[Feature]: Sampling-based robust control

[andgoldschmidt]

Feature Description

Quantum collocation currently has a UnitaryRobustnessProblem which can be used to make a control solution robust to an error operator. However, there is more than one way to make a control solution robust. For this feature request, we want to implement sampling-based robust control problem template (see also, Reference [1])

Suppose we have a qubit system $H(t) = \zeta Z + a(t) X$, where $\zeta \sim \mathcal{N}(\mu=0.01, \sigma=0.05)$. That is, we know that there is some dephasing noise on the qubit (acting via the operator Z), and we even characterized the distribution! To implement sampling-based robust control, we want to find the best control for the qubit, in expectation. This can be accomplished by drawing samples $\zeta_i$, and constructing an ensemble of quantum systems $H_i(t)$. The goal of the problem template is to maximize the expected fidelity of the sampling-based robust control by solving each of the control problems simultaneously.

A useful place to look at is UnitaryDirectSumProblem.

Implementation guidelines

To accomplish this using Quantum Collocation, follow the UnitarySmoothPulseProblem template, but make the following changes:

1. Instead of passing a static quantum system to the problem template, the user should pass a QuantumSystem with a constructor (e.g., TransmonSystem). The constructor will be used to pass parameters to create an ensemble of quantum systems.
2. Additionally, the problem template should have the user pass a distribution and number of samples, or a list of samples, which the template will use to make an ensemble of quantum systems.
3. Make a named trajectory which includes separate unitary components for each system in the ensemble, but a shared control.
4. Attach dynamics constraints for each system in the ensemble.
5. Modify the fidelity cost to be the average fidelity over the ensemble (you can add up the fidelities, which can be calculated for each member of the ensemble by changing the unitary_symbol).

Requirements

Tests of the problem template should be implemented.

Other information

A relevant example for this type of problem template is control uncertainty, $H(t) = (a(t) + \delta a)X$, which cannot be captured using the previous robustness framework. I'm not entirely sure how the sampling solution will do, but it would be cool to check and see!

Importance

1 (lowest)

What does this feature affect?

• quantum system construction
• problem setup
• problem solution
• problem performance
• solution analysis
• plotting
• documentation
• tests
• other (please specify below)

References

[1] Sampling-based Learning Control for Quantum Systems with Uncertainties

[Fe-r-oz]

I have almost completed the Issue 102 so I would like to start working on this one. This problems seems interesting.

I see, so we can directly call the TransmonSystem as well.

julia> using QuantumCollocation: TransmonSystem

[Fe-r-oz]

I read the paper [1]. I have a few questions which I would kindly request some clarification:

We don't need to use gradient-flow based iterative algorithm during step 2 of training? Instead, we use the gradient-based optimization algorithm used here like for UnitarySmoothPulseProblem ?

Instead of AbstractQuantumSystem as static parameter, we should have type TransmonSystem, right?

I am not clear on the "create an ensemble of quantum systems". We have to create a system that can cater to all three (or generally) types of systems presented in the paper namely, right?

1. 5-Type three-level quantum system
2. 2-qubit superconducting circuit and
3. 2-atom system interacting with a quantized field in a cavity.

Make a named trajectory which includes separate unitary components for each system in the ensemble, but a shared control.

Seems very interesting! Please provide some reference from the code to get some idea about this part.

I am also attaching some points from the Paper for my reference:

• Generate N samples through sampling the uncertainty parameters according to a given probability distribution (e.g., the uniform distribution).
  -- We could choose any of the combination (θ_0_n_0 ,θ_1_n_1 ,...,θ_M_n_M ) of the sampled parameters {θ_j , j = 0,1,...,M}, where θ_j_n_j is a possible value of the uncertainty parameter θ, n_j = 1,...,N_j and N_j is the number of samples of the parameter θ_j (j = 0,1,...,M).
  -- The total number of potential samples is N = ∏ (0 to M_j ) N_j .
  -- We will develop a gradient flow based learning algorithm to solve this optimization problem in an iterative way
• Numerical results show that five or seven samples for each uncertainty parameter are enough to achieve excellent performance.
• Gradient Flow based Iterative Learning: This initial value problem can be solved numerically by using a forward Euler method over the s-domain. For practical applications, converted to an iterative version.
• In practical applications, it is usually difficult to find the numerical solution to a time varying continuous control strategy u(t) using Gradient flow based learning algorithm.
• In simulation, we usually divide the time interval [0, T] equally into a number of smaller time intervals △t and assume that the controls are constant within each △t. Instead of t ∈ [0,T], the time index will be t_w = wT/W, where W = T/△t and w = 0,1,...W.
• As for the issue of choosing N samples, we generally choose them according to possible distributions of the uncertainty
  parameters θ_j ∈ [1 − E,1 + E]. The basic motivation of the proposed sampling-based approach is to design the control law using some artificial samples instead of unknown uncertainties

Three Examples in the Paper: (I think let's do with the first example)

• 1: System: 5-type three-level quantum system with uncertainties: We assume that there are no constraints on the control fields and the uncertainty parameters have uniform distributions or time-varying distributions.
  -- For simplicity, we assume no constraints on the external controls and use atomic units (i.e., setting h = 1)
  -- Assume that the initial state is |ψ(t)〉 = c_1(t)|1〉+ c_2(t)|2〉 + c_3(t)|3.
  Let C(t) = (c1(t), c2(t), c3(t)) where the c_i(t)’s are complex numbers.
  -- H_0 = diag(1.5,1,0) and choose H1, H2, H3 and H4 given in (21)
  -- For simplicity, we assume that f_0(ϑ) = f(ϑ) = ϑ have uniform distributions over [1−E,1+E]. Now the objective is
  to find a robust control strategy u(t) = {u_m(t),m = 1,2,3,4} to drive the quantum system from |ψ_0〉 = |1〉 (i.e., C0 = (1,0,0)) to |ψ_target〉 = 1/√2 (|2〉+|3)
  -- The initial state |ψ0〉= |1〉 and the target state |ψ〉_target = 1/√2 (|2〉 + |3);
  The end time is T = 5 and the total time duration [0,T] is equally discretized into W = 200 time intervals with each time interval ∆t = (t_w −t_w−1)|w=1,2,...,W = T/W = 0.025; The learning rate is η_k = 0.2;
  -- The control strategy is initialized with u^ (k=0) (t) = {u^0_m (t) = sint, m = 1, 2, 3, 4}
  -- First, we assume that there exists only the uncertainty f_0(ϑ) (i.e., f(ϑ) ≡ 1), E = 0.21 and f_0(ϑ) has a uniform distribution in the interval [0.79,1.21]
  -- To construct an augmented system for the training step, we use the training samples for this 5 type quantum system defined in (26)
  -- To test the optimal control strategy obtained from the training step, we choose 200 samples obtained by sampling the uncertainty f_0(ϑ) according to a uniform distribution

