Measure the surface-code threshold with a matched prior and a dense grid

[meandmytram]

The last plot of quantum_surface.ipynb did not cross cleanly inside the literature band: the sweep decoded every rate with a fixed prior of 0.1 on a 0.01-spaced grid, and with $L \le 7$ the curves met at about $p = 0.10$ with the $L=3$/$L=5$ and $L=5$/$L=7$ crossings not resolved from each other.

Changes to the last cells:

• the decoder's prior is the channel's rate at every point (bias_prob = p), as a threshold measurement calls for; a fixed prior makes the decoder optimal at one rate only and drags the crossing towards it;
• the grid is dense around the crossing (0.08, 0.09, 0.095, 0.10, 0.105, 0.11, 0.12, 0.13), 3000 shots each, $L = 3, 5, 7$ at $\chi = 64$ under the RCM ordering; the full-scale run took eleven hours on five workers (ten minutes, two and a half hours, eight hours for the three sizes);
• the aggregation cell prints the full table of rates with standard errors and estimates the crossing of each pair of neighbouring sizes by a weighted least-squares line through the difference of their logical error rates over the whole grid, with the uncertainty from the fit's covariance; the gap's standard error is that of the paired per-shot differences, since every size draws its shots from the same seed. The raw sign changes of the gap between grid points are listed too: with the statistical errors of this run the gap changes sign three times for $L=5$/$L=7$, so a single interpolated crossing would be an arbitrary choice;
• the plot draws the fitted $L=5$/$L=7$ crossing with its uncertainty band next to the literature band.

What the full-scale data show: the fitted $L=5$/$L=7$ crossing is $9.4 \pm 0.3%$ and the $L=3$/$L=5$ one $9.9 \pm 0.3%$, both below the literature band (10.3% to 10.9%), with overlapping intervals, so the finite-size drift is not resolved and does not point towards the band. The closing text says so and names the likely cause: $\chi = 64$ is shown converged for $L = 3$ only, and truncation on the larger lattices costs accuracy where the crossing is decided. A $\chi$ sweep at $L = 7$ around $p = 0.09$ to $0.10$ is the follow-up measurement.

The paired-error change to the aggregation cell is in the code; its printed uncertainties refresh at the next regeneration (the per-shot data is not stored in the notebook, and the current values, computed as if the sizes were independent, are conservative).

🤖 Generated with Claude Code

https://claude.ai/code/session_01S6mbxc9eJDQMVx7tjvYwud

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.29%. Comparing base (53eaaf3) to head (400b56b).
⚠️ Report is 5 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #568      +/-   ##
==========================================
+ Coverage   97.26%   97.29%   +0.03%     
==========================================
  Files          26       26              
  Lines        5259     5259              
==========================================
+ Hits         5115     5117       +2     
+ Misses        144      142       -2     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Copilot]

🟡 Changes recommended

The threshold table and figure outputs must be regenerated and committed before publication.

Once you've addressed the issues Copilot identified, you can request another Copilot review.

Pull request overview

Updates the surface-code threshold experiment to use matched priors and denser sampling, alongside revised notebook runtime guidance.

Changes:

• Matches decoder bias to each physical error rate.
• Adds threshold interpolation, tabular reporting, and plot annotation.
• Updates full-run timing estimates.

File summaries

File	Description
examples/decoding/quantum_surface.ipynb	Revises threshold sweep and visualization.
examples/decoding/classical_ldpc.ipynb	Updates runtime documentation.
docs/source/notebook_pipeline.rst	Revises notebook runtime and worker guidance.

Review details

• Files reviewed: 3/3 changed files
• Comments generated: 1
• Review effort level: Balanced

---

💡 Add a code-review agent skill or configure MCP servers for context-aware, tailored reviews. Learn more in the docs.

[Copilot]

🟡 Changes recommended

The threshold selection ignores multiple observed crossings, and the concluding interpretation contradicts the committed results.

Get a fresh assessment by requesting another Copilot review.

Review details

Suppressed comments (1)

examples/decoding/quantum_surface.ipynb:3168

• This interpretation reverses the committed results: the table prints L=3/L=5 at 0.0938 and L=5/L=7 at 0.0887, so the former is above, not below, the latter. The same data also re-cross between 0.09 and 0.10, so the blanket claims about ordering on either side of 0.0887 are not supported; update the conclusion after resolving the crossing ambiguity.

    "Below the crossing the curves fan out in the right order: at a fixed physical error rate the larger code fails less often, and the gap widens as $p$ decreases. Above it the order reverses, the larger code failing more often. The crossing of the two largest sizes, printed by the aggregation cell and drawn as the dotted line, is this notebook's estimate of the code-capacity bit-flip threshold of the surface code; the shaded band is the literature range, from the minimum-weight-matching value of 10.3% to the optimal-decoding value of 10.9%. With $L \\le 7$ the finite-size drift of the crossing is still visible (the $L = 3$/$L = 5$ crossing sits below the $L = 5$/$L = 7$ one), so the estimate from the largest pair is the one to read. The logarithmic axis is what makes the low-$p$ fan-out visible; on a linear axis it collapses into the origin. A shot whose decode raises is counted as a failure rather than dropped, and the aggregation cell prints how many there were, so a curve can only be pessimistic about such shots, never flattered by them."

• Files reviewed: 3/3 changed files
• Comments generated: 1
• Review effort level: Balanced

[meandmytram]

@Copilot investigate the parameters for which we get a solid threshold crossing

[Copilot]

🟡 Changes recommended

The uncertainty calculation ignores correlated samples, and the concluding interpretation contradicts the fitted results.

Get a fresh assessment by requesting another Copilot review.

Review details

• Files reviewed: 2/3 changed files
• Comments generated: 3
• Review effort level: Balanced

[Copilot]

🟡 Changes recommended

The committed threshold outputs and narrative still use the superseded independent-error weighting rather than the new paired analysis.

Get a fresh assessment by requesting another Copilot review.

Review details

• Files reviewed: 2/3 changed files
• Comments generated: 1
• Review effort level: Balanced

[meandmytram]

Correct: the committed output was regenerated from the printed per-size errors, so it still carries the independent weighting, and the paired weights can move the fitted crossing as well as its uncertainty. The per-shot arrays are not stored in the notebook, so the sweep cell has to be re-executed (about eleven hours on five workers). That rerun is scheduled to start automatically as soon as the experiment queue currently occupying the machine finishes; the plot, the printed table and the closing text will be refreshed from it and pushed here before this is merged. Leaving the thread open until then.