Variational learning of quantum ground states on spiking neuromorphic hardware

• URL: http://arxiv.org/abs/2109.15169v4
• Date: Thu, 25 Nov 2021 20:21:07 GMT
• Title: Variational learning of quantum ground states on spiking neuromorphic hardware
• Authors: Robert Klassert, Andreas Baumbach, Mihai A. Petrovici, Martin G\"arttner
• Abstract summary: High-dimensional sampling spaces and transient autocorrelations confront neural networks with a challenging computational bottleneck. Compared to conventional neural networks, physical-model devices offer a fast, efficient and inherently parallel substrate. We demonstrate the ability of a neuromorphic chip to represent the ground states of quantum spin models by variational energy minimization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a challenging computational bottleneck. Compared to conventional neural networks, physical-model devices offer a fast, efficient and inherently parallel substrate capable of related forms of Markov chain Monte Carlo sampling. Here, we demonstrate the ability of a neuromorphic chip to represent the ground states of quantum spin models by variational energy minimization. We develop a training algorithm and apply it to the transverse field Ising model, showing good performance at moderate system sizes ($N\leq 10$). A systematic hyperparameter study shows that scalability to larger system sizes mainly depends on sample quality, which is limited by temporal parameter variations on the analog neuromorphic chip. Our work thus provides an important step towards harnessing the capabilities of neuromorphic hardware for tackling the curse of dimensionality in quantum many-body problems.

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)
• Paths towards time evolution with larger neural-network quantum states [17.826631514127012]
  We consider a quantum quench from the paramagnetic to the anti-ferromagnetic phase in the tilted Ising model. We show that for both types of networks, the projected time-dependent variational Monte Carlo (p-tVMC) method performs better than the non-projected approach.
  arXiv  Detail & Related papers  (2024-06-05T15:32:38Z)
• Neural Quantum States in Variational Monte Carlo Method: A Brief Summary [0.0]
  variational Monte Carlo method based on neural quantum states for spin systems is reviewed. neural networks can represent relatively complex wave functions with relatively small computational resources. In quantum-state tomography, the representation method of neural quantum states has already achieved significant results.
  arXiv  Detail & Related papers  (2024-06-03T05:55:55Z)
• Coherent Feed Forward Quantum Neural Network [2.1178416840822027]
  Quantum machine learning, focusing on quantum neural networks (QNNs), remains a vastly uncharted field of study. We introduce a bona fide QNN model, which seamlessly aligns with the versatility of a traditional FFNN in terms of its adaptable intermediate layers and nodes. We test our proposed model on various benchmarking datasets such as the diagnostic breast cancer (Wisconsin) and credit card fraud detection datasets.
  arXiv  Detail & Related papers  (2024-02-01T15:13:26Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• 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)
• Quantum-tailored machine-learning characterization of a superconducting qubit [50.591267188664666]
  We develop an approach to characterize the dynamics of a quantum device and learn device parameters. This approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task.
  arXiv  Detail & Related papers  (2021-06-24T15:58:57Z)
• Random Sampling Neural Network for Quantum Many-Body Problems [0.0]
  We propose a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable 1D models, including Ising model with transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to test the applicability of RSNN.
  arXiv  Detail & Related papers  (2020-11-10T15:52:44Z)

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.