Quantum Hamiltonian Certification
Minbo Gao, Zhengfeng Ji, Qisheng Wang, Wenjun Yu, Qi Zhao · Society for Industrial and Applied Mathematics eBooks · 2026
We formalize and study the Hamiltonian certification problem, a fundamental task in quantum physics, crucial for verifying the accuracy of quantum simulations and quantum-enhanced technologies. Given access to \(e^{-iHt}\) for an unknown Hamiltonian \(H\), the goal of the problem is to determine whether \(H\) is \(\varepsilon_1\)-close to or \(\varepsilon_2\)-far from a target Hamiltonian \(H_0\). While Hamiltonian learning methods have been extensively studied, they often require restrictive assumptions and suffer from inefficiencies when adapted for certification tasks.