• 2: In the second example, we consider entanglement generation in superconducting quantum circuits. We use some practical models and relevant parameters in the literature. Bounded control fields and truncated Gaussian distributions for uncertainty parameters are assumed.

• 3: The third example considers the application of the SLC method to a two-atom system interacting with a quantized field.

In the meantime, I would have a look at the code that was mentioned in the above description.

Thanks a lot for clarification!

[Fe-r-oz]

P.S. In order to better understand the problem, I am preparing the documentation about SLC.

I think we use this form of system Hamiltonian in problem templates as mentioned in the QuickStart Guide

$$\begin{equation} \begin{aligned} H(t) = H_0 + H_c(t) = H_0 + \sum_{m=1}^{M} u_m(t) H_m. \end{aligned} \end{equation}$$

But, there is a slight modified version of system hamiltonian due to uncertanities that is assumed by the authors where the uncertainity parameters (θ) are sampled from uniform distribution.

Assumption for the first example of implementation of SLC: f_m(θ_m) = f(ϑ) for all m = 1,2,3,4 and f_0(θ_0) = f_0(ϑ). For instance, in the first example of 5-type 3-level system (please see details above), they provide H_0, H1, H2, H3, H4.

$$\begin{equation} \begin{aligned} H_{\Theta}(t) = f_0(\theta_0)H_0 + \sum_{m=1}^M f_m(\theta_m)u_m(t)H_m. \end{aligned} \end{equation}$$

[andgoldschmidt]

Let's start by making a notebook that demonstrates how to solve this problem, then we can think of packaging the code into a problem template and simplifying the notebook for the documentation.

To be specific, let's take a simple system: $H(a; \zeta) = \zeta Z + a_1(t) X + a_2(t)Y$. This is a qubit with some random dephasing noise. The noise might be due to fluctuations in the qubit frequency that persist longer than a gate but change over the timescale of multiple gates. First, we will focus on setting up and solving the control problem. Next, we can think about generalizing the QuantumSystem constructor.

1. Define an ensemble of QuantumSystem objects.
Sample to create $H(a; \zeta_i) = \zeta Z + a_1(t) X + a_2(t)Y$ for some distribution of $\zeta_i \sim \mathcal{N}(0, 0.01 I)$. (It could be fun to come back and try other distributions, later.)

From here, we could set up an independent control problem for each of these systems. Let's say we want an $X$ gate; set $T=50$ and $\Delta t = 0.2$.

2. Redo UnitarySmoothPulseProblem with the help of for loops
What we want to do now is create a joint smooth pulse problem that adds a unitary for each of our quantum systems, but when it comes time to add the controls, we only add a single, shared control! We can do this by manually recreating the NamedTrajectory container, basically following all the steps in a UnitarySmoothPulseProblem.

Check out how add_suffix can be used to attach a unique label to keys. We use this a lot in our UnitaryDirectSumProblem. We just need to create one trajectory key for each system. They can all even use the same kind of initial data that we supply in the UnitarySmoothPulseProblem.

3. Glue the trajectory together with the right dynamics
Now comes the interesting part! We can attach integrators for each system, separately! In UnitarySmoothPulseProblem, we have this block of code:

    if integrator == :pade
        unitary_integrator =
            UnitaryPadeIntegrator(system, :Ũ⃗, :a; order=pade_order, autodiff=autodiff)
    elseif integrator == :exponential
        unitary_integrator =
            UnitaryExponentialIntegrator(system, :Ũ⃗, :a)
    else
        error("integrator must be one of (:pade, :exponential)")
    end

Notice that we get to supply the keys. With diligent use of for loop and add_suffix, we can make the integrators we need for each quantum system in our ensemble.

4. Make sure we have all the pieces!
Check out the final return statement:

return QuantumControlProblem(
        system,
        traj,
        J,
        integrators;
        constraints=constraints,
        max_iter=max_iter,
        linear_solver=linear_solver,
        verbose=verbose,
        ipopt_options=ipopt_options,
        jacobian_structure=jacobian_structure,
        hessian_approximation=hessian_approximation,
        eval_hessian=!hessian_approximation,
        kwargs...
    )

Make sure you collect all the pieces you need. For example, we pass our fancy, joint trajectory and list of many integrators. We also want the quantum system to be the direct_sum of all the supplied systems!

[Fe-r-oz]

Thank you very much the description!, @andgoldschmidt. That's awesome!

I have completed Step 1, Step 2 (partially, created NamedTracjectory for each system in ensemble), and Step 3. I would highly appreciate if you have a look (Please download it!) at the notebook . Thanks for your time!

[andgoldschmidt]

For your error at

#this causes error: ArgumentError: Provided trajectories must have fixed timesteps
traj = direct_sum([add_suffix(traj, ℓ) for (traj, ℓ) ∈ zip(initial_trajectories, prob_labels)])

the issue is that you have constructed the trajectories with a free_time. This means that each trajectory has Δt as a state variable, and these Δt can become disconnected, so that the trajectories do not evolve together. Therefore, direct_sum throws an error. In fact, this is why direct_sum has free_time as a kwarg (so free time can be enabled on a single, shared Δt).

