Fix TypeError on non-spin-symmetric hamiltonians in low_rank trotter decomposition

[rosspeili]

Fixes #1105

Summary

simulate_trotter with algorithm=LOW_RANK raised a TypeError: Invalid two-body coefficient tensor specification. when given a non-spin-symmetric Hamiltonian (eg. spin-exchange operator). The error gave no indication of the actual requirement, making it a bit difficult to diagnose.

Root cause

get_chemist_two_body_coefficients silently assumed spin-symmetry when spin_basis=True, extracting only the αα→ββ block of the two-body tensor without validating the assumption. For spin-exchange Hamiltonians this block is asymmetric when reshaped, causing the downstream symmetry check in low_rank_two_body_decomposition to fail, but with a TypeError rather than a ValueError, and with no detailed info.

Changes

• circuits/low_rank.py: adds an explicit spin-symmetry check in get_chemist_two_body_coefficients before the spin downfolding. If the extracted spatial-orbital block is not symmetric when reshaped, a ValueError is raised with a clear message explaining the requirement and suggesting spin_basis=False as an alt. The downstream check in low_rank_two_body_decomposition is also changed from TypeError to ValueError for correctness.

• circuits/trotter/algorithms/low_rank.py: documents the spin-symmetry requirement in the LowRankTrotterAlgorithm class docstring.

• circuits/low_rank_test.py: updates the existing assertRaises(TypeError) assertion to assertRaises(ValueError) and adds new SpinExchangeTest class covering: spin-exchange input (must raise ValueError with informative message), and spin-symmetric input (must succeed).

• circuits/trotter/simulate_trotter_test.py: adds an integration-level test that the full simulate_trotter + LOW_RANK path raises ValueError for a spin-exchange Hamiltonian.

Testing

All existing tests pass and new tests verified against the exact reproducer from the original issue.

[gemini-code-assist]

Code Review

This pull request introduces explicit spin-symmetry validation for low-rank decompositions. Key changes include updating get_chemist_two_body_coefficients and low_rank_two_body_decomposition to validate that input tensors are spin-symmetric and real, raising descriptive ValueError exceptions when these conditions are not met. The PR also updates relevant docstrings and adds comprehensive test cases for spin-exchange Hamiltonians. Feedback focuses on improving the numerical stability of symmetry checks by using numpy.amax instead of numpy.sum to avoid false positives in large systems.