Improved machine learning algorithm for predicting ground state properties

Abstract

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an $n$-qubit gapped local Hamiltonian after learning from only $\mathcal{O}(\log (n))$ data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require $\mathcal{O}(n^c)$ data for a large constant $c$. Furthermore, the training and prediction time of the proposed ML model scale as $\mathcal{O}(n\log n)$ in the number of qubits $n$. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.

8 pages, 5 figures + 32-page appendix

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding
• Learning phase transitions by confusion
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Neural Tangents: Fast and Easy Infinite Neural Networks in Python
• Scalable neural networks for the efficient learning of disordered quantum systems
• Hardware-efficient learning of quantum many-body states
• Foundations for learning from noisy quantum experiments
• Predicting Properties of Quantum Systems with Conditional Generative Models
• Efficient learning of ground & thermal states within phases of matter

Cited by in corpus (18)

• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• Robust estimation of the Quantum Fisher Information on a quantum processor
• Machine learning on quantum experimental data toward solving quantum many-body problems
• Enhanced estimation of quantum properties with common randomized measurements
• Local minima in quantum systems
• Experimental sample-efficient quantum state tomography via parallel measurements
• Fine-tuning Neural Network Quantum States
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Unveiling quantum phase transitions from traps in variational quantum algorithms
• Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
• Efficient learning of ground & thermal states within phases of matter
• Efficient Learning of Long-Range and Equivariant Quantum Systems
• Tomography of parametrized quantum states
• Learning Density Functionals from Noisy Quantum Data
• Artificial intelligence for representing and characterizing quantum systems
• Classical Shadows with Improved Median-of-Means Estimation
• Critical Scaling of the Quantum Wasserstein Distance