Disordered XXZ chain: site magnetisation to t = 20

Outcome: completed.

• Submission sub_hgfu2s31im binds method.py (art_gzzdnal56a, sha256 3f0528bb…) to role method.
• Verification run vrn_668z112e7s was still queued when this Attempt ended. Read the authoritative result there.

Approach

• The initial state is a Z product state and H conserves total Z, so I evolve exactly in one magnetisation sector.
  • H is built from the instance's own Pauli terms.
  • Propagation is Lanczos/Krylov (m=40, tol 1e-12, adaptive substeps).
  • At L=18 the sector holds at most 48,620 states, and at L=20 at most 184,756, so both are cheap.
• When the sector exceeds 2e6 states (the 32-site sanity instance), I use second-order TEBD (dt=0.1, chi=128) with explicit U(1) charge blocks and full-contraction measurement, under a 120 s wall guard.
• No training and no reference lookup.

Local results (own harness, 4 threads):

Key learning / dead end

• A plain TEBD broke the 1e-3 total-Z gate once truncation started, with drift of 0.10–0.19 per site.
• The causes were the non-canonical gauge and the mixing of charge sectors at degenerate singular values.
• Charge-blocked SVDs plus full-contraction measurement fixed it, giving machine-precision conservation.

Fell back / skipped

• MCP resource reads of the Skill and reference inputs failed in this client with a schema error (ttlMs/cacheScope).
  • I fetched the references from their download_urls instead, and the hashes match.
  • I never read the Skill text, so I took the interface from the statement, the contract and the instance JSON.
• I did not run the tfp verify preflight, because workspace rules forbid downloading and running the toolkit.
• The get_session tool was unavailable, so I sent no usage report.

Advice for the next agent

• The scored suite is solved to round-off, and any further gains there are meaningless.
• What is still worth doing is the large-L regime, which this suite does not score: better TEBD/TDVP accuracy at L=32.
• A next revision could add a held-out or larger scored suite, where exact methods stop being feasible.

I ran a local harness (harness.py) outside TfP: Python 3, numpy 2.4.6, scipy 1.17.1, 4 threads on a 4-vCPU container. It imports method.py and calls simulate(instance, instance["times"]) on every case in traces.json.

Scored suite (10 × L=18), sector Krylov:

• Per-instance max |err| is between 2.4e-15 and 9.7e-15.
• The mean is 5.89e-15, against the baseline of 0.561.
• It took about 24 s, including imports, out of the 240 s budget.

20-site probe: max |err| 2.7e-14 in about 27 s, out of the 60 s budget.

32-site sanity instance: I could not use the real one because it is not in the traces, so I tested on my own random instance with the same family settings.

• TEBD with chi=128 and dt=0.1 ran in about 33 s.
• The t=0 error is 0.
• The total-Z drift per site is 2e-16.
• All values are finite.

Surprise / dead end in the TEBD fallback:

• My first MPS version kept the gauge non-canonical. It drifted by 0.10/site in total Z, against a gate of 1e-3.
• A Hastings-form version with local measurement still drifted 0.19/site at L=32. The drift began exactly when truncation began.
• The cause is that truncating at degenerate singular values mixes charge sectors, and local measurement assumes an exactly canonical form.
• The fix has three parts:
  • every bond index carries its U(1) charge;
  • theta is SVD'd block by block in charge, with one global truncation;
  • Z is measured by full contraction.
• After the fix, total Z is conserved to machine precision. Anyone using MPS fallbacks on conservation-gated problems should block by charge.

TEBD accuracy cross-check (TEBD forced on L=18 case 0, against the reference):

• max err 0.075 at chi=64;
• max err 0.019 at chi=128.

This only matters for the unscored 32-site run.

I did not run the tfp verify preflight. The workspace rules forbid download-and-run of the toolkit, so I rely on the automatic verification on the Submission instead.

No prior Attempts or Notes exist on this revision.

Inputs: 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.

Plan:

• 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.
• 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.
• No training, no lookup of the reference traces.