# QuanticsTCI package **URL:** \ **Category:** ITensor Julia Questions\ **Created:** [April 18, 2024, 10:01am UTC](https://itensor.discourse.group/t/quanticstci-package/1641 "2024-04-18T10:01:51Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Faridun](https://avatars.discourse-cdn.com/v4/letter/f/45deac/32.png) [@Faridun](https://itensor.discourse.group/u/Faridun)\ **Post date:** [April 18, 2024, 10:01am UTC](https://itensor.discourse.group/t/quanticstci-package/1641/1 "2024-04-18T10:01:51Z")
Hello, does anyone have information about QuanticsTCI and is it possible to apply this package together with ITensor? I am interested in obtaining ground state wavefunction by using tensor train network. ---
**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\ **Post date:** [April 18, 2024, 2:07pm UTC](https://itensor.discourse.group/t/quanticstci-package/1641/2 "2024-04-18T14:07:07Z")
You can find the TensorCrossInterpolation and QuanticsTCI packages by Marc Ritter at these links: [https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl) [https://gitlab.com/tensors4fields/QuanticsTCI.jl](https://gitlab.com/tensors4fields/QuanticsTCI.jl) The packages include a function `MPS` which converts the result of the calculation into an ITensor MPS object. I would not know how to use TCI to compute a ground state. What is your thinking about that? TCI solves the problem of evaluating a function f(s1,s2,…,sn) at a set of interpolating points and then produces an accurate approximation of this function as an MPS whose site indices are the variables s1,s2,…sn. To compute a ground state as an MPS or tensor train (which is the same thing as an MPS), the DMRG algorithm is the best choice. ---
**Author:** ![Faridun](https://avatars.discourse-cdn.com/v4/letter/f/45deac/32.png) [@Faridun](https://itensor.discourse.group/u/Faridun)\ **Post date:** [April 18, 2024, 3:04pm UTC](https://itensor.discourse.group/t/quanticstci-package/1641/3 "2024-04-18T15:04:31Z")
Thank you for your reply and clarification. Coming back to this discussion [Ground state wavefunction](https://itensor.discourse.group/t/ground-state-wavefunction/1470) I wanted to use tensor cross interpolation to obtain to obtain the ground state wavefunction for systems with large number of sites (L\>100). So I am looking for ways to do this. Is there a package in Julia or Python that does it or is it necessary to write my own code for it? ---
**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\ **Post date:** [April 18, 2024, 3:31pm UTC](https://itensor.discourse.group/t/quanticstci-package/1641/4 "2024-04-18T15:31:20Z")
You cannot use tensor cross interpolation to obtain a ground state wavefunction. Part of what I was clarifying above is that it is not the purpose of that algorithm. Is there a reason you are not wanting to use DMRG to find a ground state? What is the precise problem that you are trying to solve? E.g. do you have a Hamiltonian or some other starting point? ---
**Author:** ![Faridun](https://avatars.discourse-cdn.com/v4/letter/f/45deac/32.png) [@Faridun](https://itensor.discourse.group/u/Faridun)\ **Post date:** [April 19, 2024, 10:07am UTC](https://itensor.discourse.group/t/quanticstci-package/1641/5 "2024-04-19T10:07:28Z")
The reason is that the by using contract(Psi) I could not obtain the whole ground state wavefunction for the systems with L\>12. The problem is to calculate the following: ![Снимок экрана 2024-04-19 в 13.01.48](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/15205487ef00e294519f10c5a97a65749a9ed199.png) I am looking for an algorithm (like tensor cross interpolation) with already implemented code to solve the problem. ---
**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\ **Post date:** [April 19, 2024, 3:02pm UTC](https://itensor.discourse.group/t/quanticstci-package/1641/6 "2024-04-19T15:02:54Z")
I see. So by “obtain” you mean “access the individual amplitudes of the ground state in a given basis”. I thought by obtain you meant obtaining an MPS representation of the ground state. So yes, I do think TCI could be helpful for computing Sq. Here are the steps I would do: 1. use DMRG to find the ground state as an MPS 2. using the following code: [https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl](https://gitlab.com/tensors4fields/TensorCrossInterpolation.jl) 3. create a function which obtains individual amplitudes of your ground state from the MPS individually, using a pattern similar to [the one in this code example](https://itensor.github.io/ITensors.jl/dev/examples/MPSandMPO.html#Obtaining-Elements-of-a-Tensor-Represented-by-an-MPS) where the “el” array would be the inputs to the function called by the TCI code 4. before returning the amplitude a, compute |a|^2 and return that from the function instead 5. if all goes well, you will now have an MPS which represents |\psi(s)|^2. 6. now you can use the `inner` function from ITensor to contract this MPS with itself to obtain the result \sum\_s |\psi(s)|^2 |\psi(s)|^2 = \sum\_s |\psi(s)|^4 and finally take the log of this number If that works, it would be a very neat and interesting application of TCI! ---
**Author:** ![Faridun](https://avatars.discourse-cdn.com/v4/letter/f/45deac/32.png) [@Faridun](https://itensor.discourse.group/u/Faridun)\ **Post date:** [April 23, 2024, 6:37pm UTC](https://itensor.discourse.group/t/quanticstci-package/1641/7 "2024-04-23T18:37:23Z")
Dear Miles, Thank you for your reply. I would like to ask you about the step 3. Which function in the TCI code should I use to obtain individual amplitudes of your ground state from the MPS? I have found the `evaluate()` function and when I try to use this function with my MPS obtained from ITensors, it gives an error: ```julia import TensorCrossInterpolation as TCI using ITensors N = 10 s = siteinds(2, N) chi = 4 psi = randomMPS(s; linkdims=chi) index1 = Index(2, "index1") index2 = Index(2, "index2") index3 = Index(2, "index3") index4 = Index(2, "index4") index5 = Index(2, "index5") index6 = Index(2, "index6") index7 = Index(2, "index7") index8 = Index(2, "index8") index9 = Index(2, "index9") index10 = Index(2, "index10") indexspecs = [(index1, 1), (index2, 2), (index3, 1), (index4, 1), (index5, 2), (index6, 1), (index7, 2), (index8, 2), (index9, 2), (index10, 1)] # el = [1,2,1,1,2,1,2,2,2,1] as in an example in ITensor state = TCI.evaluate(psi, indexspecs) MethodError: no method matching evaluate(::MPS, ::Vector{Tuple{Index{Int64}, Int64}}) ``` Is it correct to use MPS obtained by using ITensors in the TCI code? Also, I have tried to put `el = [1,2,1,1,2,1,2,2,2,1]` to `evaluate(psi, el)` but the situation has not changed. Thank you so much for your time. Faridun