Many-body $k$-local ground states as probes for unitary quantum metrology

• URL: http://arxiv.org/abs/2512.02976v1
• Date: Tue, 02 Dec 2025 17:56:24 GMT
• Title: Many-body $k$-local ground states as probes for unitary quantum metrology
• Authors: Majid Hassani, Mengyao Hu, Guillem Müller-Rigat, Matteo Fadel, Jordi Tura,
• Abstract summary: Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared.<n> experimentally practical Hamiltonians often involve few-body correlators only.<n>We find that typical random ground states of $k$-body permutation-invariant Hamiltonians exhibit Heisenberg scaling.
• Score: 0.6524460254566904
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared. On the other hand, experimentally practical Hamiltonians often involve few-body correlators only. Here, we study the metrological performances under this constraint, using tools derived from the quantum Fisher information. Our work applies to any encoding generator, also including a dependence on the parameter. We find that typical random symmetric ground states of $k$-body permutation-invariant Hamiltonians exhibit Heisenberg scaling. Finally, we establish a tradeoff between the Hamiltonian's gap, which quantifies preparation hardness, and the quantum Fisher information of the corresponding ground state.

Related papers

• Learning Hamiltonians in the Heisenberg limit with static single-qubit fields [2.066606476344995]
  We present a protocol that learns a quantum Hamiltonian with the optimal Heisenberg-limited scaling.<n>By overcoming these limitations, our protocol provides new tools for device characterization and quantum sensing.
  arXiv  Detail & Related papers  (2026-01-15T13:34:50Z)
• Resource-Free Quantum Hamiltonian Learning Below the Standard Quantum Limit [0.0]
  We demonstrate a method that surpasses the standard quantum limit without requiring entanglement resources, coherent measurements, or dynamical control.<n>Our method relies on trajectory-based Hamiltonian learning, in which we apply local, randomized pre-processing to probe states.<n>Our numerics show that our method needs only one shot per Pauli measurement, making it well-suited for experimental scenarios.
  arXiv  Detail & Related papers  (2025-07-28T22:41:36Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Adiabatic echo protocols for robust quantum many-body state preparation [35.31045922824676]
  We introduce the adiabatic echo protocol, a general approach to state preparation designed to suppress the effect of static perturbations.<n>We show that such a protocol emerges naturally in a variety of settings, without requiring assumptions on the form of the control fields.<n>Our results highlight the broad applicability of this protocol, providing a practical framework for reliable many-body state preparation in present-day quantum platforms.
  arXiv  Detail & Related papers  (2025-06-13T18:01:08Z)
• 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.<n>We establish a rigorous theoretical framework proving that, given access to an unknown spin-boson type Hamiltonian, our algorithm achieves Heisenberg-limited estimation.<n>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)
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees [0.0]
  We provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications. Our results provide theoretical guarantees for efficient learning of quantum many-body states and their properties, with model-independent applications.
  arXiv  Detail & Related papers  (2023-04-10T02:22:36Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Efficient Verification of Ground States of Frustration-Free Hamiltonians [28.03059224016627]
  We propose a recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. We derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma and quantum union bound. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.
  arXiv  Detail & Related papers  (2022-06-30T13:50:56Z)
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses [58.720142291102135]
  We offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg scaling levels. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe. We illustrate that such states are close to the optimal ones even with moderate losses.
  arXiv  Detail & Related papers  (2021-08-07T09:29:23Z)
• 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)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Deep neural network predicts parameters of quantum many-body Hamiltonians by learning visualized wave-functions [0.0]
  We show that convolutional neural network (CNN) can predict the physical parameters of interacting Hamiltonians. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states as images, and a CNN that maps the images to the target physical parameters.
  arXiv  Detail & Related papers  (2020-12-05T12:22:12Z)

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.