Relying on direct sum can be trouble because it is designed to duplicate every part of the trajectory, including the controls. Instead, work one level up, where you construct the system:

components = (
    Ũ⃗ℓ=Ũ⃗,
    a = a,
    da = da,
    dda = dda,
    Δt = Δt,
)

where this is pseudocode for creating a variable number of initial trajectories, Ũ⃗ℓ---one for each system. You no longer need an outerloop, for (i, system) in enumerate(quantum_systems). Instead, you can use such a loop inside to create the keys for the single named trajectory object.

[andgoldschmidt]

Notice that to glue everything together, UnitarySmoothPulseProblem calls things like

UnitaryPadeIntegrator(system, :Ũ⃗, :a; order=pade_order, autodiff=autodiff)

while in a UnitaryDirectSumProblem we need add_suffix(:Ũ⃗, ℓ).

[Fe-r-oz]

Oh, Yeah, I did notice after you pointed out that in UnitaryDirectSumProblem, we have used add_suffix(:Ũ⃗, ℓ). Thanks a lot for your insightful comments!

[Fe-r-oz]

Hi, @andgoldschmidt, I completed the Step 4 about glueing everything together where we use add_suffix. I removed for (i, system) in enumerate(quantum_systems) from the outerloop as well. I tried to implement one trajectory key for each system as well. I get an error related to timestep being a Matrix.

Please have a look notebook. Thanks! In the meantime, I am introspecting on your comments trying to understand better.

[andgoldschmidt]

Take a look at the NamedTuple docs, in particular

julia> keys = (:a, :b, :c); values = (1, 2, 3);

julia> NamedTuple{keys}(values)
(a = 1, b = 2, c = 3)

julia> (; (keys .=> values)...)
(a = 1, b = 2, c = 3)

You can create a vector of symbols, one for each trajectory Ũ⃗ℓ, plus the controls, in order to make the components,

keys = # make all the symbols
values = # match the original data
components = (; (keys .=> values)...)

[andgoldschmidt]

Regarding your error, pay particular attention to the free_time case, and make sure you match how that is handled in UnitarySmoothPulseProblem.

[Fe-r-oz]

Thanks for your comments. My apologies if too many question in one day was bothersome.

[Fe-r-oz]

pay particular attention to the free_time case, and make sure you match how that is handled in UnitarySmoothPulseProblem.

Yeah, in Free time, we use =:Δt , where as in else, we use =Δt.

[Fe-r-oz]

        # Construct the single named trajectory object using the components tuple
        components = (; (keys .=> values)...)
        println(components[:dda_1])
        println(components)
        println(components[:a_2])

Please check out components created at system level. We want something like this, right? Thanks

[-0.008983321555970291 -0.007362786667992461 0.01752979907846178 0.003358482028558358 0.004762186770928922 0.0074342659253134056 -0.03006167529200141 0.011357904031856672 -0.013912202046682013 0.0009558940008902978 -0.002740382406237648 0.0053213027664558155 0.008616586337507916 0.011824548908561222 -0.011471659223677363 -0.007825072323053076 0.00409650459028108 -0.0009777943375473342 -0.003736766004598012 -0.00559710339134449 -0.006326787066434984 -0.0020912308068476273 0.015953101882260696 -0.011912959971461766 -0.007721907376871271 0.006134628445315372 -0.0010406531772177998 -0.0009881236383137463 -0.007287153403367684 0.014540908092917311 -0.009056141876455717 -0.012851777251688663 -0.004020866043312907 -0.00044320315718102517 -0.0016782423740662224 -0.013756400665589405 -0.017416350115068157 -0.01209104450228022 0.008958771553928744 -0.0017815376708928557 0.007944839651838153 0.0036491971494810043 -0.013236894868470109 0.007150265352299686 0.004028787316993884 -0.002815053302982428 -0.0027184255823438455 0.0041176513067688655 0.006187897095652525 0.011762789110673546; 0.019071619942739912 0.018030708995342187 0.00349028649999469 -0.0251950234225986 0.008108366840822185 0.015871802012493195 -0.006183809095214923 -0.0034733605145246694 -0.0012725753911709563 -0.006762376212986784 -0.002110433582901338 0.006343897716984821 0.015563605621883112 0.019423140407244657 -0.008033176982879251 -0.007916681602605646 0.008211444194684739 -0.02033062355878352 -0.0017406096981268126 0.00399355003443293 -0.004845244542144696 0.020777923998891112 0.008946886745547888 0.006020783900576457 0.0010891473599687574 0.00763401723697806 -0.0045798911090329875 0.001660471351019654 0.021453548289382993 -0.011375299193320481 0.005731052409876039 0.003946466139634895 -0.0023111189247169424 0.008862271745328979 -0.0006944995965475066 -0.013324295027749802 0.016711834576212753 -0.0007438821338854066 -0.02776914422442289 0.010145189425841115 -0.005927875575754684 0.015203611079217616 0.001170099354509733 -0.010678955057840243 -0.007888674651612205 0.02239137335380234 0.02216719500026103 0.014644771738572182 0.00010239668923914232 -0.01832557212429812]
(Ũ⃗_1 = [1.0 0.9989726963751682 0.9958950069116229 0.9907795784955328 0.9836474315195147 0.9745278735053341 0.963458378673011 0.9504844339512096 0.9356593520616949 0.9190440524459204 0.9007068109339783 0.8807229791845672 0.8591746750488638 0.8361504451306584 0.811744900929367 0.7860583300610849 0.7591962841552627 0.7312691451204175 0.7023916715611972 0.672682527210654 0.6422637933155163 0.6112604669781573 0.5797999475166895 0.5480115129538409 0.5160257887858277 0.48397421121417267 0.45198848704615924 0.4202000524833106 0.388739533021843 0.35773620668448386 0.3273174727893465 0.29760832843880314 0.26873085487958265 0.24080371584473764 0.21394166993891528 0.18825509907063334 0.1638495548693418 0.14082532495113648 0.11927702081543291 0.09929318906602186 0.08095594755407974 0.06434064793830535 0.049515566048790496 0.03654162132698924 0.025472126494665723 0.016352568480485365 0.009220421504467294 0.004104993088376991 0.0010273036248318428 -1.1905898466964329e-17; 0.0 0.0010273036248318282 0.004104993088376942 0.009220421504467318 0.01635256848048528 0.02547212649466566 0.03654162132698911 0.04951556604879043 0.06434064793830524 0.08095594755407966 0.09929318906602165 0.11927702081543273 0.14082532495113614 0.16384955486934155 0.1882550990706331 0.21394166993891514 0.2408037158447373 0.26873085487958226 0.2976083284388029 0.3273174727893461 0.3577362066844836 0.3887395330218426 0.42020005248331027 0.4519884870461591 0.48397421121417217 0.5160257887858273 0.5480115129538408 0.5797999475166896 0.611260466978157 0.6422637933155161 0.6726825272106536 0.7023916715611969 0.7312691451204173 0.7591962841552622 0.7860583300610848 0.8117449009293667 0.8361504451306583 0.8591746750488634 0.880722979184567 0.9007068109339782 0.9190440524459205 0.9356593520616945 0.9504844339512094 0.9634583786730107 0.9745278735053342 0.9836474315195145 0.9907795784955327 0.9958950069116229 0.998972696375168 1.0; 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[andgoldschmidt]

