Hi Arnab, yes this is a task that MPS (and ITensor) is perfectly suited for.

The simplest way to do this is to:

1. choose a target string i1, i2, i3, that you want to compute (i.e. fix the i’s)

2. apply the X^i_n operators to the MPS psi. Since these are single-site operators they can be applied very quickly and efficiently (even in parallel if you want to go there) by just multiplying each MPS by X on its physical index. In ITensor, you obtain the X operator for that site, use the * operator to contract it with the MPS, then call `noprime`

to set the site’s prime level back to 0. Of course for sites where you act with the identity, you can just skip over such sites.

3. finally take the resulting MPS, calling it Xpsi, say, then call `inner(phi,Xpsi)`

to obtain the overlap of the modified psi with phi.

Then you can repeat this for other i-strings.

Finally, if you are planning to obtain a large number, or all amplitudes this way, there should be a way to organize them where say you reuse substrings, i.e. overlap by hand the modified psi tensors with phi tensors and then attach the next ones in both combinations and so on. It would take a bit of thought to see how advantage there would be in doing this (because ultimately you’d still have to make exponentially many such “substring partial overlap” tensors anyway).

Let me know if any of those steps aren’t clear.

Oh also we have a new framework precisely for making it easier to apply various operators to MPS, but it’s not totally well documented yet. Here is a sample code file showing it off:

https://github.com/ITensor/ITensors.jl/blob/master/examples/gate_evolution/quantum_simulator.jl

But it’s overkill just for your case of single-site operators which you can definitely do with the usual ITensor interface.

Best,

Miles