-01 -3.1 3.64e-01 -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
170 1.0082789e-01 4.50e-03 1.24e+00 -2.8 4.22e-01 -2.4 1.00e+00 2.50e-01h 3
171 8.5138450e-02 1.43e-02 6.57e-01 -3.0 6.20e-01 -2.8 1.00e+00 7.65e-01h 1
172 5.9392940e-02 2.88e-02 1.40e+00 -4.0 3.03e+00 - 1.10e-01 2.31e-01h 1
173 4.7476179e-02 1.71e-02 8.39e-01 -3.3 5.71e-01 -2.4 9.12e-01 6.84e-01h 1
174 4.7124067e-02 1.40e-02 1.22e+00 -3.0 1.39e+00 -2.9 2.36e-01 1.87e-01h 1
175 2.9474316e-02 7.79e-02 9.57e-01 -3.4 2.45e+00 -3.4 1.87e-01 3.38e-01h 1
176 2.4908553e-02 7.01e-02 8.19e-01 -4.0 3.34e+00 - 1.02e-01 8.95e-02h 1
177 1.0484464e-02 2.01e-02 1.99e+02 -4.0 6.13e-01 -2.9 4.94e-01 9.43e-01h 1
178 1.3256443e-02 1.69e-02 3.82e+01 -4.0 1.32e+00 - 1.13e-01 1.93e-01h 1
179 9.9204934e-03 9.84e-04 5.64e+00 -3.5 6.33e-02 -1.6 9.34e-01 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
180 6.0344733e-03 1.44e-04 6.56e-02 -4.0 4.02e-02 -2.1 1.00e+00 1.00e+00h 1
181 6.1998405e-03 1.44e-04 2.07e-01 -4.0 1.16e-01 -2.6 1.00e+00 1.25e-01h 4
182 5.4637353e-03 3.86e-03 1.76e-01 -4.0 9.15e-01 -3.0 2.58e-01 2.33e-01h 2
183 4.3107781e-03 1.67e-02 1.99e+02 -4.0 1.91e+01 - 1.09e-02 2.38e-02h 1
184 9.4764188e-03 1.67e-02 2.18e+01 -4.0 1.44e+00 - 1.25e-01 1.10e-01h 1
185 4.9603370e-03 1.29e-02 1.68e+01 -4.1 3.36e-01 -2.6 6.89e-01 2.29e-01h 1
186 4.6286083e-03 1.30e-03 1.98e+02 -4.0 8.80e-02 -2.2 1.00e+00 1.00e+00h 1
187 9.2890850e-03 2.61e-03 1.99e+02 -3.7 2.47e-01 -2.7 1.00e+00 1.00e+00h 1
188 1.2524551e-02 1.28e-06 1.14e+00 -3.8 6.00e-03 2.3 1.00e+00 1.00e+00h 1
189 1.1490307e-02 9.56e-08 4.89e-02 -4.0 7.68e-04 1.8 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
190 9.9449741e-03 4.17e-07 2.61e-02 -4.0 1.23e-03 1.3 1.00e+00 1.00e+00h 1
191 8.5106712e-03 9.44e-07 1.24e-02 -4.0 1.75e-03 0.8 1.00e+00 1.00e+00h 1
192 7.1234938e-03 9.67e-07 9.94e-03 -4.0 2.14e-03 0.4 1.00e+00 1.00e+00h 1
193 6.2267266e-03 9.54e-07 7.86e-03 -4.0 2.02e-03 -0.1 1.00e+00 1.00e+00h 1
194 5.9417411e-03 1.36e-06 2.10e-03 -4.0 3.54e-03 -0.6 1.00e+00 1.00e+00h 1
195 5.8182547e-03 5.98e-06 5.52e-03 -4.0 1.17e-02 -1.1 1.00e+00 1.00e+00h 1
196 5.6639464e-03 3.28e-05 1.36e-02 -4.0 2.72e-02 -1.5 1.00e+00 1.00e+00h 1
197 5.4774368e-03 1.48e-04 1.86e-02 -4.0 4.66e-02 -2.0 1.00e+00 1.00e+00h 1
198 5.2580864e-03 6.70e-04 2.07e-02 -4.0 6.43e-02 -2.5 1.00e+00 1.00e+00h 1
199 4.8541139e-03 2.95e-03 3.61e-02 -4.0 1.82e-01 -3.0 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
200 3.5736593e-03 1.51e-02 1.27e-01 -4.1 4.72e-01 -3.4 1.00e+00 1.00e+00h 1