It looks like this is the right track, except I don't understand the presence of dda_1 and a_2. We should only have a single control made up of a, da, dda, which is shared by all the state variables, Ũ⃗1, Ũ⃗2, etc..

Once you have the entire trajectory, can you share the constructed NamedTrajectory components that are output by calling, e.g. traj.components? This is a simpler output that will show the keys of each component and their corresponding indices in the data matrix, without handing us a large matrix of numbers.

[Fe-r-oz]

Glad to hear that. Sure, I will share output of traj.components soon!

[Fe-r-oz]

Kindly please tell me is this what we want our keys and values to be?

keys[:a, :da, :dda, :Ũ⃗_1, :Ũ⃗_2, :Ũ⃗_3, :Ũ⃗_4, :Ũ⃗_5, :Ũ⃗_6]
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I have made an inner loop to construct keys and components. Please see the notebook here: link

[Fe-r-oz]

I think I have solved the components problem thanks to your guidance, @andgoldschmidt!

Once you have the entire trajectory, can you share the constructed NamedTrajectory components that are output by
calling, e.g. traj.components?

Please see the output of traj.components?

println(traj.components)
(Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15])

Now, I am getting the error towards the end!

Question:

Just like in the UnitaryDirectSumProblem, we do take direct sum of these quantum systems

https://github.com/aarontrowbridge/QuantumCollocation.jl/blob/36e5c619031898595befab9ed25771925954e0e0/src/problem_templates/unitary_direct_sum_problem.jl#L151

Method is present that we can take direct_sum for Abstract Vector of Quantum Systems, which we have in our case (SampleBasedControlProblem)

https://github.com/aarontrowbridge/QuantumCollocation.jl/blob/36e5c619031898595befab9ed25771925954e0e0/src/direct_sums.jl#L64

Does we take Direct_sum of Abstract Vector of Quantum Systems in our case?

system = direct_sum(quantum_systems)

This is because for all QuantumControlProblem, we have system
https://github.com/aarontrowbridge/QuantumCollocation.jl/blob/36e5c619031898595befab9ed25771925954e0e0/src/problem_templates/unitary_direct_sum_problem.jl#L197-L212

Please see the error:

MethodError: no method matching QuantumControlProblem(::QuantumSystem, ::NamedTrajectory{Float64}, ::Objective, ::Vector{Any}; constraints::Vector{AbstractConstraint}, max_iter::Int64, linear_solver::String, verbose::Bool, ipopt_options::Options{Float64}, jacobian_structure::Bool, hessian_approximation::Bool, eval_hessian::Bool)

Please find the notebook here: drive link

[Fe-r-oz]

In this other second version , I get 'timestep Δt::Symbol must be a symbol or real'. It does seems to have shared control though if we see the stacktrace. Please do let me know about this as well! Thanks a lot!

Stacktrace:
 [1] NamedTrajectory(comp_[data::@NamedTuple{Ũ⃗_1::Matrix{Float64](data::@NamedTuple{U%CC%83%E2%83%97_1::Matrix{Float64)}, Ũ⃗_2::Matrix{Float64}, Ũ⃗_3::Matrix{Float64}, Ũ⃗_4::Matrix{Float64}, Ũ⃗_5::Matrix{Float64}, Ũ⃗_6::Matrix{Float64}, a::Matrix{Float64}, da::Matrix{Float64}, dda::Matrix{Float64}}; controls::Tuple{Symbol, Symbol}, timestep::Symbol, bounds::@NamedTuple{a::Vector{Float64}, dda::Vector{Float64}, Δt::Tuple{Float64, Float64}}, initial::@NamedTuple{Ũ⃗::Vector{Float64}, a::Vector{Float64}}, final::@NamedTuple{a::Vector{Float64}}, goal::@NamedTuple{Ũ⃗::Vector{Float64}})

[andgoldschmidt]

You will want to be sure that you have a state Ũ⃗ for each system (because each unique system sys_i will determine how its Ũ⃗_i evolves under the control). For example,

|julia> println(traj.components)
(Ũ⃗_1 = 1:8, Ũ⃗_2 = 9:16, Ũ⃗_3 = 17:24, a = 25:26, da = 27:28, dda = 29:30, Δt = 31:31, ...

If you set up your problem in this way, you will not need to create a DirectSumProblem. Instead, you will have done all the direct sum-behavior yourself, and you will be able to proceed directly to solving the problem you made.

[andgoldschmidt]

Do we take Direct_sum of Abstract Vector of Quantum Systems in our case?

Yes. system = direct_sum(quantum_systems) will create a single block diagonal system that we can pass along to the control problem.

