Practical Black Box Hamiltonian Learning
This work addresses Hamiltonian learning for quantum systems, offering incremental improvements in efficiency and scalability for researchers in quantum computing.
The authors tackled the problem of learning Hamiltonian parameters for quantum many-body systems with limited access, improving scaling dependence on structural parameters like locality and providing exact bounds for optimal hyperparameter settings. They demonstrated practicality with a numerical simulation on an 80-qubit system.
We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality $k$). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.