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S-T01: Extended GHZ Validation - Rationale

Experiment ID: S-T01 Workstream: S (Shadows) Status: Planned (Target: Nov 2025) Phase: Phase 1 Foundation & R&D

Overview

S-T01 extends the GHZ smoke tests (SMOKE-SIM, SMOKE-HW) to provide statistically rigorous validation of classical shadows on IBM quantum hardware. This experiment runs ≥10 independent trials with connectivity-aware circuit layouts to demonstrate SSR ≥ 1.1× and CI coverage ≥ 80% under realistic noise conditions - both critical Phase 1 exit criteria.

Scientific Rationale

Why This Experiment?

  1. Statistical Significance: Single hardware trials (SMOKE-HW) insufficient for Phase 1 gate review. Need ≥10 trials to compute SSR with confidence intervals.

  2. Phase 1 Exit Criterion: Roadmap requires "SSR ≥ 1.1× on IBM hardware" - S-T01 provides the evidence.

  3. Noise Characterization: Multiple trials quantify run-to-run variance from calibration drift, queue-dependent errors, and stochastic noise.

  4. Connectivity-Aware Validation: Test on 4-5 qubit GHZ with hardware topology constraints (not just 3-qubit linear).

  5. Baseline for v1 Comparison: S-T01 (v0 baseline) + S-T02 (v1 noise-aware) pair enables direct mitigation effectiveness measurement.

Connection to Larger Research Plan

Phase 1 Critical Path: 

SMOKE-HW ──> S-T01 (≥10 trials, connectivity-aware) ──> Phase 1 Gate Review
              │                                                │
              ├─> SSR ≥ 1.1× validation                       │
              ├─> CI coverage ≥ 80% validation                │
              └─> Enables S-T02 (v1 comparison baseline)       └─> Phase 2 Entry

Unblocks: - Phase 1 completion (provides SSR evidence) - S-T02 noise-aware comparison (needs S-T01 baseline) - Cross-workstream confidence (if shadows work for GHZ, chemistry/QAOA credible)

Expected Outcomes and Success Criteria

Primary Success Criteria

Criterion Target Rationale
SSR (mean) ≥ 1.1× Phase 1 exit requirement
SSR Stability σ_SSR < 0.3 Consistent performance
CI Coverage ≥ 80% Statistical validity
Trial Count ≥ 10 Statistical power
System Size 4-5 qubits Connectivity-aware scaling

Observable Targets

  • 4-qubit GHZ: Estimate 7 observables (4Z + 3ZZ), SSR ≥ 1.1× per trial
  • 5-qubit GHZ: Estimate 9 observables (5Z + 4ZZ), SSR ≥ 1.0× (relaxed for larger system)

Relevant Literature

  • Huang et al. (2020): Theoretical sample complexity for Pauli observables
  • Chen et al. (2021): Noise robustness of classical shadows on NISQ hardware
  • IBM Quantum Roadmap (2024): Error rates and calibration procedures for ibm_fez/torino

Next Steps After Completion

  1. S-T02 Noise-Aware: Run v1 + MEM on same backend, compare SSR improvement
  2. Phase 1 Gate Review: Submit S-T01 results as SSR ≥ 1.1× evidence
  3. Extended Workstreams: Launch O-T01, B-T01, M-T01 with validated shadow methodology

Part of Phase 1 Research Plan

S-T01 is the Phase 1 exit gate experiment for shadows workstream. Without S-T01 SSR ≥ 1.1× demonstration, Phase 1 cannot close.

Dependencies: SMOKE-HW (completed Nov 3, 2025) Blocks: Phase 1 gate review, S-T02 execution Timeline: Target completion by Nov 15, 2025