Please see the error:

Notice what the error message is telling you. There is no method matching the arguments. Look at the argument that did not match (in red). It is the integrators, which in your code is a type Vector{Any}, but the error tells you it needs to be Vector{<:AbstractIntegrator}.

Create integrators with

integrators = AbstractIntegrator[]

Then, instead of rewriting the object,

    integrators = vcat(
        integrators,
        DerivativeIntegrator(:a, :da, traj),
        DerivativeIntegrator(:da, :dda, traj)
    )

try

push!(integrators, DerivativeIntegrator(:a, :da, traj))
push!(integrators, DerivativeIntegrator(:da, :dda, traj))

[Fe-r-oz]

Thank you very much!

[Fe-r-oz]

Pardon me for a naive Question:

In the UnitarySmoothControlProblem, I have noticed that the components are set up diferently, meaning if free_time, we push Δt = Δt in the components as well. We don't do that in the other case.

https://github.com/aarontrowbridge/QuantumCollocation.jl/blob/88c5ef13e18b92e43773d70b608584ea11a17dfd/src/problem_templates/unitary_smooth_pulse_problem.jl#L217-L255

So, we should follow similar approach in our case, right? Like

             # Assuming each Ũ⃗_i has n elements
            nₑ = size(Ũ⃗, 1)  

            # Populate keys and values arrays for state variables for each system
            #Address the commments: You will want to be sure that you have a state Ũ⃗ for each system
            #(because each unique system sys_i will determine how its Ũ⃗_i evolves under the control)
            
            for (i, system) in enumerate(quantum_systems)
                ℓ = prob_labels[i]
                startᵢ = (i-1) * nₑ + 1
                stopᵢ = i * nₑ
                Ũ⃗ᵢ = Ũ⃗[:, startᵢ:stopᵢ]
                push!(keys, Symbol("Ũ⃗_", ℓ))
                push!(values, Ũ⃗ᵢ)
            end

            # Populate keys and values arrays for shared controls
            push!(keys, :a)
            push!(values, a)
            push!(keys, :da)
            push!(values, da)
            push!(keys, :dda)
            push!(values, dda)
             
        if free_time
            #we do this 
            push!(keys, :Δt) # this considers the Line 223 of Unitary Smooth Problem
            push!(values, Δt) # this considers the Line 223 of Unitary Smooth Problem
            
            components = (; (keys .=> values)...)
            #instead of
            #components = ( 
             #Ũ⃗ = Ũ⃗, 
             #a = a, 
             #da = da, 
             #dda = dda, 
             #Δt = Δt, 
         #)  
        bounds = merge(bounds, (Δt = (Δt_min, Δt_max),))
           traj = NamedTrajectory(
                components;
                controls=(:dda, :Δt),
                timestep=:Δt,
                bounds=bounds,
                initial=initial,
                final=final,
                goal=goal
            )
        else
            components = (; (keys .=> values)...)
                
            traj = NamedTrajectory(
                components;
                controls=(:dda,),
                timestep=Δt,
                bounds=bounds,
                initial=initial,
                final=final,
                goal=goal
            )
        end
    end

In a way, you already answered this question above as following:

pay particular attention to the free_time case, and make sure you match how that is handled in UnitarySmoothPulseProblem.

The error now
AssertionError: all([k ∈ keys(comp_data) for k = keys(initial)])

Please find the latestnotebook here: drivelink Thanks!

[andgoldschmidt]

AssertionError: all([k ∈ keys(comp_data) for k = keys(initial)])

Check that things like bounds are all in the components you provide, for example bounds = merge(bounds, (Δt = (Δt_min, Δt_max),)) should only be added for free_time

[Fe-r-oz]

I checked and cross-verified with the UnitarySmoothPulseProblem. It seems to be related to something else.

Error Location: The error occurs in if free_time when making NamedTrajectory container

if free_time
#everything before that runs, Error message originate afterwords this point
.
.
.
traj = NamedTrajectory(
                components;
                controls=(:dda, :Δt),
                timestep=:Δt,
                bounds=bounds,
                initial=initial,
                final=final,
                goal=goal
            )

Output of println(components) : I hope we want something like the following:

