Quantum-Enhanced Neural Exchange-Correlation Functionals

Abstract

Kohn-Sham Density Functional Theory (KS-DFT) provides the exact ground state energy and electron density of a molecule, contingent on the as-yet-unknown universal exchange-correlation (XC) functional. Recent research has demonstrated that neural networks can efficiently learn to represent approximations to that functional, offering accurate generalizations to molecules not present during the training process. With the latest advancements in quantum-enhanced machine learning (ML), evidence is growing that Quantum Neural Network (QNN) models may offer advantages in ML applications. In this work, we explore the use of QNNs for representing XC functionals, enhancing and comparing them to classical ML techniques. We present QNNs based on differentiable quantum circuits (DQCs) as quantum (hybrid) models for XC in KS-DFT, implemented across various architectures. We assess their performance on 1D and 3D systems. To that end, we expand existing differentiable KS-DFT frameworks and propose strategies for efficient training of such functionals, highlighting the importance of fractional orbital occupation for accurate results. Our best QNN-based XC functional yields energy profiles of the H${}_2$ and planar H${}_4$ molecules that deviate by no more than 1 mHa from the reference DMRG and FCI/6-31G results, respectively. Moreover, they reach chemical precision on a system, H${}_2$H${}_2$, not present in the training dataset, using only a few variational parameters. This work lays the foundation for the integration of quantum models in KS-DFT, thereby opening new avenues for expressing XC functionals in a differentiable way and facilitating computations of various properties.

References in corpus (47)

• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Quantum Circuit Learning
• Quantum Convolutional Neural Networks
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• The effect of data encoding on the expressive power of variational quantum machine learning models
• By-passing the Kohn-Sham equations with machine learning
• Towards Practical Quantum Variational Algorithms
• Efficient Learning for Deep Quantum Neural Networks
• Data re-uploading for a universal quantum classifier
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum advantage in learning from experiments
• High-threshold and low-overhead fault-tolerant quantum memory
• Understanding and reducing errors in density functional calculations
• Fractional spins and static correlation error in density functional theory
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Is quantum advantage the right goal for quantum machine learning?
• Accurate and efficient linear scaling DFT calculations with universal applicability
• Solving nonlinear differential equations with differentiable quantum circuits
• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Density functional theory with fractional orbital occupations
• Can single-reference coupled cluster theory describe static correlation?
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Circuit-Based Quantum Random Access Memory for Classical Data
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Learning the exchange-correlation functional from nature with fully differentiable density functional theory
• Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Density Functional Theory is Not Straying from the Path toward the Exact Functional
• One qubit as a Universal Approximant
• Precise measurement of quantum observables with neural-network estimators
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems
• Computing the Self-Consistent Field in Kohn-Sham Density Functional Theory
• Evolving symbolic density functionals
• Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond
• Engineered dissipation to mitigate barren plateaus
• Machine learning density functionals from the random-phase approximation
• Grad DFT: a software library for machine learning enhanced density functional theory
• Density functional theory and quantum computation
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?
• Hardware-Tailored Diagonalization Circuits
• Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low rank approximation of the dielectric matrix
• Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
• Learning Density Functionals from Noisy Quantum Data