The advantage of quantum control in many-body Hamiltonian learning

Alicja Dutkiewicz; Thomas E. O'Brien; Thomas Schuster

doi:10.22331/q-2024-11-26-1537

The advantage of quantum control in many-body Hamiltonian learning

Alicja Dutkiewicz^1,2, Thomas E. O'Brien^1,2, and Thomas Schuster^1,3

¹Google Quantum AI, Munich 80636, Germany
²Instituut-Lorentz, Universiteit Leiden, 2300RA Leiden, The Netherlands
³Department of Physics, University of California, Berkeley, California 94720 USA

Published:	2024-11-26, volume 8, page 1537
Eprint:	arXiv:2304.07172v3
Doi:	https://doi.org/10.22331/q-2024-11-26-1537
Citation:	Quantum 8, 1537 (2024).

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Abstract

We study the problem of learning the Hamiltonian of a many-body quantum system from experimental data. We show that the rate of learning depends on the amount of control available during the experiment. We consider three control models: one where time evolution can be augmented with instantaneous quantum operations, one where the Hamiltonian itself can be augmented by adding constant terms, and one where the experimentalist has no control over the system's time evolution. With continuous quantum control, we provide an adaptive algorithm for learning a many-body Hamiltonian at the Heisenberg limit: $T = \mathcal{O}(\epsilon^{-1})$, where $T$ is the total amount of time evolution across all experiments and $\epsilon$ is the target precision. This requires only preparation of product states, time-evolution, and measurement in a product basis. In the absence of quantum control, we prove that learning is standard quantum limited, $T = \Omega(\epsilon^{-2})$, for large classes of many-body Hamiltonians, including any Hamiltonian that thermalizes via the eigenstate thermalization hypothesis. These results establish a quadratic advantage in experimental runtime for learning with quantum control.

Featured image: (Left) Schematics of the three models of quantum control that we consider in this work. Colors denote when the experimentalist has complete control (red), some control (light blue-red gradient), or no control (light blue) over the operation. The allowed operations are state preparation (half-ellipse), unitary operation or time-evolution (labeled rectangle) or measurement (dial symbol).
(Right) Flowchart of our Heisenberg-limited algorithm.

Presentation “The advantage of quantum control in many body Hamiltonian learning” by Alicja Dutkiewicz at Quantum Information Processing, Taipei 2024

► BibTeX data

@article{Dutkiewicz2024advantageofquantum,
  doi = {10.22331/q-2024-11-26-1537},
  url = {https://doi.org/10.22331/q-2024-11-26-1537},
  title = {The advantage of quantum control in many-body {H}amiltonian learning},
  author = {Dutkiewicz, Alicja and O'Brien, Thomas E. and Schuster, Thomas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1537},
  month = nov,
  year = {2024}
}

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