Ũ⃗_1 = [1.0 0.9989726963751682 0.9958950069116229 0.9907795784955328 0.9836474315195147 0.9745278735053341 0.963458378673011 0.9504844339512096; 0.0 0.0010273036248318282 0.004104993088376942 0.009220421504467318 0.01635256848048528 0.02547212649466566 0.03654162132698911 0.04951556604879043; 0.0 0.032035109990356456 0.06393858084225298 0.09557931435068613 0.12682729195475365 0.15755410901181027 0.18763350243968702 0.21694186955877906; 0.0 -0.03203510999035645 -0.06393858084225297 -0.0955793143506861 -0.12682729195475365 -0.15755410901181033 -0.18763350243968707 -0.21694186955877906; 0.0 0.0010273036248318284 0.004104993088376942 0.009220421504467318 0.01635256848048528 0.025472126494665653 0.03654162132698911 0.04951556604879043; 1.0 0.9989726963751681 0.995895006911623 0.9907795784955327 0.9836474315195147 0.9745278735053343 0.9634583786730111 0.9504844339512095; 0.0 -0.03203510999035645 -0.06393858084225297 -0.09557931435068613 -0.12682729195475367 -0.1575541090118103 -0.18763350243968707 -0.21694186955877906; 0.0 0.03203510999035645 0.06393858084225298 0.09557931435068612 0.12682729195475365 0.15755410901181033 0.18763350243968707 0.21694186955877903]
Ũ⃗_2 = [0.9356593520616949 0.9190440524459204 0.9007068109339783 0.8807229791845672 0.8591746750488638 0.8361504451306584 0.811744900929367 0.7860583300610849; 0.06434064793830524 0.08095594755407966 0.09929318906602165 0.11927702081543273 0.14082532495113614 0.16384955486934155 0.1882550990706331 0.21394166993891514; 0.24535877600196881 0.2727674506052743 0.29905526524560794 0.32411419765389415 0.34784127530174314 0.3701389985376577 0.3909157412340148 0.41008612729847793; -0.2453587760019688 -0.27276745060527435 -0.29905526524560794 -0.32411419765389415 -0.3478412753017431 -0.3701389985376577 -0.3909157412340148 -0.410086127298478; 0.06434064793830524 0.08095594755407966 0.09929318906602164 0.11927702081543272 0.14082532495113614 0.16384955486934152 0.18825509907063306 0.21394166993891514; 0.9356593520616948 0.9190440524459202 0.9007068109339784 0.8807229791845673 0.8591746750488638 0.8361504451306584 0.8117449009293669 0.786058330061085; -0.2453587760019688 -0.2727674506052743 -0.29905526524560794 -0.3241141976538941 -0.3478412753017431 -0.37013899853765764 -0.39091574123401485 -0.410086127298478; 0.24535877600196876 0.2727674506052743 0.299055265245608 0.32411419765389415 0.34784127530174314 0.37013899853765775 0.39091574123401474 0.41008612729847793]
Ũ⃗_3 = [0.7591962841552627 0.7312691451204175 0.7023916715611972 0.672682527210654 0.6422637933155163 0.6112604669781573 0.5797999475166895 0.5480115129538409; 0.2408037158447373 0.26873085487958226 0.2976083284388029 0.3273174727893461 0.3577362066844836 0.3887395330218426 0.42020005248331027 0.4519884870461591; 0.42757138150267304 0.4432996531865 0.45720631150790614 0.46923421102488017 0.47933392651833023 0.48746395609091175 0.49359089170722503 0.49768955647459906; -0.427571381502673 -0.44329965318649994 -0.45720631150790625 -0.4692342110248801 -0.47933392651833023 -0.4874639560909117 -0.49359089170722503 -0.4976895564745991; 0.2408037158447373 0.2687308548795823 0.2976083284388029 0.3273174727893461 0.3577362066844836 0.3887395330218426 0.42020005248331027 0.4519884870461591; 0.7591962841552627 0.7312691451204176 0.7023916715611972 0.6726825272106539 0.6422637933155164 0.6112604669781573 0.5797999475166895 0.5480115129538411; -0.427571381502673 -0.4432996531865 -0.45720631150790614 -0.4692342110248801 -0.47933392651833023 -0.4874639560909118 -0.4935908917072249 -0.4976895564745992; 0.42757138150267293 0.4432996531865 0.4572063115079062 0.46923421102488017 0.4793339265183303 0.48746395609091175 0.49359089170722503 0.49768955647459917]
Ũ⃗_4 = [0.5160257887858277 0.48397421121417267 0.45198848704615924 0.4202000524833106 0.388739533021843 0.35773620668448386 0.3273174727893465 0.29760832843880314; 0.48397421121417217 0.5160257887858273 0.5480115129538408 0.5797999475166896 0.611260466978157 0.6422637933155161 0.6726825272106536 0.7023916715611969; 0.49974310810034406 0.499743108100344 0.4976895564745991 0.49359089170722514 0.48746395609091187 0.4793339265183303 0.4692342110248803 0.45720631150790636; -0.49974310810034395 -0.49974310810034384 -0.49768955647459906 -0.49359089170722514 -0.4874639560909118 -0.4793339265183303 -0.4692342110248803 -0.45720631150790625; 0.4839742112141723 0.5160257887858273 0.5480115129538408 0.5797999475166897 0.611260466978157 0.6422637933155161 0.6726825272106535 0.7023916715611969; 0.5160257887858277 0.4839742112141725 0.4519884870461591 0.42020005248331055 0.3887395330218429 0.357736206684484 0.3273174727893463 0.297608328438803; -0.49974310810034406 -0.49974310810034384 -0.49768955647459906 -0.49359089170722525 -0.4874639560909117 -0.4793339265183304 -0.46923421102488017 -0.45720631150790625; 0.49974310810034384 0.49974310810034384 0.49768955647459906 0.49359089170722514 0.48746395609091175 0.4793339265183304 0.46923421102488017 0.45720631150790614]
Ũ⃗_5 = [0.26873085487958265 0.24080371584473764 0.21394166993891528 0.18825509907063334 0.1638495548693418 0.14082532495113648 0.11927702081543291 0.09929318906602186; 0.7312691451204173 0.7591962841552622 0.7860583300610848 0.8117449009293667 0.8361504451306583 0.8591746750488634 0.880722979184567 0.9007068109339782; 0.4432996531865002 0.42757138150267315 0.41008612729847793 0.39091574123401496 0.37013899853765786 0.3478412753017436 0.3241141976538945 0.2990552652456082; -0.4432996531865003 -0.42757138150267315 -0.41008612729847793 -0.390915741234015 -0.3701389985376579 -0.3478412753017434 -0.3241141976538945 -0.2990552652456082; 0.7312691451204172 0.7591962841552621 0.7860583300610848 0.8117449009293667 0.8361504451306583 0.8591746750488636 0.8807229791845671 0.9007068109339782; 0.2687308548795828 0.24080371584473764 0.21394166993891522 0.18825509907063337 0.16384955486934177 0.14082532495113642 0.11927702081543294 0.09929318906602191; -0.4432996531865002 -0.4275713815026732 -0.41008612729847793 -0.390915741234015 -0.3701389985376581 -0.34784127530174336 -0.32411419765389443 -0.2990552652456084; 0.4432996531865002 0.42757138150267304 0.4100861272984781 0.390915741234015 0.370138998537658 0.34784127530174347 0.32411419765389426 0.2990552652456083]
Ũ⃗_6 = [0.08095594755407974 0.06434064793830535 0.049515566048790496 0.03654162132698924 0.025472126494665723 0.016352568480485365 0.009220421504467294 0.004104993088376991; 0.9190440524459205 0.9356593520616945 0.9504844339512094 0.9634583786730107 0.9745278735053342 0.9836474315195145 0.9907795784955327 0.9958950069116229; 0.27276745060527424 0.2453587760019692 0.2169418695587793 0.18763350243968746 0.15755410901181074 0.12682729195475398 0.09557931435068623 0.06393858084225346; -0.27276745060527446 -0.2453587760019691 -0.21694186955877914 -0.18763350243968724 -0.15755410901181072 -0.12682729195475384 -0.09557931435068628 -0.06393858084225323; 0.9190440524459202 0.9356593520616945 0.9504844339512095 0.9634583786730109 0.9745278735053342 0.9836474315195146 0.9907795784955326 0.995895006911623; 0.08095594755407973 0.0643406479383054 0.04951556604879051 0.03654162132698918 0.02547212649466578 0.01635256848048533 0.0092204215044673 0.004104993088376942; -0.27276745060527446 -0.24535877600196904 -0.21694186955877925 -0.1876335024396873 -0.15755410901181072 -0.12682729195475384 -0.09557931435068617 -0.06393858084225335; 0.27276745060527446 0.2453587760019691 0.21694186955877914 0.1876335024396873 0.1575541090118107 0.1268272919547539 0.09557931435068619 0.06393858084225333]
