S-BELL: Parallel Bell Pairs - Rationale

Experiment ID: S-BELL Workstream: S (Shadows) Status: Planned (Phase 1) Target: Nov 2025

Overview

S-BELL demonstrates classical shadows on 4-8 qubit systems with disjoint Bell pair structure. This tests multi-subsystem observable estimation (CHSH inequalities, pairwise entanglement) and validates shot-savings for parallel independent measurements.

Scientific Rationale

1. Multi-Subsystem Observables: Estimate ZZ, XX, CHSH for each pair simultaneously from single shadow dataset
2. Entanglement Validation: Verify Bell state preparation under hardware noise + MEM
3. Scaling Validation: Test 2-4 independent Bell pairs (4-8 qubits total)
4. CHSH Demonstration: Measure S > 2 (quantum advantage) with mitigated shadows

Expected Outcomes

• Observables: 3-4 pairs × 3 observables/pair (ZZ, XX, CHSH) = 9-12 terms
• Shadow Budget: 300-500 shadows for all pairs
• SSR Target: ≥ 1.2× vs. per-pair measurement
• CHSH: S > 2 for ≥1 pair (demonstrates entanglement)

Relevant Literature

• Huang et al. (2020): Multi-observable estimation from single dataset
• Bell (1964): Original CHSH inequality - quantum entanglement test

Part of Phase 1 Research Plan

Purpose: Validates shadows for multi-subsystem parallel measurements Timeline: Nov 2025 Priority: Medium (Phase 1 optional, valuable for Phase 2)