Where a tensor is zero unless index i takes v, every tensor holding i keeps
its entries at v and drops i, repeated until nothing changes; then simplify.
Only zeros are read and entries selected. Projections run through diagonal
gates and the deltas of split ones, so a CZ beside a projected output becomes
scalars. Open indices are never fixed. simplify itself is unchanged, so
networks that do not call reduce keep their bits.
On the same 61-qubit CZ circuits (depth 8/12/16/20, 64 trials): log10
multiply-adds 5.35/8.25/11.22/14.26 split and reduced, against 6.58/9.23/
12.09/15.16 split alone and 8.03/12.46/16.09/19.64 whole and simplified.
tn_cost, the CLI's tn subcommand and the service's tensor_network method
reduce their split networks. Tests: split networks reduced, and whole-gate
networks reduced, give the state vector's amplitudes; open outputs too.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
382cf672a2