Obtaining elements of tensors

ITensor Julia Questions
1

Hi all,
I was going through this example code in the itensor documentation for extacting out the MPS elements.

N = 10
s = siteinds(2,N)
chi = 4
psi = random_mps(s;linkdims=chi)

# Make an array of integers of the element we
# want to obtain
el = [1,2,1,1,2,1,2,2,2,1]

V = ITensor(1.)
for j=1:N
  V *= (psi[j]*state(s[j],el[j]))
end
v = scalar(V)

# v is the element we wanted to obtain:
@show v

If the MPS had a quantum number description added to it, would it suffice to adjust the line in the for loop to

V *= (psi[j] * dag(state(s[j],el[j])))

My aim is to replace the psi by some time-evolved state and to extract out the probabilities of certain bit-string configurations. I was wondering if I am doing this correctly.

Thanks a lot!

1 Like
2

That looks right, though I didnā€™t try it, try it out and see.

1 Like
3

This seems to work. That brings me to a follow-up on this. As I mentioned in the OP, I wanted to use this to extract the probabilities for some Z-like measurements done in a custom Hilbert space. My workflow is as follows:

  1. I use sample() to obtain the configurations from a time-evolved MPS.
  2. I feed back this information into the above function and get back the probabilities.
    The problem Iā€™m running into is that this probability is of the order 10^{-24}, essentially zero. This seems weird since the sample function seems to ā€œworkā€ without throwing any errors.
    I cross-checked this with another method. Instead of using this ā€œclampingā€ method, I create an explicit MPS from the configurations and take its inner product with the time-evolved MPS. This also turns out to be of the order 10^{-24} and matches what I got from the clamping method (Iā€™m not sure if ā€˜matchesā€™ is the right term to use, since these are extremely small numbers).

I suspect this is due to the system size being very large (N = 128), which makes probabilities exponentially small. So, how reliable is this sampling, given that the numbers are very small and there may be precision issues?

Maybe itā€™s better to implement incomplete sampling (as described here: https://arxiv.org/pdf/1201.3974 Sec V) to ensure accurate results?

Any help in understanding this is appreciated. TIA!