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Phase 1 Research Plan: Foundation & R&D (Nov 2025)

Phase Duration: Now → November 30, 2025 Status: In Progress (Smoke Tests Complete, Extended Validation Pending) Last Updated: November 3, 2025

Executive Summary

Phase 1 establishes QuartumSE's foundational research program, delivering validated classical shadows implementations (v0-v1), cross-workstream starter experiments, and comprehensive provenance infrastructure. The phase targets SSR ≥ 1.2× on simulator and SSR ≥ 1.1× on IBM hardware to demonstrate shot-efficiency advantages before opening Early Access in Phase 4.

Key Milestones: - ✅ Core SDK infrastructure (estimator, shadows v0/v1, reporting) - ✅ Simulator validation (SSR 17.37× on 3-qubit GHZ) - ✅ Hardware integration (ibm_fez, 7.82s execution) - ✅ Chemistry data drop (C-T01 H₂ experiment) - ⏳ Extended hardware validation (S-T01/S-T02, target SSR ≥ 1.1×) - ⏳ Cross-workstream starters (O-T01, B-T01, M-T01)

Workstream Organization

Phase 1 research is organized into 5 parallel workstreams, each with specific experiments and exit criteria:

Workstream S (Shadows)

Goal: Validate classical shadows v0-v1 on simulator and hardware

Experiment Status Description Priority SSR Target
SMOKE-SIM ✅ Complete 3-5q GHZ on aer_simulator CRITICAL 17.37× achieved
SMOKE-HW ✅ Complete 3q GHZ on ibm_fez CRITICAL ~1.0× (prelim)
S-T01 📋 Planned Extended GHZ (≥10 trials, 4-5q) CRITICAL ≥ 1.1×
S-T02 📋 Planned Noise-aware GHZ with MEM (v1) CRITICAL ≥ 1.1×
S-BELL 📋 Planned Parallel Bell pairs (4-8q) MEDIUM ≥ 1.2×
S-CLIFF 📋 Planned Random Clifford (5q, ≥50 Paulis) MEDIUM ≥ 1.5×
S-ISING 📋 Planned Ising chain Trotter (6q TFIM) MEDIUM ≥ 1.3×

Exit Criteria: - ✅ SSR ≥ 1.2× on simulator (achieved: 17.37×) - ⏳ SSR ≥ 1.1× on IBM hardware (pending S-T01/S-T02) - ⏳ CI coverage ≥ 80% (pending extended validation)

Workstream C (Chemistry)

Goal: Demonstrate shadow-based Hamiltonian estimation for molecular systems

Experiment Status Description Priority Molecules
C-T01 ✅ Complete H₂@STO-3G (4q, 12 terms) CRITICAL H₂

Exit Criteria: - ✅ First chemistry data drop generated (C-T01 manifest + shot data) - ⏳ Energy accuracy 0.02-0.05 Ha (pending real Hamiltonian) - ⏳ SSR ≥ 1.1× vs. grouped Pauli (pending baseline)

Phase 2 Pipeline: - C-T02: LiH@minimal (6q, 20 terms) - C-T03: BeH₂@minimal (8q, 30-40 terms)

Workstream O (Optimization)

Goal: Validate shot-frugal QAOA using shadow-based cost estimation

Experiment Status Description Priority Graph
O-T01 📋 Planned QAOA MAX-CUT (5-node ring, p=1-2) HIGH Ring-5

Exit Criteria: - First optimization data drop (manifest + convergence data) - Optimizer steps ↓ ≥ 20% vs. standard QAOA - Solution quality ≥ 0.90 (approximation ratio)

Workstream B (Benchmarking)

Goal: Apply shadows to device characterization (RB/XEB)

Experiment Status Description Priority Metrics
B-T01 📋 Planned RB/XEB (1-3q RB, depth-limited XEB) MEDIUM Fidelity, purity

Exit Criteria: - First benchmarking data drop - Sample efficiency ≥ 2× vs. direct fidelity estimation

Workstream M (Metrology)

Goal: Explore shadows for quantum sensing applications

Experiment Status Description Priority Application
M-T01 📋 Planned GHZ phase sensing (3-4q, Z-phase) LOW Phase estimation

Exit Criteria: - First metrology data drop (exploratory) - CI coverage ≥ 80% on simulator

Experiment Tree (Dependencies)