201 3.6256964e-03 2.07e-02 1.31e-01 -4.0 1.04e+00 -3.9 4.45e-01 7.42e-01h 1
202 2.7992730e-03 8.37e-04 2.20e-02 -4.2 2.86e-01 -2.6 1.00e+00 1.00e+00h 1
203 3.1256048e-03 1.40e-04 4.48e-02 -4.0 4.13e-02 -2.2 1.00e+00 1.00e+00h 1
204 3.0974848e-03 5.13e-04 3.89e-02 -4.0 5.95e-02 -2.6 1.00e+00 1.00e+00h 1
205 3.2042137e-03 1.33e-04 2.87e-02 -4.0 3.34e-02 -2.2 1.00e+00 1.00e+00h 1
206 3.1928337e-03 2.22e-04 9.79e-03 -4.0 6.51e-02 -2.7 1.00e+00 1.00e+00h 1
207 2.9865357e-03 3.34e-05 5.60e-03 -4.1 2.07e-02 -2.3 1.00e+00 1.00e+00h 1
208 2.7112709e-03 1.47e-03 1.99e+02 -4.0 1.21e-01 -2.7 1.00e+00 1.00e+00h 1
209 2.5885455e-03 9.04e-03 3.87e+01 -4.0 2.56e+00 - 2.66e-01 1.95e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
210 4.3462817e-03 1.52e-03 1.99e+02 -4.0 1.22e-01 -1.4 1.00e+00 1.00e+00h 1
211 3.0330185e-03 1.01e-03 1.32e+02 -4.1 9.04e-02 -1.9 4.50e-01 3.37e-01h 1
212 5.3802479e-03 4.89e-05 1.99e+02 -4.1 1.16e-02 -0.6 7.36e-01 1.00e+00h 1
213 2.4987815e-03 1.01e-05 6.49e+00 -4.1 4.87e-03 1.7 1.00e+00 1.00e+00h 1
214 4.2645033e-03 4.97e-07 1.84e-02 -4.0 1.19e-03 1.2 1.00e+00 1.00e+00h 1
215 3.5311606e-03 6.27e-07 1.54e-02 -4.0 1.56e-03 0.7 1.00e+00 1.00e+00h 1
216 3.0608754e-03 5.76e-07 1.06e-02 -4.0 1.56e-03 0.2 1.00e+00 1.00e+00h 1
217 2.8310981e-03 1.42e-06 1.01e-02 -4.0 1.84e-03 -0.2 1.00e+00 1.00e+00h 1
218 2.7512207e-03 2.44e-06 8.82e-03 -4.0 2.34e-03 -0.7 1.00e+00 1.00e+00h 1
219 2.5687894e-03 3.45e-06 3.51e-03 -4.1 4.24e-03 -1.2 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
220 2.5267716e-03 1.15e-05 6.07e-03 -4.1 9.57e-03 -1.7 1.00e+00 1.00e+00h 1
221 2.4379760e-03 4.54e-05 6.63e-03 -4.1 1.50e-02 -2.2 1.00e+00 1.00e+00h 1
222 2.4856677e-03 5.19e-04 2.10e-02 -4.0 4.60e-02 -2.6 1.00e+00 1.00e+00h 1
223 2.3674794e-03 2.65e-05 3.16e-03 -4.1 1.47e-02 -2.2 1.00e+00 1.00e+00h 1
224 2.2052633e-03 1.14e-03 1.99e+02 -4.0 1.03e-01 -2.7 1.00e+00 1.00e+00h 1
225 2.3357578e-03 2.57e-02 6.12e+01 -4.0 2.86e+00 - 2.56e-01 3.08e-01h 1
226 6.5569191e-03 5.10e-03 1.89e+02 -4.1 3.49e-01 -0.4 9.32e-01 8.39e-01h 1
227 4.3892409e-03 1.42e-04 1.99e+02 -4.1 6.32e-02 -0.9 1.00e+00 1.00e+00h 1
228 3.9615816e-03 2.30e-07 1.06e+00 -4.1 8.32e-04 2.2 1.00e+00 1.00e+00h 1
229 2.9060756e-03 5.29e-07 7.18e-02 -4.0 1.32e-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
230 1.8410384e-03 1.08e-06 3.59e-02 -4.0 1.99e-03 1.3 1.00e+00 1.00e+00h 1
231 1.8259199e-03 6.81e-07 9.85e-03 -4.0 1.63e-03 0.8 1.00e+00 1.00e+00h 1