a = [0.0 0.4857278797618563 0.7365060759315791 -0.4841762688733442 -0.9597430109485634 -0.6196621024362703 -0.3553998707623198 -0.7581008206364113 -0.6780305371249222 -0.6297019486385855 0.9091681364859718 0.3800990709660077 0.5133789196691152 -0.9341118846509777 0.04035782657611464 -0.41317714235782077 0.5004059581418718 -0.15834768212133077 -0.6054271953024224 0.8148021759630688 0.1208624656121482 -0.45437620274208146 -0.20614179961867873 -0.7736476615681955 0.8368040111930899 -0.045815774360007167 0.015245457689124775 0.27092153709416733 -0.24630887692366477 0.341348299182217 0.9853036284666123 -0.46234362627348213 0.14096314498464424 -0.05862524205096631 -0.20268064505349748 0.5599620438329844 0.6080839310342281 0.07749694795126483 0.4064767050429925 -0.2256146706734834 0.805768655929636 0.5475612893166357 -0.8950880497159079 -0.4386954383005097 -0.908402925640406 -0.016836365329296 0.4285215991506881 -0.27398798924839096 0.36943352540462415 0.0; 0.0 -0.13650694509727246 -0.008000793250816152 -0.6354045242293564 -0.9586523066427721 -0.17058439622052268 0.32527305736099676 -0.3373071410597861 -0.32921060938016455 0.21606538608062276 0.9835596932637181 0.8050591181852678 0.9491870995315945 0.9618222231944877 -0.592534277491575 -0.8139516870676231 0.530203902521025 0.45163191402324343 0.6956481455053414 0.7413068472917224 0.5723629785353486 0.4675975965857966 0.08323111514681036 -0.8804587748503827 0.9020593057260213 0.8793377706255527 0.11441273807786967 0.34030101686027514 -0.08868690526821199 0.7362056365051886 -0.6140375550641017 -0.3288137844634136 -0.3669968557479941 -0.4577424189387187 0.672892872774876 0.5769948003036178 -0.4064149635384875 -0.0700278168330093 0.5921507397186512 0.38725737739914634 -0.4943278590613367 -0.47217569030419315 -0.23833991136708033 0.7590555341186773 -0.6783394990955129 0.7263619690791883 -0.12387136575621227 0.2590558372788716 0.2404320779633482 0.0]
da = [-0.003553698401682227 -0.001994382876398032 0.0046956981385722005 -0.020838392577588908 -0.002054730255530348 -0.0036355583118205725 0.015193347758446267 -0.0011995352186843853 0.012847844909732817 0.008405368511737139 0.021019566273065098 -0.009164653424763903 0.013396380163078033 0.0048304803919825045 0.0027255684256605873 0.021451875978540366 0.0005121586659542902 0.015888162399550574 -0.022225633168867276 0.01929366801301198 -0.004043659996361559 -0.01346403594699404 -0.02592423000712969 0.004581316690715464 -0.006745892252527632 -0.012831343714077214 -0.00917654443224781 0.004922903554742925 0.010453494765184925 0.0017562678203589146 -0.0038154273518014726 -0.014131733124959947 0.012012158800713829 -0.0031201413021592927 0.008830827050094402 0.0049163613318425475 -0.007164727581151385 -0.008389393568172884 -0.0039054760870509174 0.0017253572540891582 0.0002371802437287196 0.010342529805818197 -0.01660024548214948 -0.0031850389168325915 -0.00927539392180171 0.0024988197353928137 -0.005410556469659548 0.008702473754301472 -0.015186088774870838 0.0011917043549413194; -0.024224406397485146 -0.007450903552328402 -0.0005297670096880921 0.012980245404777118 0.009714954894520757 0.012826724843885971 -0.012159500235265335 0.025634107194162203 0.021900248950701418 -0.012326631081002421 -0.002090264047136365 0.002390609923929658 0.001228764567805831 -0.012308472587955116 0.0014021560473301054 0.004051526275007416 0.01123648484456596 0.01976874165882589 -0.01932475123759827 -0.0014556289657281956 -0.003268271665804759 0.006062831326463381 -0.006302802926652559 -0.01244299674963572 -0.0021294248147050135 0.011092530774383295 0.0020892078193842653 0.0019879306092673724 0.0014863056427861813 -0.03271175712359134 -0.002151266014894415 -0.0032118509274162116 0.005001327876265422 0.00774076630794405 -0.006917223028646038 0.0018458041800071157 -0.010829310052690794 -0.008125182740016602 0.0008417555366600692 -0.000886556192040401 0.015043236344396626 -0.018324583321719247 -0.002815287959359579 -0.009291171919110615 -0.0041232403231863815 -0.0007075129582797789 -0.008070854317464533 0.009300710741968808 0.01072400401327039 -0.004721235311103501]
dda = [-0.008282176083209575 -0.011192609898081468 0.004369296877691191 0.01883623483510199 0.009127073985363734 -0.003764974826395723 -0.003549315191599146 0.003032356041302269 -0.004602698238905534 0.00853133985083874 -0.007560906008626855 0.02081246296828524 0.009020043853014305 -0.012445221157164786 -0.006013247671094781 0.004934782241046482 0.009724315807119036 -0.006668962429966098 0.0016745123112077145 -0.0004198580275815096 -0.00460361767812688 -0.008770710472505472 0.005372016901507385 -0.006427191934114124 0.007073731252053049 0.016439665584647913 0.017354359182084063 -0.001390325704364019 -0.006119945492623147 0.00708090141562844 0.026417548575485835 -0.008694039512333584 0.004766884589239975 -0.003282972759356434 0.009820334337584271 0.01991120160287654 -0.0024948030369985755 0.004625812375300457 0.0076414854771677644 0.0031205275479654782 -0.01840001511958325 0.0017517388650625093 0.0009945229860026663 -0.0035876951853356987 -0.007866699107204589 0.000508628136208335 -0.02314950889714289 -0.005432946998246737 0.005832406867988583 0.004850107490826906; -0.0022409524127603615 -0.006036983417208687 -0.0012956678267188417 -0.0032515409087294817 0.0047580065721568926 -0.00468295406527747 -0.005864002064804577 -0.008240676428154705 -0.0030435043084211387 -0.0010096965377612524 -0.007557154008398255 -0.008569259569328086 0.00796599760007228 0.012920079349432812 -0.007814172603983678 0.009646501513353696 0.0038971760365155007 0.009234939546850346 -0.0022145832469797773 -0.0037461507871233844 0.0009038453861454997 0.0007304012932234206 0.002965611912599197 -0.017093071456674575 0.013121245648444989 -0.0014390627954898887 -0.005858816909946976 -0.007195901676052337 0.010916082989201726 0.0028128815460647305 -0.0063000799311367026 -0.008111849729762219 -0.005624769719840787 -0.014009974243433034 -0.0034344646266405536 0.0039876306517853365 0.008109246722865188 0.010368209015316026 0.0020886268383063884 -0.006466718559410242 -0.0065175832540356375 0.00726010155804787 -0.00822829293677248 0.0005857336735930547 0.01127516318968799 0.0014041177789221153 -0.007445870040035186 -0.015458952857029232 -0.018283873884025584 0.0016776833041113818]
Δt = [0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2])

