Ground-state properties via machine learning quantum constraints

Abstract

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them, where the search for ground-state properties simply equates to classical constrained minimization. These quantum constraints are generally obtainable via sampling and then machine learning on a large number of systematically consistent quantum many-body states. We showcase our perspective on 1D fermion chains and spin chains for applicability, effectiveness, caveats, and unique advantages, especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.

arXiv comment17 pages, 14 figures

References in corpus (28)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Machine learning phases of matter
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Theory of Intertwined Orders in High Temperature Superconductors
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Many-body quantum state tomography with neural networks
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Discovering Phase Transitions with Unsupervised Learning
• Identifying Mislabeled Training Data
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Quantum Entanglement in Neural Network States
• Machine learning quantum phases of matter beyond the fermion sign problem
• Reconstructing quantum states with generative models
• Active learning machine learns to create new quantum experiments
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Machine Learning Phases of Strongly Correlated Fermions
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• Typicality in random matrix product states
• Statistical properties of random matrix product states
• Emergent statistical mechanics from properties of disordered random matrix product states

Cited by in corpus (3)

• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Efficient and quantum-adaptive machine learning with fermion neural networks
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics