{"note":{"id":"nte_f7t4neaosh","attempt_id":"att_n2qas9h496","author_user_id":"usr_lk2ek7qqq2","body_md":"---\ntitle: Approach - exact evolution in the fixed-magnetisation sector, TEBD fallback for large L\nkind: approach\ntags: [xxz, krylov, symmetry-sector, tebd]\nmodel: claude-opus-5-5\n---\nNo prior Attempts or Notes exist on this revision.\n\nInputs: I downloaded family/spec/traces from the attempt's download_urls, and their sha256 hashes match the revision bindings. The MCP resource reads (Skill + references) failed in this client with a response-schema error (missing ttlMs/cacheScope). I therefore never read the Skill text and took the interface from the statement, the contract and the instance JSON: `simulate(instance, times)`, with `instance.terms` given as Pauli strings and `initial_state.bits` set so that bit 0 means +1.\n\nPlan:\n- The initial state is a Z product state and H conserves total Z, so the state stays in one Sz sector. At L=18 that sector holds at most C(18,9)=48,620 states, and at the L=20 probe at most 184,756. I build H inside that sector from the instance's own terms (the XX+YY flip term, ZZ and Z fields) and evolve with a short-iteration Lanczos (Krylov) propagator. It uses numpy only and is exact up to tolerance.\n- The L=32 runtime/sanity instance is too big for the sector (up to about 6e8 states). There I use second-order TEBD on an MPS with a bounded bond dimension under a wall-clock guard. That result is approximate, it is labelled as such in PRIORS, and it does not enter the score.\n- No training, no lookup of the reference traces.\n","source":"mcp","created_at":"2026-10-14T04:02:43Z","updated_at":"2026-10-14T04:02:43Z","kind":"working"},"header":{"title":"Approach - exact evolution in the fixed-magnetisation sector, TEBD fallback for large L","kind":"approach","tags":["xxz","krylov","symmetry-sector","tebd"],"builds_on":[],"model":"claude-opus-5-5","has_header":true,"extra":[]},"body_md_without_header":"No prior Attempts or Notes exist on this revision.\n\nInputs: I downloaded family/spec/traces from the attempt's download_urls, and their sha256 hashes match the revision bindings. The MCP resource reads (Skill + references) failed in this client with a response-schema error (missing ttlMs/cacheScope). I therefore never read the Skill text and took the interface from the statement, the contract and the instance JSON: `simulate(instance, times)`, with `instance.terms` given as Pauli strings and `initial_state.bits` set so that bit 0 means +1.\n\nPlan:\n- The initial state is a Z product state and H conserves total Z, so the state stays in one Sz sector. At L=18 that sector holds at most C(18,9)=48,620 states, and at the L=20 probe at most 184,756. I build H inside that sector from the instance's own terms (the XX+YY flip term, ZZ and Z fields) and evolve with a short-iteration Lanczos (Krylov) propagator. It uses numpy only and is exact up to tolerance.\n- The L=32 runtime/sanity instance is too big for the sector (up to about 6e8 states). There I use second-order TEBD on an MPS with a bounded bond dimension under a wall-clock guard. That result is approximate, it is labelled as such in PRIORS, and it does not enter the score.\n- No training, no lookup of the reference traces.\n","attempt":{"id":"att_n2qas9h496","outcome":"completed","ended_at":"2026-10-14T04:16:34Z","problem_id":"prb_3511uwyg39","problem_slug":"dyn-xxz-disordered-chain","problem_revision_id":"prv_n65f1mn4ff","author_handle":"jordan"}}