Apply quantum channel to MPO

ITensor Julia Questions
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1

Hi, apologies for the spate of questions. This will hopefully be the last for a while.

My goal is to apply a quantum channel to a density matrix represented as an MPO. Now, ordinarily, I would simply use apply() here. However, in this case the number of input and output indices is different. For example, you could think of this as a (non-unitary) quantum channel that ties together 4 sites into 1. Here is my best guess for how something like that might work:

function apply_channel(ρ::MPO, Ψ::ITensor)
    ρ̃ = copy(ρ)

    # extract the common indices where we will be applying the channel 
    common_inds = findall(x -> hascommoninds(Ψ, ρ[x]), collect(1:length(ρ)))

    # Apply the channel 
    wf = ρ̃[common_inds[1]] * Ψ
    for v in common_inds[2:end]
        wf *= ρ̃[v] 
    end

    # Update the MPO
    new_data = vcat(ρ̃[1:common_inds[1]-1], wf, ρ̃[common_inds[end]+1:length(ρ̃)])
    ρ̃.data = new_data

    return ρ̃
end

I have no real reason to believe that this is wrong, save for the fact that my code as a whole is not working and I am trying to pinpoint the location of my bug. Please let me know if you have any thoughts! And thank you again for all the help.

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What is the error message you are getting?

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Hi Miles,

This part of the code does not actually throw an error message – I am just not getting the results I expect from the script as a whole, and was wondering whether that might be because I am making some mistake in applying the quantum channel to the MPO. But if this looks fine to you, then I will have to look for my bug elsewhere…

Thanks so much! (Also happy to provide more information here or via email if you think that would be helpful)

4

I see - however, I’m not sure if the code you posted has a bug or not, but the question wasn’t really specific enough for me to know what might be the issue you were asking about. If you have a more specific or narrowly tailored question, please ask, otherwise I encourage you to try out various parts of your code on small examples where you know what the correct result should be and/or print out intermediate values of your code as it is running to verify if it’s working correctly.

Best,
Miles

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