The advantage of quantum control in many-body Hamiltonian learning

• URL: http://arxiv.org/abs/2304.07172v3
• Date: Mon, 5 Aug 2024 15:17:46 GMT
• Title: The advantage of quantum control in many-body Hamiltonian learning
• Authors: Alicja Dutkiewicz, Thomas E. O'Brien, Thomas Schuster,
• Abstract summary: 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.
• Score: 0.11704154007740832
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

Related papers

• Hamiltonian Learning at Heisenberg Limit for Hybrid Quantum Systems [0.7499722271664147]
  Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. We establish a rigorous theoretical framework proving that, given access to an unknown spin-boson type Hamiltonian, our algorithm achieves Heisenberg-limited estimation. Our results provide a scalable and robust framework for precision Hamiltonian characterization in hybrid quantum platforms.
  arXiv  Detail & Related papers  (2025-02-27T18:47:47Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Long-lived entanglement of molecules in magic-wavelength optical tweezers [41.94295877935867]
  We present the first realisation of a microwave-driven entangling gate between two molecules. We show that the magic-wavelength trap preserves the entanglement, with no measurable decay over 0.5 s. The extension of precise quantum control to complex molecular systems will allow their additional degrees of freedom to be exploited across many domains of quantum science.
  arXiv  Detail & Related papers  (2024-08-27T09:28:56Z)
• Learning interacting fermionic Hamiltonians at the Heisenberg limit [0.6906005491572401]
  We provide an algorithm to learn a class of fermionic Hubbard Hamiltonians at the Heisenberg limit. The protocol is robust to a constant amount of state preparation and measurement error.
  arXiv  Detail & Related papers  (2024-02-29T19:01:05Z)
• Dissipation-enabled bosonic Hamiltonian learning via new information-propagation bounds [1.0499611180329802]
  We show that a bosonic Hamiltonian can be efficiently learned from simple quantum experiments. Our work demonstrates that a broad class of bosonic Hamiltonians can be efficiently learned from simple quantum experiments.
  arXiv  Detail & Related papers  (2023-07-27T17:35:07Z)
• Improving Metrology with Quantum Scrambling [0.520082039162174]
  Quantum scrambling describes the fast spreading of quantum information into many degrees of freedom of a many-body quantum system. We probe the exponential scrambling nature of the Lipkin-Meshkov-Glick (LMG) many-body Hamiltonian. Our experiment paves the way to the investigation of quantum chaos and scrambling in controlled tabletop experiments.
  arXiv  Detail & Related papers  (2022-12-24T20:00:52Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Experimental observation of thermalization with noncommuting charges [53.122045119395594]
  Noncommuting charges have emerged as a subfield at the intersection of quantum thermodynamics and quantum information. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state.
  arXiv  Detail & Related papers  (2022-02-09T19:00:00Z)
• Active Learning of Quantum System Hamiltonians yields Query Advantage [3.07869141026886]
  Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Standard techniques for Hamiltonian learning require careful design of queries and $O(epsilon-2)$ queries in achieving learning error $epsilon$ due to the standard quantum limit. We introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data.
  arXiv  Detail & Related papers  (2021-12-29T13:45:12Z)
• Variational principle for optimal quantum controls in quantum metrology [2.29042212865183]
  We develop a variational principle to determine the quantum controls and initial state which optimize the quantum Fisher information. We find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one and two-body interaction, that the Heisenberg scaling can still be approximately achieved.
  arXiv  Detail & Related papers  (2021-11-07T16:11:55Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.