From Architectures to Applications: A Review of Neural Quantum States

• URL: http://arxiv.org/abs/2402.09402v3
• Date: Fri, 26 Jul 2024 08:59:17 GMT
• Title: From Architectures to Applications: A Review of Neural Quantum States
• Authors: Hannah Lange, Anka Van de Walle, Atiye Abedinnia, Annabelle Bohrdt,
• Abstract summary: We review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS) NQS overcomes the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.

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)
• Comment on "Can Neural Quantum States Learn Volume-Law Ground States?" [44.99833362998488]
  We show that suitably chosen NQS can learn ground states with volume-law entanglement both for spin and fermionic problems. We argue that the setup utilized in the aforementioned letter reveals the inefficiency of non-fermionic NQS to learn fermionic states.
  arXiv  Detail & Related papers  (2023-09-20T14:44:04Z)
• 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)
• Reconstructing complex states of a 20-qubit quantum simulator [0.6646556786265893]
  We demonstrate an efficient method for reconstruction of significantly entangled multi-qubit quantum states. We observe superior state reconstruction quality and faster convergence compared to the methods based on neural network quantum state representations. Our results pave the way towards efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.
  arXiv  Detail & Related papers  (2022-08-09T15:52:20Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Adaptive Quantum State Tomography with Active Learning [0.0]
  We propose and implement an efficient scheme for quantum state tomography using active learning. We apply the scheme to reconstruct different multi-qubit states with varying degree of entanglement as well as to ground states of the XXZ model in 1D and a kinetically constrained spin chain. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for benchmarking and characterizing quantum devices.
  arXiv  Detail & Related papers  (2022-03-29T16:23:10Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Infinite Neural Network Quantum States: Entanglement and Training Dynamics [1.0878040851638]
  We study infinite limits of neural network quantum states ($infty$-NNQS), which exhibit representation power through ensemble statistics. A general framework is developed for studying the gradient descent dynamics of neural network quantum states. $infty$-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications.
  arXiv  Detail & Related papers  (2021-12-01T18:57:17Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

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.