                                SMOKE-SIM (v0 simulator)
                                     ✅
                                     │
                                     ▼
                                SMOKE-HW (v0 hardware)
                                     ✅
                                     │
                     ┌───────────────┴────────────────┐
                     ▼                                ▼
                 S-T01 (Extended)               Cross-Workstream
            (≥10 trials, 4-5q)                  Integration
                  📋                                  │
                  │                        ┌──────────┼──────────┐
                  ▼                        ▼          ▼          ▼
             S-T02 (v1 + MEM)         C-T01      O-T01      B-T01
         (Compare v0 vs v1)             ✅         📋         📋
                  📋                     │
                  │                      │
        ┌─────────┴──────────┐          ▼
        ▼                    ▼      Phase 2
   S-BELL                S-CLIFF    C-T02 (LiH)
 (Parallel pairs)    (Random Clifford)  S-T03 (Fermionic)
       📋                   📋

    S-ISING
 (Ising Trotter)
       📋

Legend: - ✅ Complete - 📋 Planned - ⏳ In Progress

Timeline and Execution Schedule

Week 1 (Nov 3-9, 2025)

Completed: - ✅ SMOKE-SIM: Simulator validation (SSR 17.37×) - ✅ SMOKE-HW: Hardware integration (ibm_fez) - ✅ C-T01: H₂ chemistry data drop

This Week: - [ ] S-T01: Execute ≥10 trials on ibm_fez - [ ] S-T02: Run v1 + MEM comparison - [ ] C-T01 Re-Run: Real H₂ Hamiltonian + optimized ansatz

Week 2 (Nov 10-16, 2025)

  • [ ] O-T01: QAOA MAX-CUT execution
  • [ ] B-T01: RB/XEB benchmarking
  • [ ] S-BELL: Parallel Bell pairs (if time permits)

Week 3 (Nov 17-23, 2025)

  • [ ] M-T01: GHZ phase sensing (exploratory)
  • [ ] S-CLIFF: Random Clifford (optional)
  • [ ] S-ISING: Ising Trotter (optional)

Week 4 (Nov 24-30, 2025)

  • [ ] Data aggregation and analysis
  • [ ] Phase 1 completion report
  • [ ] Patent theme shortlist finalization
  • [ ] Phase 1 Gate Review preparation

Exit Criteria Mapping

Critical (Must Pass for Phase 1 Completion)

Criterion Source Experiment Target Status
SSR ≥ 1.2× (sim) SMOKE-SIM 1.2× ✅ 17.37×
SSR ≥ 1.1× (IBM) S-T01, S-T02 1.1× ⏳ Pending
CI Coverage ≥ 80% S-T01, S-T02 80% ⏳ Pending
Chemistry Data Drop C-T01 Generated ✅ Complete
Optimization Data Drop O-T01 Generated 📋 Planned
End-to-End IBM Run SMOKE-HW 1+ backend ✅ ibm_fez
Manifest Provenance All experiments Complete ✅ Validated

Optional (Valuable but Not Blocking)

Criterion Source Experiment Target Status
Benchmarking Data Drop B-T01 Generated 📋 Planned
Metrology Data Drop M-T01 Generated 📋 Planned
Multi-Observable Demos S-BELL, S-CLIFF ≥50 observables 📋 Planned
Ising Simulation S-ISING Energy variance 📋 Planned

Roadmap Milestone Connections

Phase 1 → Phase 2 Gate

Required Evidence for Phase 2 Entry:

  1. ✅ Simulator Validation: SMOKE-SIM (17.37×) exceeds threshold
  2. ⏳ Hardware Validation: S-T01/S-T02 must demonstrate SSR ≥ 1.1×
  3. ✅ Chemistry Validation: C-T01 provides first cross-workstream evidence
  4. 📋 Optimization Validation: O-T01 planned (nice-to-have)
  5. ✅ Provenance System: Manifest generation validated across experiments
  6. 📋 Patent Themes: Shortlist (VACS, Shadow-VQE, Shadow-Benchmarking) in progress

Gate Review Decision: - PASS: If S-T01 OR S-T02 achieves SSR ≥ 1.1× + C-T01 completed - CONDITIONAL PASS: If SSR = 1.0-1.1× but CI coverage ≥ 80% (can improve in Phase 2) - FAIL: If SSR < 1.0× AND CI coverage < 80% (requires rethinking)

Phase 2 Roadmap (Dec 2025)

Enabled by Phase 1: - S-T03 (Fermionic Shadows v2): Depends on C-T01 validation - S-T04 (Adaptive Shadows v3): Depends on S-T01/S-T02 performance data - C-T02 (LiH): Depends on C-T01 methodology - IBM Campaign #1: Depends on operational workflows (S-T01 multi-trial)

Cross-Experiment Integration Points

Shared Infrastructure

Calibration Workflow: - MEM confusion matrices reusable across experiments - Calibration cadence: Refresh if > 12 hours old or topology changes - Storage: validation_data/calibrations/{backend}/q{indices}/confusion_matrix.npz

Observable Estimation: - Same ShadowEstimator API across all workstreams - Observable class: Unified Pauli string representation - Bootstrap CI: 1000 samples standard across experiments

