Learning ManyBody Hamiltonians with HeisenbergLimited Scaling
Abstract
Learning a manybody Hamiltonian from its dynamics is a fundamental problem in physics. In this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N qubit local Hamiltonian. After a total evolution time of O (ε^{1}) , the proposed algorithm can efficiently estimate any parameter in the N qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N qubit Hamiltonian H into noninteracting patches and learns H using a quantumenhanced divideandconquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog(ε^{1}) experiments. In contrast, the best existing algorithms require O (ε^{2}) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.
 Publication:

Physical Review Letters
 Pub Date:
 May 2023
 DOI:
 10.1103/PhysRevLett.130.200403
 arXiv:
 arXiv:2210.03030
 Bibcode:
 2023PhRvL.130t0403H
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 Computer Science  Machine Learning;
 Mathematics  Numerical Analysis
 EPrint:
 11 pages, 1 figure + 27page appendix