232 2.1043589e-03 1.11e-07 8.39e-03 -4.0 9.29e-04 0.3 1.00e+00 1.00e+00h 1
233 2.1748298e-03 3.43e-07 5.09e-03 -4.0 2.23e-03 -0.2 1.00e+00 1.00e+00h 1
234 2.0951438e-03 1.04e-06 7.79e-03 -4.1 4.42e-03 -0.7 1.00e+00 1.00e+00h 1
235 2.0489546e-03 3.95e-06 9.75e-03 -4.1 1.01e-02 -1.1 1.00e+00 1.00e+00h 1
236 2.0018203e-03 5.95e-06 8.51e-03 -4.1 1.10e-02 -1.6 1.00e+00 1.00e+00h 1
237 1.9592311e-03 2.04e-05 5.82e-03 -4.1 1.38e-02 -2.1 1.00e+00 1.00e+00h 1
238 1.7434305e-03 2.61e-04 3.84e-02 -4.1 5.48e-02 -2.6 1.00e+00 1.00e+00h 1
239 1.7391552e-03 1.14e-04 1.99e+02 -4.0 5.11e-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
240 2.4532545e-03 5.68e-02 8.96e+01 -4.0 3.22e+00 - 3.23e-01 4.51e-01h 1
241 5.0397693e-03 4.23e-02 1.33e+02 -4.1 7.40e-01 1.0 3.73e-02 2.67e-01h 1
242 2.8319527e-03 2.92e-02 9.17e+01 -4.1 6.05e-01 0.5 3.66e-01 3.10e-01h 1
243 1.6347319e-02 8.84e-03 1.70e+02 -4.1 4.57e-01 0.0 2.17e-01 6.92e-01h 1
244 2.0933722e-02 7.13e-03 1.37e+02 -4.1 1.26e-01 2.3 1.00e+00 1.93e-01h 1
245 3.1769505e-02 9.19e-04 1.75e+01 -4.1 1.03e-01 1.8 1.00e+00 8.73e-01h 1
246 1.6950756e-02 1.50e-05 1.91e+00 -4.1 1.42e-02 1.3 1.00e+00 1.00e+00f 1
247 2.5160207e-03 9.57e-06 1.99e+02 -4.1 6.54e-03 0.8 1.00e+00 1.00e+00h 1
248 1.2708361e-02 8.31e-06 1.99e+02 -4.1 5.35e-03 0.4 1.00e+00 1.00e+00h 1
249 1.0363521e-02 8.56e-07 1.65e+00 -4.1 2.22e-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
250 6.1557406e-03 2.65e-06 4.70e-02 -4.1 2.81e-03 1.2 1.00e+00 1.00e+00h 1
Number of Iterations....: 250
(scaled) (unscaled)
Objective...............: 6.1557406030901948e-03 6.1557406030901948e-03
Dual infeasibility......: 4.7045423606571178e-02 4.7045423606571178e-02
Constraint violation....: 2.6513034000474889e-06 2.6513034000474889e-06
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 7.9271489062693738e-05 7.9271489062693738e-05
Overall NLP error.......: 4.7045423606571178e-02 4.7045423606571178e-02
Number of objective function evaluations = 275
Number of objective gradient evaluations = 251
Number of equality constraint evaluations = 275
Number of inequality constraint evaluations = 275
Number of equality constraint Jacobian evaluations = 251
Number of inequality constraint Jacobian evaluations = 251
Number of Lagrangian Hessian evaluations = 250
Total seconds in IPOPT = 2373.981
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: 0.9999429222580105and 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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