MPS add a const

ITensor Julia Questions
1

Hello,

I created an MPS by
f_mps = MPS(psi, sites_full; cutoff=tol_mps, maxdim=chi_mps), and I’m wondering how to implement f_mps + a constant element wisely.

If I do f_mps + 64, it output errors as “MethodError: no method matching +(::MPS, ::Float64)
The function + exists, but no method is defined for this combination of argument types.”.

Thanks

2

It is not clear what you really want to do. Do you want to add 64 to each ITensor of the MPS? or do you want to add it to each element of the ITensor ? But in both cases I can’t see why you’d want/have to do that. Please explain better what is your aim

3

Thank you for your response. I have an MPS and aim to add 64 to each element of its full tensor. This operation is necessary for applying tensor network algorithms to solve a partial differential equation.

4

Can you write mathematically what you’re trying to do? There is an implicit basis that has to be considered when adding elements.

For example in GitHub - JoeyT1994/ITensorNumericalAnalysis.jl, there is a const_itensornetwork which returns the same value for any input (something like c \sum_r |r\rangle)

If you want to do the same in ITensorMPS, then you can do

c = 64.0
const_state = MPS(s)
for i=1:N
  const_state[i] = ITensor([1 / sqrt(2), 1 / sqrt(2)], inds(const_state[i]))
end
const_state = orthogonalize(const_state,1)
const_state *= c

or you can split up the factor within each tensor to be more numerically stable like the above code

5

If I’ve interpreted right the question, you could write a function similar to this

function add constant(psi::MPS, c::Float64)
    phi =similar(psi)
    for i in 1:length(psi)
        setstorage!(phi[i],storage(psi[i]) .+ c)
    end
    return phi
end

This function would return an MPS where the constant c is added to each element of each Tensor of the starting MPS. Note that the state on exit is not normalized

6

Thanks @VinceNeede and Ryan for your solutions.

But I do want to emphasize Ryan’s good point about adding such an elementwise constant being very dependent on what basis the MPS tensors are in. More specifically, MPS tensors are only well defined up to “gauge transformations” on the bonds and unless you are very clear about what gauge an MPS is in, adding numbers to the entries of the tensors may not give “gauge invariant” results i.e. you could essentially get sort of random results each time you run your program!

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