Manifest Schema: - Provenance Manifest v1: Consistent across S/C/O/B/M - Required fields: circuit, backend, shadow_config, observables, timestamps - Checksums: SHA-256 for circuit hash, confusion matrix, shot data

Methodological Synergies

S ↔ C (Shadows + Chemistry): - C-T01 uses S-validated shadows v1 + MEM - Observable structure: Chemistry Hamiltonians are multi-term Paulis (like S-T01 GHZ) - Lesson: Z-basis terms perform better than X/Y (inform C-T02 Hamiltonian design)

S ↔ O (Shadows + Optimization): - O-T01 uses S-validated shot-frugal estimation for QAOA cost function - Iterative setting: Each optimizer step is a mini-experiment - Lesson: Need fast shadows (300-500) to enable many optimizer iterations

S ↔ B (Shadows + Benchmarking): - B-T01 estimates fidelity/purity from S-validated shadow infrastructure - Lesson: Multi-observable reuse (fidelity + purity + entropy from same dataset)

Cross-Workstream Insight: If shadows work for GHZ (S-T01), they should work for: - Chemistry Hamiltonians (C-T01) ← Z-heavy observables - QAOA cost functions (O-T01) ← ZZ-based objectives - Device benchmarking (B-T01) ← State properties from shadows

Patent Strategy Integration

Phase 1 Patent Themes

1. Variance-Aware Adaptive Classical Shadows (VACS) - Evidence: S-T01/S-T02 variance characterization, observable-dependent performance - Claim: Adaptive shadow allocation based on observable complexity and device calibration - Status: Requires S-T04 (v3) implementation (Phase 2)

2. Shadow-VQE Readout Integration - Evidence: C-T01 demonstrates multi-term Hamiltonian estimation from single dataset - Claim: Shot-frugal VQE via reusable shadow datasets at each optimizer iteration - Status: C-T01 provides readout stage; full VQE loop in Phase 2 (C-T02)

3. Shadow-Benchmarking Workflow - Evidence: B-T01 fidelity/purity/entropy from single shadow dataset - Claim: Unified device characterization from shadows (vs. separate protocols) - Status: Requires B-T01 completion + B-T02 (Phase 2) for comprehensive workflow

Patent Filing Timeline

  • Nov 2025: Collect Phase 1 experimental evidence (S-T01, C-T01, O-T01)
  • Dec 2025: Draft provisional patent applications
  • Jan 2026: File provisional patents (Shadow-VQE, VACS)
  • Mar 2026: Convert to non-provisional after Phase 3 validation

Publication Strategy

Target Venues

arXiv Preprints (Jan 2026): 1. "Classical Shadows on IBM Quantum Hardware: Performance and Mitigation Strategies" - Data: SMOKE-SIM, SMOKE-HW, S-T01, S-T02 - Focus: Hardware validation, SSR measurement, v0 vs. v1 comparison

  1. "Shadow-VQE: Shot-Efficient Variational Quantum Eigensolver for Molecular Hamiltonians"
  2. Data: C-T01, C-T02 (Phase 2)
  3. Focus: Chemistry application, multi-observable reuse, baseline comparison

Journal Submissions (Mar 2026): - PRX Quantum or npj Quantum Information - Papers submitted after Phase 3 internal validation

Conference Presentations: - APS March Meeting 2026 (Abstract deadline: Nov 2025) - ACS Fall 2026 (Chemistry applications)

Risk Management

High-Risk Items

Risk: S-T01 fails to achieve SSR ≥ 1.1× on IBM hardware - Impact: Blocks Phase 1 → Phase 2 progression - Mitigation: S-T02 (v1 + MEM) may rescue; increase shadow_size to 1000; try better backend (ibm_marrakesh) - Fallback: Adjust Phase 1 exit criterion to SSR ≥ 1.0× if CI coverage ≥ 90%

Risk: ibm_fez queue saturates, delays experiments - Impact: Timeline slip (1-2 weeks) - Mitigation: Monitor queue with quartumse runtime-status; use ibm_marrakesh as backup - Fallback: Execute S-BELL/S-CLIFF/S-ISING as simulator-only (reduce to optional)

Medium-Risk Items

Risk: C-T01 baseline measurement shows SSR < 1.1× - Impact: Chemistry workstream SSR claim weakened - Mitigation: Increase shadow_size for C-T02; use fermionic shadows (v2) in Phase 2 - Fallback: Focus on multi-observable reuse advantage (vs. absolute SSR)

Risk: O-T01/B-T01/M-T01 delayed due to resource constraints - Impact: Phase 1 optional experiments incomplete - Mitigation: These are "nice-to-have" for Phase 1; can defer to Phase 2 - Fallback: Submit Phase 1 gate review with S+C evidence only

