[Pyhroff]

Summary

• Validate register dimensions before starting a simulation, preventing empty-register division by zero.
• Require an odd surface-code distance of at least 3.
• Require finite noise probabilities in [0, 1] and integer-or-None seeds.
• Add regression tests for invalid parameters and a valid deterministic register result.

Validation status

• The default branch currently has no configured CI workflow, so this PR may not receive automated checks until the existing CI-enabling PR is merged.
• Common token, private-key, and credential-assignment pattern scan found no matches.
• Changed paths are backend/qec/register.py and new backend/tests/test_register.py; these do not overlap files changed by the existing open PRs.

Per repository merge policy, leave this PR open unless all configured CI checks can be verified green.