Quantum Hamiltonian Certification
Minbo Gao, Zhengfeng Ji, Qisheng Wang, Wenjun Yu, and Qi Zhao

TL;DR
This paper introduces an optimal, efficient framework for quantum Hamiltonian certification that surpasses previous methods in certain norms and is practical for near-term quantum devices.
Contribution
It presents a direct, resource-efficient certification method achieving optimal time complexity and extending to various norms, with proven lower bounds and a practical ancilla-free approach.
Findings
Achieves optimal total evolution time for certification under Frobenius norm.
Extends certification to all Pauli and Schatten p-norms with one-sided error.
Provides lower bounds and shows Schatten infinity-norm certification is coQMA-hard.
Abstract
We formalize and study the Hamiltonian certification problem. Given access to for an unknown Hamiltonian , the goal of the problem is to determine whether is -close to or -far from a target Hamiltonian . While Hamiltonian learning methods have been extensively studied, they often require restrictive assumptions and suffer from inefficiencies when adapted for certification tasks. This work introduces a direct and efficient framework for Hamiltonian certification. Our approach achieves \textit{optimal} total evolution time for certification under the normalized Frobenius norm, without prior structural assumptions. This approach also extends to certify Hamiltonians with respect to all Pauli norms and normalized Schatten -norms for in the one-sided error setting…
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