Success Metrics Dashboard

Quantitative Targets

Metric Target Current Status
SSR (Simulator) ≥ 1.2× 17.37× ✅ PASS
SSR (Hardware) ≥ 1.1× ~1.0× (prelim) ⏳ S-T01/S-T02
CI Coverage ≥ 80% 100% (sim) ⏳ Hardware
Experiments Completed ≥ 3 3 (SMOKE×2, C-T01) ✅ Met
Workstreams Active ≥ 2 2 (S, C) ✅ Met
Manifests Generated ≥ 5 30+ ✅ Exceeded
Hardware Backends ≥ 1 2 (fez, torino) ✅ Exceeded

Qualitative Targets

  • ✅ End-to-End Workflow: Validated from notebook → manifest → report
  • ✅ Provenance System: Complete circuit/backend/calibration capture
  • ✅ Reproducibility: Seed-based exact replication demonstrated
  • ⏳ Multi-Backend: ibm_fez validated, ibm_marrakesh/torino tested
  • ⏳ Cross-Workstream: S+C complete, O+B+M planned

Operational Learnings

Backend Selection Criteria

Optimal Backend (as of Nov 3, 2025): - ibm_fez (156q, 77 pending jobs) ← BEST CHOICE - Queue depth < 200 jobs - Calibration < 24 hours old - Qubits 0-3 readout error < 2.5%, T1 > 60 μs

Backup Options: - ibm_marrakesh (156q, 298 pending) - ibm_torino (133q, 485 pending)

Avoid: - ibm_brisbane (3175 pending) ← Severely congested

Execution Best Practices

  1. Pre-Flight Checks:
  2. Run quartumse runtime-status to check queue and calibration
  3. Verify target qubits have good T1/T2 and low readout error

  4. Confirm MEM calibration not stale (< 24 hours)

  5. Shot Budgeting:

  6. 100 shadows: Smoke tests only
  7. 300 shadows: Chemistry/Optimization (acceptable CI width)
  8. 500 shadows: Extended validation (S-T01, good statistical power)

  9. 1000 shadows: Large observables (S-CLIFF ≥50 Paulis)

  10. Calibration Reuse:

  11. MEM confusion matrices valid for ~24 hours
  12. Refresh if backend re-calibrated or qubit mapping changes

  13. Store with checksum for provenance

  14. Manifest Naming:

  15. Pattern: {workstream}-{experiment_id}-trial-{N}-{uuid}.json
  16. Example: s-t01-trial-03-2a89df46-3c81-4638-9ff4-2f60ecf3325d.json
  17. Enables easy aggregation and analysis

Next Steps (Immediate)

Week of Nov 3-9, 2025

  1. S-T01 Execution (CRITICAL)
  2. Run ≥10 trials with seeds 42, 123, 456, 789, 1011, 1213, 1415, 1617, 1819, 2021
  3. Shadow size: 500 per trial
  4. Backend: ibm_fez (monitor queue depth)

  5. Goal: Demonstrate SSR ≥ 1.1× with statistical significance

  6. S-T02 Execution (CRITICAL)

  7. Run v1 + MEM on same ibm_fez backend
  8. ≥3 trials for comparison to S-T01

  9. Goal: Show 20-30% variance reduction vs. v0

  10. C-T01 Validation (HIGH)

  11. Load real H₂@STO-3G Hamiltonian from qiskit-nature
  12. Optimize ansatz parameters via simulator VQE
  13. Re-run on ibm_fez with real Hamiltonian

  14. Execute grouped Pauli baseline for rigorous SSR

  15. O-T01 Preparation (MEDIUM)

  16. Finalize QAOA circuit for 5-node ring MAX-CUT
  17. Test on simulator first
  18. Schedule ibm_fez execution

Week of Nov 10-16, 2025

  1. Phase 1 Data Aggregation
  2. Collect all manifests and shot data
  3. Compute aggregate SSR statistics across experiments

  4. Prepare Phase 1 completion report

  5. Patent Theme Shortlist

  6. Draft VACS patent outline (pending S-T01 data)
  7. Draft Shadow-VQE patent outline (using C-T01 evidence)
  8. Consult IP counsel for filing strategy

Document Maintenance

Version: 1.0 Last Updated: November 3, 2025 Next Review: November 10, 2025 (after S-T01 completion) Maintained By: Research Lead Cross-References: - docs/strategy/roadmap.md - Overall project roadmap - docs/strategy/phase1_task_checklist.md - Detailed task tracking - docs/research/experiments/ - Individual experiment documentation - docs/strategy/STRATEGIC_ANALYSIS.md - Current status and next actions