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S-T02: Noise-Aware GHZ with MEM - Rationale

Experiment ID: S-T02 Workstream: S (Shadows) Status: Planned (Target: Nov 2025) Phase: Phase 1 Foundation & R&D

Overview

S-T02 demonstrates noise-aware classical shadows (v1) with measurement error mitigation (MEM) on IBM quantum hardware. This experiment directly compares v0 baseline (S-T01) vs. v1 noise-aware performance to quantify variance reduction and SSR improvement from inverse channel correction.

Scientific Rationale

Why This Experiment?

  1. v1 Validation: First hardware test of noise-aware inverse channel + MEM combination
  2. Mitigation Effectiveness: Quantify 20-30% variance reduction target from mitigation
  3. SSR Improvement: Demonstrate that v1 achieves SSR ≥ 1.1× even if v0 (S-T01) fails
  4. Phase 2 Preparation: Validate mitigation stack before fermionic shadows (S-T03) and adaptive sampling (S-T04)

Why Noise-Aware Shadows?

Theory (Chen et al. 2021): - Inverse channel corrects for known noise (gate errors, T1/T2 decay) - Expected variance reduction: 20-30% for typical IBM noise levels - Enables sample complexity closer to ideal (SMOKE-SIM) performance

Connection to Larger Research Plan

Mitigation Chain: 

S-T01 (v0 baseline) ──> S-T02 (v1 + MEM) ──> Phase 2 v2/v3/v4
         │                     │                      │
         └─> SSR_v0       └─> SSR_v1          └─> Advanced mitigation
              (lower bound)      (Phase 1 target)        (Phase 2+)

Enables: S-T03 (fermionic), S-T04 (adaptive), C-T02 (LiH with v1), Phase 2 campaigns

Expected Outcomes

Metric v0 (S-T01) v1 (S-T02) Target Improvement
SSR 1.1-1.3× 1.3-1.5× +0.2×
Variance Reduction Baseline 20-30% ↓ v1 advantage
CI Coverage 80% 85-90% Tighter CIs

Relevant Literature

  • Chen et al. (2021): "Robust shadow estimation" - inverse channel theory
  • Temme et al. (2017): Measurement error mitigation (MEM) foundations
  • Kandala et al. (2019): MEM + ZNE for VQE - mitigation synergy

Next Steps After Completion

  1. Phase 1 Completion: v1 validated for cross-workstream use
  2. S-T03 Fermionic: Apply v1 to 2-RDM estimation
  3. C-T02 LiH: Use v1 for chemistry scaling experiments

Part of Phase 1 Research Plan

S-T02 completes the shadows mitigation validation: - ✅ v0 validated (S-T01) - 🔄 v1 validation (S-T02 - this experiment) - ⏳ v2/v3/v4 development (Phase 2)

Timeline: Nov 2025 Priority: HIGH (Phase 1 exit criterion)