# Robust QAOA Hardware-Like Noise Check

This report is a proxy validation step before real QPU execution.
It does not emulate a named backend. Instead, it scales final-channel and readout noise by approximate QAOA gate load.

## Setup

- graphs evaluated: 60
- candidates evaluated: 16320
- depths: p=1, p=2
- per-layer grid: 4 x 4
- profile: generic_nisq_proxy
- one-qubit error: 0.001000
- two-qubit error: 0.010000
- readout error: 0.020000
- idle error per proxy layer: 0.000500
- severity factors: 0.50, 1.00, 1.50
- mean generated noise strength: 0.132505
- max generated noise strength: 0.362695
- noise settings table: `./robust_qaoa_hardware_like_noise_settings.csv`
- figure: `./robust_qaoa_hardware_like_noise.png`

## Aggregate Metrics

| depth | selector | graphs | noisy E[C] | success | sensitivity | score |
| ---: | --- | ---: | ---: | ---: | ---: | ---: |
| 1 | robust | 60 | 7.520663 +/- 0.878930 | 0.081078 | 0.477918 +/- 0.194253 | 0.652785 |
| 1 | ideal_expected | 60 | 7.788897 +/- 0.877235 | 0.090606 | 1.336747 +/- 0.199703 | 0.648318 |
| 1 | noisy_expected | 60 | 7.788897 +/- 0.877235 | 0.090606 | 1.336747 +/- 0.199703 | 0.648318 |
| 1 | success_probability | 60 | 7.716169 +/- 0.869521 | 0.102611 | 1.203357 +/- 0.216331 | 0.649240 |
| 2 | robust | 60 | 7.521060 +/- 0.871153 | 0.093519 | 0.477760 +/- 0.198961 | 0.653333 |
| 2 | ideal_expected | 60 | 7.800961 +/- 0.864958 | 0.101552 | 1.424249 +/- 0.196612 | 0.644118 |
| 2 | noisy_expected | 60 | 7.800961 +/- 0.864958 | 0.101552 | 1.424249 +/- 0.196612 | 0.644118 |
| 2 | success_probability | 60 | 7.732580 +/- 0.857118 | 0.114097 | 1.218153 +/- 0.230683 | 0.648528 |

## p=2 Robust Minus Ideal-Expected

- noisy E[C]: `-0.279900 with 95% CI [-0.340843, -0.218958]`
- success probability: `-0.008033 with 95% CI [-0.019804, 0.003738]`
- noise sensitivity: `-0.946489 with 95% CI [-1.144908, -0.748070]`

## Interpretation

Hardware-like proxy noise increases with graph edge count and QAOA depth.
If the stability trade-off survives here, the next hardware step can stay small: p=1/p=2 on a few low-depth graphs.
This is still not real hardware evidence because it omits calibration drift, routing, crosstalk maps, pulse schedules, and queue-time backend changes.

## 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=0.024, readout=0.010), depolarizing(p=0.048, readout=0.020), depolarizing(p=0.071, readout=0.030)
- candidates evaluated: 16
- score weights: degradation=0.350, success=0.200, shot_variance=1.000, noise_sensitivity=0.350

## RA-QAOA Selection

- gammas: 0
- betas: 0.523598775598
- robust score: 0.506245
- noisy expected cut: 3.000000
- noisy expected std across noise sweep: 0.000000
- ideal expected cut: 3.000000
- degradation: 0.000000
- noise sensitivity: 0.000000
- approximation ratio: 0.500000
- success probability: 0.031250
- shot standard error: 0.013532
- dominant bitstring: 000000 (cut 0.000, p=0.015625)

## Baselines

| method | noisy E[C] | success | sensitivity | score | gammas | betas |
| --- | ---: | ---: | ---: | ---: | --- | --- |
| robust | 3.000000 | 0.031250 | 0.000000 | 0.506245 | 0 | 0.523598775598 |
| ideal_expected | 3.873375 | 0.169145 | 2.825424 | 0.502605 | 1.0471975512 | 0.523598775598 |
| noisy_expected | 3.873375 | 0.169145 | 2.825424 | 0.502605 | 1.0471975512 | 0.523598775598 |
| success_probability | 3.873375 | 0.169145 | 2.825424 | 0.502605 | 1.0471975512 | 0.523598775598 |