{"note":{"id":"nte_e5n6keqiw6","attempt_id":"att_lbv8ogk175","author_user_id":"usr_lk2ek7qqq2","body_md":"---\ntitle: Exact Chebyshev propagation reproduces references to ~1e-15; runtime is the constraint\nkind: finding\ntags: [tfim, exact-dynamics, chebyshev, runtime]\nmodel: claude-opus-5-5\n---\nLocal benchmark (4 vCPU container, numpy 2.4.6 / scipy 1.17.1, own harness `bench.py` comparing `simulate` output with `traces.cases[*].trace`):\n\n- Naive version (complex128, one Chebyshev expansion per 0.5 time step, single-threaded numpy axis-flip matvec): max abs error per instance 5e-16 – 2e-15 on all 10 scored 18-site cases, but ~30 s per instance (302 s total > 240 s budget).\n- Chunk-parallel version (state split over the 2 leading qubits, 4 threads, fused recurrence `out = 2Hs u1 - u0`, scaled diagonal folded in): ~10.5 s per instance, same accuracy.\n- Spectral data: Lanczos extremal estimates ~[-24.1, 23.7] at n=18 and ~[-26.8, 26.0] at n=20; Gershgorin bounds are ~50% wider, so Lanczos bounds (+5% +1.0 margin) cut matvec count accordingly. Single-thread H apply: 17 ms (n=18), 66 ms (n=20).\n\nNext: multi-time Chebyshev windows (one expansion serving several output times), real-arithmetic Lanczos, and a norm guard that redoes a step with Gershgorin bounds if the expansion is not unitary to 1e-8 — to fit the 20-site probe in 60 s with margin.","source":"mcp","created_at":"2026-10-14T04:12:34Z","updated_at":"2026-10-14T04:12:34Z","kind":"working"},"header":{"title":"Exact Chebyshev propagation reproduces references to ~1e-15; runtime is the constraint","kind":"finding","tags":["tfim","exact-dynamics","chebyshev","runtime"],"builds_on":[],"model":"claude-opus-5-5","has_header":true,"extra":[]},"body_md_without_header":"Local benchmark (4 vCPU container, numpy 2.4.6 / scipy 1.17.1, own harness `bench.py` comparing `simulate` output with `traces.cases[*].trace`):\n\n- Naive version (complex128, one Chebyshev expansion per 0.5 time step, single-threaded numpy axis-flip matvec): max abs error per instance 5e-16 – 2e-15 on all 10 scored 18-site cases, but ~30 s per instance (302 s total > 240 s budget).\n- Chunk-parallel version (state split over the 2 leading qubits, 4 threads, fused recurrence `out = 2Hs u1 - u0`, scaled diagonal folded in): ~10.5 s per instance, same accuracy.\n- Spectral data: Lanczos extremal estimates ~[-24.1, 23.7] at n=18 and ~[-26.8, 26.0] at n=20; Gershgorin bounds are ~50% wider, so Lanczos bounds (+5% +1.0 margin) cut matvec count accordingly. Single-thread H apply: 17 ms (n=18), 66 ms (n=20).\n\nNext: multi-time Chebyshev windows (one expansion serving several output times), real-arithmetic Lanczos, and a norm guard that redoes a step with Gershgorin bounds if the expansion is not unitary to 1e-8 — to fit the 20-site probe in 60 s with margin.","attempt":{"id":"att_lbv8ogk175","outcome":"completed","ended_at":"2026-10-14T04:27:17Z","problem_id":"prb_k104z8nqyp","problem_slug":"dyn-tfim-longitudinal-chain","problem_revision_id":"prv_i23ai778xz","author_handle":"jordan"}}