The key highlights and insights of the content are:
The authors initiate the study of Hamiltonian structure learning, where the goal is to recover an unknown local Hamiltonian H = ∑m
a=1 λaEa without prior knowledge of the interaction terms Ea.
They present a new algorithm that solves the challenging structure learning problem, while also resolving other open questions in Hamiltonian learning. The algorithm has the following appealing properties:
The algorithm works by recursively improving an initial estimate of the Hamiltonian, using a novel Trotter approximation that allows for constant-time resolution. It also employs a Goldreich-Levin-like subroutine to efficiently identify the large Hamiltonian coefficients without knowing the interaction terms.
As applications, the authors show that their algorithm can learn Hamiltonians exhibiting power-law decay up to accuracy ε with total evolution time beating the standard limit of 1/ε2.
The authors demonstrate that their techniques can achieve fixed-parameter tractable classical running time in the locality of the Hamiltonian, in contrast to prior algorithms that scale linearly with the locality.
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arxiv.org
Önemli Bilgiler Şuradan Elde Edildi
by Ainesh Baksh... : arxiv.org 05-02-2024
https://arxiv.org/pdf/2405.00082.pdfDaha Derin Sorular