The quantum Gaussian process state: A kernel-inspired state with quantum support data

Abstract

We introduce the quantum Gaussian process state, motivated via a statistical inference for the wave function supported by a data set of unentangled product states. We show that this condenses down to a compact and expressive parametric form, with a variational flexibility shown to be competitive or surpassing established alternatives. The connections of the state to its roots as a Bayesian inference machine as well as matrix product states, also allow for efficient deterministic training of global states from small training data with enhanced generalization, including on application to frustrated spin physics.

References in corpus (47)

• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Many-body quantum state tomography with neural networks
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Quantum Entanglement in Neural Network States
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Symmetries and many-body excited states with neural-network quantum states
• Fermionic neural-network states for ab-initio electronic structure
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Constructing exact representations of quantum many-body systems with deep neural networks
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Optimizing large parameter sets in variational quantum Monte Carlo
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Solving frustrated quantum many-particle models with convolutional neural networks
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Neural tensor contractions and the expressive power of deep neural quantum states
• Ground-state phase diagram of the quantum J1-J2 model on the honeycomb lattice
• Neural Gutzwiller-projected variational wave functions
• Neural network wave functions and the sign problem
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Geometry of learning neural quantum states
• Transfer learning for scalability of neural-network quantum states
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
• Variational optimization in the AI era: Computational Graph States and Supervised Wave-function Optimization
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• Group Convolutional Neural Networks Improve Quantum State Accuracy
• Approximating power of machine-learning ansatz for quantum many-body states
• Artificial Neural Networks as Trial Wave Functions for Quantum Monte Carlo
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• Gaussian Process States: A data-driven representation of quantum many-body physics
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Compact Neural-network Quantum State representations of Jastrow and Stabilizer states

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• A framework for efficient ab initio electronic structure with Gaussian Process States
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• Impact of conditional modelling for a universal autoregressive quantum state
• Boltzmann machines and quantum many-body problems
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Gaussian Processes for Finite Size Extrapolation of Many-Body Simulations