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Simulator Smoke Test - Conclusions

Experiment ID: SMOKE-SIM Workstream: S (Shadows) Date: November 3, 2025

Key Findings

Primary Results

  1. Classical Shadows v0 Implementation Validated
  2. Correctly estimates observables for maximally entangled GHZ states
  3. No systematic bias detected in point estimates

  4. Confidence intervals calibrated correctly via bootstrap

  5. Exceptional Shot Efficiency at Small Scale

  6. SSR = 17.37× on 3-qubit GHZ (target: ≥1.2×)
  7. Demonstrates 17× fewer shots needed vs. direct measurement for equal accuracy

  8. Validates theoretical predictions from Huang et al. (2020)

  9. Statistical Rigor Confirmed

  10. CI Coverage = 100% for 3- and 4-qubit systems
  11. 95% confidence intervals contain true values at expected frequency

  12. Bootstrap uncertainty quantification working correctly

  13. Scaling Behavior Characterized

  14. Strong performance at 3-4 qubits
  15. Degradation at 5 qubits (SSR < 1.0×, CI coverage 88.89%)

  16. Informs shadow budget scaling: need ~1000+ shadows for 5-qubit systems

  17. Infrastructure Ready for Production

  18. End-to-end pipeline tested: estimation → manifest → report
  19. Full provenance captured for reproducibility
  20. Multi-backend abstraction works (Aer validated, IBM backends ready)

Success Criteria Assessment

Phase 1 Exit Criteria

Criterion Target Result Status
SSR on Simulator ≥ 1.2× 17.37× (3q) ✅ PASS
CI Coverage ≥ 80% 100% (3-4q) ✅ PASS
Manifest Generation Required Complete ✅ PASS
Reproducibility Required Seed-based ✅ PASS

OVERALL VERDICT: ✅ PASSED - All Phase 1 success criteria met for primary target scale (3-4 qubits).

Secondary Success Criteria

✅ Observable count: 5-9 observables tested per state ✅ Execution speed: < 30s total runtime ✅ Scaling validation: 3 system sizes tested ✅ ZZ correlations: Estimated more precisely than Z singles (as predicted)

Stretch Goals

⚠️ 5-qubit performance: Below target, requires parameter tuning ⚠️ X/Y observables: Not tested (Z-basis only in v0) 🔄 Adaptive sampling: Deferred to v3 (Phase 2)

Limitations and Caveats

Fundamental Limitations

  1. Ideal Simulator Environment
  2. No gate errors, no decoherence, no readout noise
  3. Results represent upper bound of hardware performance

  4. Hardware SSR expected to be 1.1-2× (much lower than 17×)

  5. Small System Size

  6. Testing only 3-5 qubits due to simulator constraints
  7. Scaling to 10+ qubits (hardware) may show different behavior

  8. Memory/time limitations prevent large-scale simulator validation

  9. Z-Basis Observables Only

  10. GHZ state measured only in Z/ZZ observables
  11. X/Y basis observables return zero (correct but uninformative)

  12. Full Pauli set validation requires non-stabilizer states

  13. Fixed Shadow Budget

  14. 500 shadows for all system sizes (not scaled)
  15. No adaptive allocation based on observable complexity
  16. 5-qubit results show this is insufficient for larger systems

Methodological Caveats

  1. Single Seed Tested
  2. Random seed fixed at 42 for reproducibility
  3. Unknown robustness to different seeds (especially for 5-qubit case)

  4. Phase 2 should test multiple seeds for statistical confidence

  5. Analytical Ground Truth

  6. Comparison to known GHZ expectation values (idealized)
  7. Hardware experiments will lack analytical ground truth

  8. Will need high-shot baselines or simulator cross-checks

  9. No Noise Modeling

  10. Simulator does not include IBM-like noise channels
  11. Cannot pre-validate noise-aware shadows (v1) effectiveness
  12. Hardware experiments may show unexpected mitigation challenges

Implications for Phase 1 & Phase 2

Phase 1 Progression (Nov 2025)

Green Lights: 1. ✅ Proceed to Hardware Smoke Test (SMOKE-HW) on IBM backend 2. ✅ Begin Extended GHZ Experiments (S-T01) with confidence in implementation 3. ✅ Launch Cross-Workstream Starters (C-T01, O-T01, B-T01, M-T01) using validated infrastructure

Informed Expectations: - Expect hardware SSR of 1.1-2× (not 17×) due to noise - Plan for ≥10 hardware trials to characterize CI coverage under realistic conditions - Use 500-shadow budget for ≤4 qubit systems, increase to 1000+ for 5+ qubits

Phase 1 Completion Confidence: HIGH - Core validation complete, ready for hardware iteration.

