# Robust QAOA Benchmark

This benchmark is a reproducible scaffold for RA-QAOA paper experiments.
It compares robust-score selection against ideal, noisy, and success-probability baselines.

## Setup

- graphs evaluated: 150
- candidates evaluated: 40800
- depths: p=1, p=2
- per-layer grid: 4 x 4
- noise profile: depolarizing(p=0.000, readout=0.020), depolarizing(p=0.040, readout=0.020), depolarizing(p=0.080, readout=0.020), depolarizing(p=0.160, readout=0.020)
- score weights: degradation=0.350, success=0.200, shot_variance=1.000, noise_sensitivity=0.350
- figure: `./robust_qaoa_expanded_benchmark.png`
- paired delta table: `./robust_qaoa_expanded_paired_deltas.csv`

## Aggregate Metrics

| depth | selector | graphs | noisy E[C] | ratio | success | sensitivity | shot stderr | score |
| ---: | --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| 1 | robust | 150 | 7.473259 +/- 0.520202 | 0.672190 | 0.096414 +/- 0.015816 | 0.940701 +/- 0.116235 | 0.022259 | 0.644709 |
| 1 | ideal_expected | 150 | 7.571989 +/- 0.525444 | 0.681188 | 0.093903 +/- 0.015455 | 1.223291 +/- 0.099737 | 0.027741 | 0.643228 |
| 1 | noisy_expected | 150 | 7.571989 +/- 0.525444 | 0.681188 | 0.092764 +/- 0.015313 | 1.223291 +/- 0.099737 | 0.027819 | 0.643000 |
| 1 | success_probability | 150 | 7.529282 +/- 0.522290 | 0.676995 | 0.100584 +/- 0.015600 | 1.161866 +/- 0.104756 | 0.027188 | 0.643011 |
| 2 | robust | 150 | 7.521788 +/- 0.511921 | 0.679718 | 0.124451 +/- 0.019502 | 1.078907 +/- 0.129239 | 0.022683 | 0.649509 |
| 2 | ideal_expected | 150 | 7.665358 +/- 0.517314 | 0.693633 | 0.107529 +/- 0.018255 | 1.491835 +/- 0.101414 | 0.037169 | 0.644514 |
| 2 | noisy_expected | 150 | 7.665358 +/- 0.517314 | 0.693633 | 0.107529 +/- 0.018255 | 1.491835 +/- 0.101414 | 0.036143 | 0.644515 |
| 2 | success_probability | 150 | 7.569052 +/- 0.513497 | 0.683879 | 0.126597 +/- 0.019397 | 1.259562 +/- 0.118853 | 0.035601 | 0.648340 |

## Pairwise Deltas

| depth | baseline | metric | better | mean delta | 95% CI | robust win rate |
| ---: | --- | --- | --- | ---: | ---: | ---: |
| 1 | ideal_expected | noisy_expected_cut | higher | -0.098730 | [-0.130106, -0.067354] | 0.7% |
| 1 | ideal_expected | success_probability | higher | 0.002510 | [-0.000121, 0.005142] | 19.3% |
| 1 | ideal_expected | noise_sensitivity | lower | -0.282590 | [-0.372942, -0.192238] | 32.7% |
| 1 | noisy_expected | noisy_expected_cut | higher | -0.098730 | [-0.130106, -0.067354] | 0.0% |
| 1 | noisy_expected | success_probability | higher | 0.003650 | [0.000332, 0.006967] | 20.7% |
| 1 | noisy_expected | noise_sensitivity | lower | -0.282590 | [-0.372942, -0.192238] | 32.7% |
| 1 | success_probability | noisy_expected_cut | higher | -0.056024 | [-0.088662, -0.023385] | 6.7% |
| 1 | success_probability | success_probability | higher | -0.004170 | [-0.006080, -0.002261] | 0.0% |
| 1 | success_probability | noise_sensitivity | lower | -0.221164 | [-0.310977, -0.131352] | 20.7% |
| 2 | ideal_expected | noisy_expected_cut | higher | -0.143569 | [-0.171938, -0.115201] | 10.0% |
| 2 | ideal_expected | success_probability | higher | 0.016922 | [0.011660, 0.022183] | 55.3% |
| 2 | ideal_expected | noise_sensitivity | lower | -0.412928 | [-0.494519, -0.331337] | 84.0% |
| 2 | noisy_expected | noisy_expected_cut | higher | -0.143569 | [-0.171938, -0.115201] | 0.0% |
| 2 | noisy_expected | success_probability | higher | 0.016922 | [0.011660, 0.022183] | 54.7% |
| 2 | noisy_expected | noise_sensitivity | lower | -0.412928 | [-0.494519, -0.331337] | 82.0% |
| 2 | success_probability | noisy_expected_cut | higher | -0.047264 | [-0.071888, -0.022641] | 14.0% |
| 2 | success_probability | success_probability | higher | -0.002146 | [-0.002958, -0.001334] | 0.0% |
| 2 | success_probability | noise_sensitivity | lower | -0.180655 | [-0.245976, -0.115333] | 59.3% |

## Interpretation

Use this report as evidence for the paper only after checking both mean performance and stability.
A robust selector is useful when it preserves noisy E[C] while reducing sensitivity or shot error.
If all selectors choose the same parameters, the graph suite or grid is not yet discriminative enough.

## Sample Single-Graph Report

# Robust QAOA Report: g000_n6_s101

- graph: 6 nodes, 6 edges
- depth: p=1
- exact optimum: 6.000 at 001011, 110100
- noise settings: depolarizing(p=0.000, readout=0.020), depolarizing(p=0.040, readout=0.020), depolarizing(p=0.080, readout=0.020), depolarizing(p=0.160, readout=0.020)
- candidates evaluated: 16
- score weights: degradation=0.350, success=0.200, shot_variance=1.000, noise_sensitivity=0.350

## RA-QAOA Selection

- gammas: 1.0471975512
- betas: 0.523598775598
- robust score: 0.515961
- noisy expected cut: 3.822966
- noisy expected std across noise sweep: 0.139525
- ideal expected cut: 4.078125
- degradation: 0.255159
- noise sensitivity: 2.366976
- approximation ratio: 0.637161
- success probability: 0.158824
- shot standard error: 0.015303
- dominant bitstring: 110100 (cut 6.000, p=0.079412)

## Baselines

| method | noisy E[C] | success | sensitivity | score | gammas | betas |
| --- | ---: | ---: | ---: | ---: | --- | --- |
| robust | 3.822966 | 0.158824 | 2.366976 | 0.515961 | 1.0471975512 | 0.523598775598 |
| ideal_expected | 3.822966 | 0.158824 | 2.366976 | 0.515961 | 1.0471975512 | 0.523598775598 |
| noisy_expected | 3.822966 | 0.158824 | 2.366976 | 0.515961 | 1.0471975512 | 0.523598775598 |
| success_probability | 3.822966 | 0.158824 | 2.366976 | 0.515961 | 1.0471975512 | 0.523598775598 |