[andgoldschmidt]

Compare the output keys of the components with the keys in bounds, initial, and final, as it the error may indicate that some of the latter are keys are not in the components. For example, perhaps Ũ⃗ is sought but only Ũ⃗_j are available.

[Fe-r-oz]

 println(initial)
        println(final)
        println(bounds)
        println(goal)
        println(bound_unitary)
(Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0])
(a = [0.0, 0.0],)
(a = [1.0, 1.0], dda = [1.0, 1.0])
(Ũ⃗ = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0],)

In order to correct this, I am trying something like

        println(initial)
        println(final)
        println(bounds)
        println(goal)
(Ũ⃗_4 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], Ũ⃗_1 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], Ũ⃗_6 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], Ũ⃗_3 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], Ũ⃗_2 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], Ũ⃗_5 = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0])
(a = [0.0, 0.0],)
(a = [1.0, 1.0], dda = [1.0, 1.0])
(Ũ⃗_4 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], Ũ⃗_1 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], Ũ⃗_6 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], Ũ⃗_3 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], Ũ⃗_2 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], Ũ⃗_5 = [0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0])

DimensionMismatch: number of columns of each array must match (got (8, 8, 8, 8, 8, 8, 50, 50, 50, 50))
I get some dimensionmismatch now!

Please find the notebook attached: link Thanks!

[Fe-r-oz]

It seems that the DimensionMismatch is coming from the boundsdict of NamedTrajectory (L91)

https://github.com/aarontrowbridge/NamedTrajectories.jl/blob/355528a88e70827fa1d1d7ecf350bfd16d1f0b85/src/struct_named_trajectory.jl#L91

DimensionMismatch: number of columns of each array must match (got (8, 8, 8, 8, 8, 8, 50, 50, 50, 50))

Stacktrace:
 [1] _typed_vcat(::Type{Float64}, A::NTuple{10, Matrix{Float64}})
   @ Base ./abstractarray.jl:1702
 [2] typed_vcat(::Type{Float64}, ::Matrix{Float64}, ::Matrix{Float64}, ::Matrix{Float64}, ::Vararg{Matrix{Float64}})
   @ Base ./abstractarray.jl:1716
 [3] vcat(::Matrix{Float64}, ::Matrix{Float64}, ::Matrix{Float64}, ::Vararg{Matrix{Float64}})
   @ SparseArrays ~/.julia/juliaup/julia-1.10.2+0.x64.linux.gnu/share/julia/stdlib/v1.10/SparseArrays/src/sparsevector.jl:1239
 [4] NamedTrajectory(comp_[data::@NamedTuple{Ũ⃗_1::Matrix{Float64](data::@NamedTuple{U%CC%83%E2%83%97_1::Matrix{Float64)}, Ũ⃗_2::Matrix{Float64}, Ũ⃗_3::Matrix{Float64}, Ũ⃗_4::Matrix{Float64}, Ũ⃗_5::Matrix{Float64}, Ũ⃗_6::Matrix{Float64}, a::Matrix{Float64}, da::Matrix{Float64}, dda::Matrix{Float64}, Δt::Matrix{Float64}}; controls::Tuple{Symbol, Symbol}, timestep::Symbol, bounds::@NamedTuple{a::Vector{Float64}, dda::Vector{Float64}, Δt::Tuple{Float64, Float64}}, initial::Dict{Any, Any}, final::Dict{Symbol, Vector{Float64}}, goal::Dict{Any, Any})
   @ NamedTrajectories.StructNamedTrajectory ~/.julia/packages/NamedTrajectories/e22hU/src/struct_named_trajectory.jl:91

[Fe-r-oz]

Hi, @andgoldschmidt, Could you please re-open the PR that was closed 2 weeks ago about this? I would like to add the notebook for review.