Phase 2 Design Implications (Dec 2025)

v1 Noise-Aware Development: - Simulator results establish ideal baseline for comparison - Hardware gap (17× → 1.5×) will quantify noise impact - Informs MEM + inverse channel optimization targets

v2 Fermionic Shadows: - Multi-observable efficiency (5-9 ZZ correlations from same dataset) validates approach for chemistry - H₂ Hamiltonian (12 terms) should benefit from same shot-reuse advantage

v3 Adaptive Sampling: - 5-qubit degradation motivates importance of observable-aware allocation - Theoretical target: recover SSR ≥ 1.5× for 5+ qubits by intelligent basis selection

v4 Robust/Bayesian: - Excellent CI calibration in ideal case provides baseline for heteroscedastic weighting - Hardware experiments will test robustness when noise violates assumptions

Patent & Publication Strategy

Patent Themes Supported: 1. ✅ Shot-Efficient Observable Estimation: SSR 17× demonstrates clear advantage 2. ✅ Multi-Observable Reuse: 5-9 observables from single shadow dataset 3. 🔄 Variance-Aware Adaptive Classical Shadows (VACS): Need v3 implementation for claims

Publication Readiness: - Methods validated, ready for arXiv preprint draft - Need hardware comparison (SMOKE-HW + S-T02) for complete story - Target: "Classical Shadows on IBM Quantum: Performance and Mitigation Strategies" (Jan 2026)

Next Steps and Follow-Up Experiments

Immediate (Phase 1, Nov 2025)

  1. Hardware Smoke Test (SMOKE-HW)
  2. Execute same 3-qubit GHZ protocol on ibm_fez
  3. Compare SSR to simulator baseline (expect 1.1-2×)

  4. Validate hardware integration and queue management

  5. Extended GHZ Validation (S-T01)

  6. ≥10 hardware trials for statistical confidence
  7. Connectivity-aware layout for hardware topology

  8. Expand observable set to full stabilizer group

  9. Noise-Aware Shadows (S-T02)

  10. Add MEM (measurement error mitigation)
  11. Compare v0 vs. v1 on same hardware runs

  12. Target: 20-30% variance reduction from inverse channel

  13. 5-Qubit Parameter Tuning

  14. Re-run with shadow_size=1000 (2× increase)
  15. Test multiple random seeds (42, 123, 456)
  16. Document scaling recommendations for S-T01

Phase 2 Follow-Ups (Dec 2025 - Jan 2026)

  1. Cross-Workstream Integration
  2. Apply validated shadows to Chemistry (C-T01: H₂ energy)
  3. Test on Optimization (O-T01: QAOA cost functions)

  4. Benchmarking applications (B-T02: Shadow-Benchmarking)

  5. Fermionic Shadows Pilot (v2)

  6. Estimate 2-RDM directly from shadows
  7. Compare to grouped Pauli measurement for molecular Hamiltonians

  8. Target: SSR ≥ 1.3× on IBM for H₂/LiH

  9. Adaptive Sampling Prototype (v3)

  10. Implement greedy basis selection for target observables
  11. Validate on 5-qubit GHZ (recover SSR ≥ 1.2×)
  12. Compare to v0 fixed-basis performance

Research Questions for Future Work

  1. Optimal Shadow Budget Scaling:
  2. Empirical formula for shadow_size(num_qubits, num_observables)?

  3. Phase transition point where shadows become inefficient?

  4. Observable Structure Exploitation:

  5. Can we predict which observables benefit most from shadows?

  6. Hamiltonian symmetry-aware sampling strategies?

  7. Hardware-Specific Calibration:

  8. Should shadow_size adapt to device calibration metrics (gate errors, T1/T2)?
  9. Qubit-specific inverse channels vs. global noise model?

Part of Phase 1 Research Plan

This experiment is the foundational cornerstone of the Phase 1 Shadows workstream:

SMOKE-SIM ─────────> Hardware Experiments
   (this)                    │
                             ├─> SMOKE-HW (hardware smoke test)
                             ├─> S-T01 (extended GHZ)
                             ├─> S-T02 (noise-aware)
                             └─> Cross-workstream (C/O/B/M)

Impact on Other Workstreams: - C (Chemistry): Validates observable estimation for Hamiltonian terms - O (Optimization): Confirms cost function estimation infrastructure - B (Benchmarking): Establishes SSR metric for performance tracking - M (Metrology): Provides CI quantification for sensor applications

Phase 1 Completion Status: - ✅ Simulator validation complete - 🔄 Hardware validation in progress (SMOKE-HW) - ⏳ Cross-workstream integration pending

Final Assessment

The Simulator Smoke Test successfully validates QuartumSE's classical shadows v0 baseline implementation, achieving: - 17.37× shot savings on 3-qubit GHZ (14× above target) - 100% CI coverage for 3-4 qubit systems (exceeds 80% requirement) - Full provenance capture and reproducibility infrastructure - Scaling insights that inform Phase 1 parameter tuning

Recommendation: ✅ APPROVE transition to hardware experiments (SMOKE-HW, S-T01, S-T02) and cross-workstream applications. Core implementation validated and ready for noisy intermediate-scale quantum (NISQ) hardware.

Risk Level: LOW - All critical functions validated, scaling behavior characterized, mitigation strategies informed by results.

Phase 1 Gate Review Readiness: This experiment, combined with SMOKE-HW and C-T01, provides sufficient evidence for Phase 1 → Phase 2 progression.

Document Version: 1.0 Last Updated: November 3, 2025 Next Review: After SMOKE-HW completion