Learning Density Functionals from Noisy Quantum Data

Abstract

The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi-Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn-Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.

13 pages, 6 figures

References in corpus (32)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Quantum computational chemistry
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Quantum algorithms for quantum chemistry and quantum materials science
• Elucidating Reaction Mechanisms on Quantum Computers
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Power of data in quantum machine learning
• By-passing the Kohn-Sham equations with machine learning
• Towards Practical Quantum Variational Algorithms
• Finding Density Functionals with Machine Learning
• Quantum Error Mitigation
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Solving strongly correlated electron models on a quantum computer
• A Transferable Machine-Learning Model of the Electron Density
• Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
• Low Depth Quantum Simulation of Electronic Structure
• Provably efficient machine learning for quantum many-body problems
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Deep Learning and Density Functional Theory
• Machine learning and density functional theory
• Performance comparison of optimization methods on variational quantum algorithms
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
• Shadows of quantum machine learning
• Machine learning density functional theory for the Hubbard model
• Improved machine learning algorithm for predicting ground state properties
• Grad DFT: a software library for machine learning enhanced density functional theory
• Optimizing the information extracted by a single qubit measurement
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Deep learning nonlocal and scalable energy functionals for quantum Ising models

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• Learning Minimal Representations of Fermionic Ground States
• Quantum-Enhanced Neural Exchange-Correlation Functionals