Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems

• URL: http://arxiv.org/abs/2401.14179v1
• Date: Thu, 25 Jan 2024 13:41:34 GMT
• Title: Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• Authors: Johannes Mellak, Enrico Arrigoni, and Wolfgang von der Linden
• Abstract summary: We show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

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)
• Training-efficient density quantum machine learning [2.918930150557355]
  Quantum machine learning requires powerful, flexible and efficiently trainable models. We present density quantum neural networks, a learning model incorporating randomisation over a set of trainable unitaries.
  arXiv  Detail & Related papers  (2024-05-30T16:40:28Z)
• Towards Efficient Quantum Hybrid Diffusion Models [68.43405413443175]
  We propose a new methodology to design quantum hybrid diffusion models. We propose two possible hybridization schemes combining quantum computing's superior generalization with classical networks' modularity.
  arXiv  Detail & Related papers  (2024-02-25T16:57:51Z)
• Neural Network Solutions of Bosonic Quantum Systems in One Dimension [0.0]
  We benchmark the methodology by using neural networks to study several different integrable bosonic quantum systems in one dimension. While testing the scalability of the procedure to systems with many particles, we also introduce using symmetric function inputs to the neural network to enforce exchange symmetries of indistinguishable particles.
  arXiv  Detail & Related papers  (2023-09-05T16:08:48Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• 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)
• Positive-definite parametrization of mixed quantum states with deep neural networks [0.0]
  We show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. We benchmark this architecture by the steady state of the dissipative transverse-field Ising model.
  arXiv  Detail & Related papers  (2022-06-27T17:51:38Z)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Group Convolutional Neural Networks Improve Quantum State Accuracy [1.52292571922932]
  We show how to create maximally expressive models for quantum states with specific symmetry properties. We implement group equivariant convolutional networks (G-CNN) citecohen2016group, and demonstrate that performance improvements can be achieved without increasing memory use.
  arXiv  Detail & Related papers  (2021-04-11T19:45:10Z)
• Searching for Low-Bit Weights in Quantized Neural Networks [129.8319019563356]
  Quantized neural networks with low-bit weights and activations are attractive for developing AI accelerators. We present to regard the discrete weights in an arbitrary quantized neural network as searchable variables, and utilize a differential method to search them accurately.
  arXiv  Detail & Related papers  (2020-09-18T09:13:26Z)
• 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.