feat(simplett): complete MPO canonical form conversions and MPS×MPO contraction

[shinaoka]

Summary

The MPO contraction algorithms (naive, zipup, fit) are already implemented, but supporting infrastructure for canonical forms is incomplete.

Current Status

Implemented:

• contract_naive ✓
• contract_zipup ✓
• contract_fit ✓
• MPO, SiteMPO, VidalMPO, InverseMPO type definitions ✓
• ContractionAlgorithm dispatch ✓

Stubs (not implemented):

• SiteMPO::move_center_left/right - only updates index, no QR decomposition
• VidalMPO::from_mpo / into_mpo - returns error
• InverseMPO::from_mpo / into_mpo - returns error
• MPS×MPO contraction

Tasks

High Priority

1. SiteMPO center movement (site_mpo.rs)

   • Implement QR decomposition in move_center_left and move_center_right
   • Required for correct contract_fit behavior

2. MPS×MPO contraction (new mps_mpo_contract.rs)

   • Contract MPS (Tensor3) with MPO (Tensor4) → MPS (Tensor3)
   • Promote MPS to 4D, contract, demote result

Medium Priority

3. VidalMPO conversions (vidal_mpo.rs)

   • from_mpo: QR canonicalization + SVD to extract singular values
   • into_mpo: Gamma × Lambda reconstruction

4. InverseMPO conversions (inverse_mpo.rs)

   • from_mpo: Convert via VidalMPO, invert singular values
   • into_mpo: Invert back and reconstruct

Reference

• Julia implementation: T4AMPOContractions.jl/src/contraction.jl
• Rust MPO module: crates/tensor4all-simplett/src/mpo/

Out of Scope

• TCI-based contraction (depends on future tensor4all-tci crate)
• Distributed/MPI contraction