When Less is More: Approximating the Quantum Geometric Tensor with Block Structures

• URL: http://arxiv.org/abs/2510.08430v2
• Date: Tue, 04 Nov 2025 10:31:05 GMT
• Title: When Less is More: Approximating the Quantum Geometric Tensor with Block Structures
• Authors: Ahmedeo Shokry, Alessandro Santini, Filippo Vicentini,
• Abstract summary: We introduce a block-diagonal quantum geometric tensor that partitions the metric by network layers, analogous to block-structured Fisher methods such as K-FAC.<n> Experiments on Heisenberg and frustrated $J_1$-$J$ models show faster convergence, lower energy, and improved stability.
• Score: 43.39839287869652
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The natural gradient is central in neural quantum states optimizations but it is limited by the cost of computing and inverting the quantum geometric tensor, the quantum analogue of the Fisher information matrix. We introduce a block-diagonal quantum geometric tensor that partitions the metric by network layers, analogous to block-structured Fisher methods such as K-FAC. This layer-wise approximation preserves essential curvature while removing noisy cross-layer correlations, improving conditioning and scalability. Experiments on Heisenberg and frustrated $J_1$-$J_2$ models show faster convergence, lower energy, and improved stability.

Related papers

• Designing quantum technologies with a quantum computer [1.4951795042951048]
  We develop a quantum-computer-aided framework for simulating devices using a general electron spin resonance Hamiltonian.<n>Within this model, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding algorithm.<n> Numerical simulations demonstrate the computation of autocorrelation functions up to $sim100$ ns, together with microwave absorption spectra.<n>We benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost.
  arXiv  Detail & Related papers  (2026-01-29T18:26:54Z)
• Quantum-Enhanced Neural Contextual Bandit Algorithms [50.880384999888044]
  This paper introduces the Quantum Neural Tangent Kernel-Upper Confidence Bound (QNTK-UCB) algorithm.<n>QNTK-UCB is a novel algorithm that leverages the Quantum Neural Tangent Kernel (QNTK) to address these limitations.
  arXiv  Detail & Related papers  (2026-01-06T09:58:14Z)
• Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study [42.40832340604796]
  We show that even the broken symmetry phase observed around 130GPa requires revisiting due to its intricate coupling of electronic and nuclear degrees of freedom.<n>Our calculations reveal an unreported ground-state structure candidate for the broken symmetry phase with $Cmcm$ space group symmetry.<n>These results shed new light on the phase diagram of high-pressure hydrogen and call for further experimental verifications.
  arXiv  Detail & Related papers  (2025-12-19T15:36:27Z)
• Molecular Properties in Quantum-Classical Auxiliary-Field Quantum Monte Carlo: Correlated Sampling with Application to Accurate Nuclear Forces [1.2189422792863451]
  We extend correlated sampling from classical auxiliary-field quantum Monte Carlo to the quantum-classical (QCAFQMC) framework.<n>We demonstrate significant improvements over single-reference methods in force evaluations for N$ wave$ and stretched linear H$_4$, particularly in strongly correlated regions.<n>We also apply our methodology to the MEA-CO$$ carbon capture reaction, employing quantum information metrics for active space selection and matchgate shadows.
  arXiv  Detail & Related papers  (2025-07-23T23:51:10Z)
• Quantum Spin Glass in the Two-Dimensional Disordered Heisenberg Model via Foundation Neural-Network Quantum States [0.0]
  We investigate the frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework.<n>We find compelling evidence that the spin glass phase is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.
  arXiv  Detail & Related papers  (2025-07-07T15:00:55Z)
• Quantum channel for modeling spin-motion dephasing in Rydberg chains [44.99833362998488]
  We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions.<n>We benchmark the accuracy of our approach against exact diagonalization for small systems, identifying its regime of validity and the onset of perturbative breakdown.<n>We then apply the quantum channel to compute fidelity loss during transport of single-spin excitations across extended Rydberg chains in intractable regimes via exact diagonalization.
  arXiv  Detail & Related papers  (2025-06-30T17:37:38Z)
• Enhancing Quantum Diffusion Models with Pairwise Bell State Entanglement [35.436358464279785]
  This paper introduces a novel quantum diffusion model designed for Noisy Intermediate-Scale Quantum (NISQ) devices. By leveraging quantum entanglement and superposition, this approach advances quantum generative learning.
  arXiv  Detail & Related papers  (2024-11-24T20:14:57Z)
• A quantum eigenvalue solver based on tensor networks [0.0]
  Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases. This study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
  arXiv  Detail & Related papers  (2024-04-16T02:04:47Z)
• Non-adiabatic holonomies as photonic quantum gates [36.136619420474766]
  We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization.
  arXiv  Detail & Related papers  (2024-01-08T16:44:45Z)
• Scalable Imaginary Time Evolution with Neural Network Quantum States [0.0]
  The representation of a quantum wave function as a neural network quantum state (NQS) provides a powerful variational ansatz for finding the ground states of many-body quantum systems. We introduce an approach that bypasses the computation of the metric tensor and instead relies exclusively on first-order descent with Euclidean metric. We make this method adaptive and stable by determining the optimal time step and keeping the target fixed until the energy of the NQS decreases.
  arXiv  Detail & Related papers  (2023-07-28T12:26:43Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term [0.0]
  We show that the quantum theory is massless in the strong-coupling regime. We also highlight the limitations of current quantum algorithms, designed for noisy intermediate-scale quantum devices.
  arXiv  Detail & Related papers  (2022-10-07T16:35:03Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)

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.