Simple algorithms to test and learn local Hamiltonians

• URL: http://arxiv.org/abs/2404.06282v1
• Date: Tue, 9 Apr 2024 13:08:28 GMT
• Title: Simple algorithms to test and learn local Hamiltonians
• Authors: Francisco Escudero Gutiérrez,
• Abstract summary: We consider the problems of testing and learning an $n$-qubit $k$-local Hamiltonian from queries to its evolution operator. For learning up to error $epsilon$, we show that $exp(O(k2+klog(1/epsilon))$ queries suffice.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\epsilon_1$-close to $k$-local or $\epsilon_2$-far from $k$-local, we show that $O(1/(\epsilon_2-\epsilon_1)^{8})$ queries suffice. This solves two questions posed in a recent work by Bluhm, Caro and Oufkir. For learning up to error $\epsilon$, we show that $\exp(O(k^2+k\log(1/\epsilon)))$ queries suffice. Our proofs are simple, concise and based on Pauli-analytic techniques.

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