S-ISING: Ising Chain Trotter - Rationale

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

Overview

S-ISING applies shadows to Trotterized Ising Hamiltonian evolution (6-qubit transverse-field Ising model). Estimates energy, magnetization, and correlators from single shadow dataset, demonstrating shadows for time-evolution simulations.

Scientific Rationale

1. Hamiltonian Simulation: Ising model is canonical quantum simulation target
2. Energy + Auxiliary Observables: Estimate energy, magnetization, ZZ correlators simultaneously
3. Trotter Circuit: First-order Trotter (depth-limited) tests shadows on structured circuits
4. Phase 2 Chemistry Prep: Ising model shares structure with fermionic Hamiltonians

Expected Outcomes

• System: 6-qubit 1D Ising chain
• Observables: Energy (6 ZZ + 6 X terms), magnetization (6 Z), correlators (5 ZZ adjacent)
• Shadow Budget: 500-1000
• SSR Target: ≥ 1.3× vs. grouped measurement

Relevant Literature

• Lloyd (1996): Universal quantum simulator - Ising models
• Trotter (1959): Product formula for time evolution

Part of Phase 1 Research Plan

Purpose: Validates shadows for Hamiltonian simulation (bridge to chemistry) Timeline: Nov 2025 Priority: Medium (Phase 1 valuable for Phase 2 design)