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S-T01: Extended GHZ Validation - Setup & Methods

Experiment ID: S-T01 Status: [PLANNED] Executable: C:\Users\User\Desktop\Projects\QuartumSE\experiments\shadows\S_T01_ghz_baseline.py

Circuit Description

Connectivity-Aware GHZ (4-5 Qubits)

4-Qubit GHZ (Primary Target): 

Target Qubits: Select based on ibm_fez topology (linear or star)
Depth: 4 (1H + 3CX)
Observables: 7 (4×Z + 3×ZZ)

5-Qubit GHZ (Stretch Goal): 

Target Qubits: Select 5 connected qubits with best T1/T2/readout
Depth: 5 (1H + 4CX)
Observables: 9 (5×Z + 4×ZZ)

Backend Configuration

  • Primary: ibm:ibm_fez (156q, typical queue < 200)
  • Backup: ibm:ibm_marrakesh (156q)
  • Calibration: Refresh if > 12 hours old

Classical Shadows Configuration

v0 Baseline (No Mitigation)

shadow_config = ShadowConfig(
    shadow_size=500,              # 5× SMOKE-HW budget
    random_seed=[42, 123, 456, ...],  # Different per trial
    confidence_level=0.95,
    version=ShadowVersion.V0_BASELINE,
    apply_inverse_channel=False
)

Trial Structure: - Trials: ≥10 independent runs - Seeds: Unique per trial (42, 123, 456, 789, 1011, 1213, 1415, 1617, 1819, 2021) - Shadow Size: 500 per trial

Baseline Comparison

Direct Measurement: - 1000 shots per observable (7-9 observables) - Run once alongside S-T01 trials - Use for SSR calculation: SSR = (baseline_shots × baseline_error) / (shadow_shots × shadow_error)

Execution Workflow

# Execute ≥10 trials with different seeds
for seed in 42 123 456 789 1011 1213 1415 1617 1819 2021; do
  python experiments/shadows/S_T01_ghz_baseline.py \
    --backend ibm:ibm_fez \
    --variant st01 \
    --shadow-size 500 \
    --seed $seed \
    --data-dir ./data
done

# Aggregate results
python experiments/shadows/analyze_ghz_trials.py \
  --experiment-id s-t01 \
  --trials 10

Data Storage

  • Manifests: data/manifests/s-t01-trial-{01-10}-{experiment_id}.json
  • Shot Data: data/shots/s-t01-trial-{01-10}-{experiment_id}.parquet
  • Aggregated Results: results/s-t01-summary.json

Validation Checks

  1. SSR per Trial: Compute for each trial independently
  2. SSR Aggregate: Mean ± std across all trials
  3. CI Coverage: Fraction of observables within 95% CI
  4. Pass/Fail: SSR_mean ≥ 1.1× AND CI_coverage ≥ 80%

Expected Results

4-Qubit GHZ: - SSR (per trial): 1.1-1.5× - SSR (mean ± std): 1.3 ± 0.2× - CI Coverage: 80-90%

5-Qubit GHZ: - SSR (per trial): 1.0-1.3× - SSR (mean ± std): 1.15 ± 0.25× - CI Coverage: 75-85%

notebooks/experiments/shadows/s-t01-analysis.ipynb [TBD]

Next Experiments

  • S-T02: v1 noise-aware with MEM (uses S-T01 as baseline)
  • S-BELL: Parallel Bell pairs (uses S-T01 methodology)