Quantum Annealing — Adiabatic Gap & Schedule
Transverse-field Ising model: energy spectrum, gap closing, annealing schedules
Model Parameters
N spins =
6
Ising coupling J =
1.00
Final field h_z =
0.20
Schedule type:
Linear
0=Linear, 1=Quadratic, 2=Roland-Cerf
Current s =
0.50
Spectral Analysis
Ground energy E₀
--
First excited E₁
--
Gap Δ(s)
--
Min gap (s*)
--
QA runtime T*
--
Adiabatic theorem
: T* ∝ 1/Δ_min²
H(s) = -(1-s)Σσˣᵢ - s(JΣσᶻᵢσᶻᵢ₊₁ + hΣσᶻᵢ)
Gap closes at phase transition → exponential runtime
Roland-Cerf
schedule: optimal for Grover (polynomial gap)