Quantum Hamiltonian Certification
Abstract
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.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Quantum Information and Cryptography
Quantum Mechanics and Applications
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Publisher
- Society for Industrial and Applied Mathematics
- Pages
- 1424–1467
- Publication date
- 1 January 2026
- Language
- EN
- Document type
- Book chapter