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beam_search: stabilize tie handling and per-shot state on symmetric instances#2

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aleverrier wants to merge 5 commits intoionq-publications:mainfrom
aleverrier:codex/gross-beam-stability-fix
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beam_search: stabilize tie handling and per-shot state on symmetric instances#2
aleverrier wants to merge 5 commits intoionq-publications:mainfrom
aleverrier:codex/gross-beam-stability-fix

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This PR stabilizes beam decoding on symmetric instances (observed on Gross [[144,12,12]]).

Changes in decoder/src_cpp/beam_search.hpp:

  • replace <=0 with <0 in sign/tie checks
  • add deterministic micro-jitter (~1e-10) to initial LLRs
  • reset decode output state at start of each shot
  • add decode_calls counter used for deterministic jitter seeding

Result:

  • removes the p=0.05 syndrome-failure/non-convergence spike in our Gross-code tests.

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