Simple algorithms to test and learn local Hamiltonians

2024/04/09 by Francisco Escudero Gutiérrez, Gutiérrez, Francisco Escudero · 4 citations
Engineering · #Computational Complexity (cs.CC) #Control and Stability of Dynamical Systems #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2404.06282

openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We consider the problems of testing and learning an n-qubit k-local Hamiltonian from queries to its evolution operator with respect the 2-norm of the Pauli spectrum, or equivalently, the normalized Frobenius norm. For testing whether a Hamiltonian is ε₁-close to k-local or ε₂-far from k-local, we show that O(1/(ε₂-ε₁)⁸) queries suffice. This solves two questions posed in a recent work by Bluhm, Caro and Oufkir. For learning up to error ε, we show that exp(O(k²+klog(1/ε))) queries suffice. Our proofs are simple, concise and based on Pauli-analytic techniques.

Cited by

• Optimal certification of constant-local Hamiltonians
• Efficiently learning non-Markovian noise in many-body quantum simulators
• On Estimating the Quantum Tsallis Relative Entropy
• Hamiltonian Locality Testing via Trotterized Postselection

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