bug(itensorlike): linsolve() broken — missing IndexMapping to treetn solver

[shinaoka]

Summary

tensor4all_itensorlike::linsolve() is non-functional. All calls fail with index structure mismatch errors.

Root Cause

The high-level linsolve() wrapper calls treetn's square_linsolve() without passing IndexMapping objects. The treetn solver requires these mappings to know how MPO input/output indices correspond to MPS site indices. Without them, the MPO's output indices remain after contraction as new indices that don't match the MPS site indices.

Error Examples

• Identity operator solve: "Index count mismatch: self has 3 indices, other has 4"
• Shifted identity: "index structure mismatch between operator output (hx) and input (x)"

Workaround

Use the treetn-level API directly with SquareLinsolveUpdater::with_index_mappings().

Suggested Fix

Either:

1. Accept IndexMapping in LinsolveOptions and pass it through, or
2. Auto-infer the mapping from shared DynIndex IDs between MPO and MPS

Also add integration tests for linsolve at the itensorlike level (currently none exist).

Found by

Automated feature test (test-feature-20260327-itensorlike)