Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization

• URL: http://arxiv.org/abs/2406.17937v1
• Date: Tue, 25 Jun 2024 20:58:03 GMT
• Title: Using a Feedback-Based Quantum Algorithm to Analyze the Critical Properties of the ANNNI Model Without Classical Optimization
• Authors: G. E. L. Pexe, L. A. M. Rattighieri, A. L. Malvezzi, F. F. Fanchini,
• Abstract summary: We investigate the critical properties of the Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model using a feedback-based quantum algorithm (FALQON) This approach allows us to compute both ground and excited states without relying on classical optimization methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the critical properties of the Anisotropic Next-Nearest-Neighbor Ising (ANNNI) model using a feedback-based quantum algorithm (FALQON). This approach allows us to compute both ground and excited states without relying on classical optimization methods. We study the quantum phase transitions using the Finite Size Scaling method, analyze correlation functions through spin correlations in the ground state, and examine magnetic structure by calculating structure factors via the Discrete Fourier Transform. Our results demonstrate the algorithm's capability to identify quantum phase transitions and efficiently map the ANNNI model's magnetic phases, establishing FALQON as a powerful tool to study complex magnetic systems.

Related papers

• 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)
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids [14.379311972506791]
  We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model, and use a trainable symmetry-guided ansatz for preparing its ground state.
  arXiv  Detail & Related papers  (2024-07-05T01:09:18Z)
• Exploring quantum localization with machine learning [39.58317527488534]
  We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the pattern recognition capabilities of a modified convolutional model.
  arXiv  Detail & Related papers  (2024-06-01T08:50:26Z)
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering [0.13108652488669736]
  Hamiltonian simulation is a domain where quantum computers have the potential to outperform classical counterparts. One of the main challenges of such quantum algorithms is up-scaling the system size. We present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian.
  arXiv  Detail & Related papers  (2024-01-17T09:52:24Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• 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)
• Digital quantum simulation of strong correlation effects with iterative quantum phase estimation over the variational quantum eigensolver algorithm: $\mathrm{H_4}$ on a circle as a case study [0.0]
  We generate the initial state by using the classical-quantum hybrid variational quantum eigensolver algorithm with unitary coupled cluster ansatz. We demonstrate that a carefully and appropriately prepared initial state can greatly reduce the effects of noise due to sampling in the estimation of the desired eigenphase.
  arXiv  Detail & Related papers  (2021-10-06T15:48:53Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation [58.720142291102135]
  We present a novel hybrid-classical algorithm that computes a molecule's all-electron energy and properties on the classical computer. We demonstrate the ability of the quantum-classical hybrid algorithms to achieve chemically relevant results and accuracy on currently available quantum computers.
  arXiv  Detail & Related papers  (2021-06-22T18:00:00Z)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)

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.