Obtaining Elements of a Tensor Represented as an MPS

A matrix product state (MPS) or tensor train (TT) is a format for representing a large tensor having N indices in terms of N smaller tensors. Given an MPS represeting a tensor @@T@@ we can obtain a particular element @@T^{s_1 s_2 s_3 \cdots s_N}@@ of that tensor using code similar to the following code below.

In this code we will obtain the element @@T^{1,2,1,1,2,1,2,2,2,1}@@ of the tensor @@T@@ which is (implicitly) defined by the MPS psi:

#include "itensor/all.h"
#include "itensor/util/print_macro.h"
using namespace itensor;

int main()
    {

    //Make a random MPS with N=10 indices (10 sites)
    //with each physical index of dimension 2
    //and each link index (bond dimension) of dimension 4
    auto N = 10;
    auto s = SiteSet(N,2);
    auto chi = 4;
    auto psi = randomMPS(s,chi);

    //Make an array of integers of the element we 
    //want to obtain
    auto el = std::vector<int>{{1,2,1,1,2,1,2,2,2,1}};

    auto T = ITensor(1.);
    for(auto j : range1(N))
        {
        T *= (psi(j)*setElt(s(j)=el[j-1]));
        }
    auto val = elt(T);

    //"val" is the element we wanted to obtain:
    Print(val);

    return 0;
    }

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