Expand TreeTN AD coverage with generic real/complex integration harness

[shinaoka]

Summary

Broaden TreeTN automatic differentiation coverage beyond the initial #373 pass by introducing a generic test harness that runs the same integration logic for both f64 and Complex64, with forward-mode and reverse-mode conventions handled explicitly.

Current Status

Merged in #373 / commit 9334934:

• TensorDynLen::backward()
• TreeTN forward/backward AD integration tests for to_dense
• forward AD tangent preservation checks for canonicalize and truncate
• finite-difference validation for the current real-valued path

That closes the original gap tracked in #362, but the current coverage is still narrow:

• tests are mostly real-only
• there is no shared generic harness for f64 / Complex64
• representative TreeTN operations such as add, evaluate, and swap_site_indices are not covered by AD integration tests
• higher-level operator/contraction paths remain untested from an AD perspective

Scope

Phase 1: Generic real/complex TreeTN AD harness

• add a shared test harness for TreeTN AD integration tests that can run for both f64 and Complex64
• encode the scalar-specific convention differences explicitly:
  • forward-mode: standard JVP on C ~= R^2
  • reverse-mode: real-valued losses only for complex tests
• avoid duplicated test logic between real and complex variants

Phase 2: Representative TreeTN operation coverage

Add AD integration coverage for representative state-space operations:

• to_dense
• canonicalize
• truncate
• add
• evaluate
• swap_site_indices
• inner where the chosen test shape makes the AD convention unambiguous

For each operation, prefer:

• forward-mode tangent-preservation or finite-difference checks
• reverse-mode gradient-propagation and finite-difference checks when the operation returns a tensor and the loss can be made real-valued

Phase 3: Follow-up algorithmic/operator coverage

Once the generic harness is in place, extend coverage to higher-level paths such as:

• apply_linear_operator
• contract_fit
• contract_zipup

This phase may be split again if any of these paths expose separate AD bugs.

Design Notes

Generic test structure

Follow the repo's generic-testing guidance from AGENTS.md:

• write test bodies once
• use thin f64 / Complex64 wrapper tests
• keep scalar-specific behavior in a small helper trait or helper functions

Complex convention

../chainrules-rs currently documents:

• forward-mode complex rules use standard JVP on C ~= R^2
• reverse-mode complex rules use conjugate-Wirtinger for real-valued losses

TreeTN integration tests should match that convention.

Backward-mode losses for complex tests

Do not backpropagate through arbitrary complex-valued losses.
Use explicitly real-valued objectives such as:

• real(inner(x, ref))
• squared residuals
• norm-like objectives

Acceptance Criteria

• a generic real/complex AD test harness exists for TreeTN integration tests
• duplicated real/complex test logic is minimized
• representative TreeTN operations listed above are covered by integration tests where applicable
• complex tests use the documented forward/reverse AD conventions consistently
• any newly exposed AD bug is fixed or split into a dedicated follow-up issue with a reproducer