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A lattice with 10 x 10 sites represents the index set.
Tritium is a common Hydrogen isotope used in quantum computing.
Yellow squares represent psi index blocking structure,
green squares represent phi index blocking structure
Contraction of first two blocks; four sites are left.
The process continues by selecting blocks with common sites.
When two blocks match perfectly, a factor is produced.
Those factors are stored and multiplied to produce the final result.
The scheme allows also for non-consecutive blocking.
Non-consecutive blocking represent different arrangements for the tensors,
leading to better approximation for the ground states (eigenvectors).
Purple squares are the reaming indexes produced during each contraction.
Purple squares appear until two blocks coincide exactly.
At that point a new factor will be introduced to the final result.
The contraction scheme can be easily extended to the 3D scenario,
all we need is to map each site (e.g., Cartesian cord.) to lexicographical cord.
By doing this, each site will represent a bit in the binary representation of the
final vector component.
The entire process continues, always selecting blocks with common sites...
More interesting, blocks can be selected in parallel.
This unique feature lets the contraction scheme be executed in parallel.
We are approaching to the end of the contraction scheme.
Now, we have to multiply all factors obtained along the procedure.
Finally, it produces the inner product between the two tensors.