Diffusion-Enhanced Optimization of Variational Quantum Eigensolver for General Hamiltonians

• URL: http://arxiv.org/abs/2501.05666v1
• Date: Fri, 10 Jan 2025 02:32:46 GMT
• Title: Diffusion-Enhanced Optimization of Variational Quantum Eigensolver for General Hamiltonians
• Authors: Shikun Zhang, Zheng Qin, Yongyou Zhang, Yang Zhou, Rui Li, Chunxiao Du, Zhisong Xiao,
• Abstract summary: Variational quantum algorithms (VQAs) have emerged as a promising approach for achieving quantum advantage on current noisy quantum devices. However, their large-scale applications are significantly hindered by optimization challenges, such as the barren plateau (BP) phenomenon, local minima, and numerous iteration demands. In this work, we leverage denoising diffusion models (DMs) to address these difficulties.
• Score: 17.975555487972166
• License:
• Abstract: Variational quantum algorithms (VQAs) have emerged as a promising approach for achieving quantum advantage on current noisy intermediate-scale quantum devices. However, their large-scale applications are significantly hindered by optimization challenges, such as the barren plateau (BP) phenomenon, local minima, and numerous iteration demands. In this work, we leverage denoising diffusion models (DMs) to address these difficulties. The DM is trained on a few data points in the Heisenberg model parameter space and then can be guided to generate high-performance parameters for parameterized quantum circuits (PQCs) in variational quantum eigensolver (VQE) tasks for general Hamiltonians. Numerical experiments demonstrate that DM-parameterized VQE can explore the ground-state energies of Heisenberg models with parameters not included in the training dataset. Even when applied to previously unseen Hamiltonians, such as the Ising and Hubbard models, it can generate the appropriate initial state to achieve rapid convergence and mitigate the BP and local minima problems. These results highlight the effectiveness of our proposed method in improving optimization efficiency for general Hamiltonians.

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)
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models [0.0]
  We introduce a systematic procedure for ansatz building based on approximate Quantum Mutual Information (QMI) Our approach generates a layered-structured ansatz, where each layer's qubit pairs are selected based on their QMI values, resulting in more efficient state preparation and optimization routines. Our results show that the Multi-QIDA method reduces the computational complexity while maintaining high precision, making it a promising tool for quantum simulations in lattice spin models.
  arXiv  Detail & Related papers  (2024-08-05T17:07:08Z)
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries [0.0]
  We develop a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems.
  arXiv  Detail & Related papers  (2024-01-04T16:53:47Z)
• Variational waveguide QED simulators [58.720142291102135]
  Waveguide QED simulators are made by quantum emitters interacting with one-dimensional photonic band-gap materials. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-02-03T18:55:08Z)
• Maximum-Likelihood-Estimate Hamiltonian learning via efficient and robust quantum likelihood gradient [4.490097334898205]
  We propose an efficient strategy combining maximum likelihood estimation, gradient descent, and quantum many-body algorithms. Compared with previous approaches, it also exhibits better accuracy and overall stability toward noises, fluctuations, and temperature ranges.
  arXiv  Detail & Related papers  (2022-12-28T06:54:15Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• 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)
• 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)
• Variational quantum solver employing the PDS energy functional [6.822193536884916]
  A new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. Here we find that the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima.
  arXiv  Detail & Related papers  (2021-01-21T10:12:38Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Variational Quantum Eigensolver for Frustrated Quantum Systems [0.0]
  A variational quantum eigensolver, or VQE, is designed to determine a global minimum in an energy landscape specified by a quantum Hamiltonian. Here we consider the performance of the VQE technique for a Hubbard-like model describing a one-dimensional chain of fermions. We also study the barren plateau phenomenon for the Hamiltonian in question and find that the severity of this effect depends on the encoding of fermions to qubits.
  arXiv  Detail & Related papers  (2020-05-01T18:00:01Z)

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.