M-T01: GHZ Phase Sensing - Rationale

Experiment ID: M-T01 Workstream: M (Metrology) Status: Planned (Phase 1) Target: Nov 2025

Overview

M-T01 demonstrates classical shadows for quantum sensing/metrology applications. Uses GHZ(3-4) states as variational sensor probes to estimate encoded Z-phase parameter, testing shadow-based readout for metrology tasks.

Scientific Rationale

1. Quantum Metrology Application: GHZ states provide Heisenberg-limited phase sensing
2. Shadow-Based Readout: Estimate phase from optimal observables using shadows
3. Uncertainty Quantification: CI widths reflect sensing precision
4. ZNE Integration: Test zero-noise extrapolation (ZNE) for readout bias correction

Why Shadows for Metrology?

Challenge: Quantum sensors require precise expectation value estimation Opportunity: Shadows provide: - Multi-observable estimation (optimally-weighted phase estimator) - Tight confidence intervals (uncertainty quantification) - Shot-efficient readout (more sensing iterations per shot budget)

Expected Outcomes

• System: GHZ(3-4) with Z-phase encoding
• Observables: Optimal linear combination of Z/ZZ terms for phase estimation
• CI Coverage: ≥ 80% on simulator, ≥ 70% on hardware (with noise)
• ZNE Integration: Demonstrate readout bias correction (Phase 2 preview)

Relevant Literature

• Giovannetti et al. (2004): Quantum metrology - Heisenberg limit
• Pezzè & Smerzi (2014): Entanglement-enhanced sensing with GHZ states
• Aaronson et al. (2018): Shadow tomography for quantum sensing

Part of Phase 1 Research Plan

Purpose: Extends shadows to metrology workstream Timeline: Nov 2025 Priority: LOW (Phase 1 optional, exploratory for Phase 2)