Abstract

Artificial intelligence is becoming an increasingly important computational instrument for solving, accelerating, approximating, and interpreting problems in quantum mechanics. Quantum-mechanical systems are fundamentally difficult to simulate because the mathematical description of many interacting particles rapidly becomes computationally expensive as the number of degrees of freedom increases.

This thesis examines the integration of artificial intelligence and computational quantum mechanics, beginning with the mathematical foundations of quantum mechanics and progressing through numerical quantum methods, machine learning, deep neural networks, generative models, reinforcement learning, quantum machine learning, and hybrid AI–quantum computational architectures.

Particular attention is given to the use of AI for electronic-structure calculations, density functional theory, molecular dynamics, potential-energy surfaces, wavefunctions, electron densities, quantum Monte Carlo, excited states, materials discovery, molecular simulation, and inverse design.

Recent research demonstrates several distinct strategies: AI can learn relationships from quantum-mechanical data, accelerate existing quantum calculations, improve approximations within quantum-mechanical methods, or participate directly in representations of quantum states.

The ultimate objective is not simply to replace quantum-mechanical calculations with machine learning, but to construct computational systems in which physics-based algorithms and AI complement one another.

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1. Introduction

Quantum mechanics provides the fundamental framework for describing matter and energy at atomic and subatomic scales. It governs electrons, atoms, molecules, solids, semiconductors, superconductors, photons and many other physical systems.

The fundamental challenge is that the Schrödinger equation can be written relatively compactly, while solving it exactly for realistic many-body systems can be extraordinarily difficult.

For a time-independent system,

HΨ = EΨ

where:

• H = Hamiltonian operator
• Ψ = quantum-mechanical wavefunction
• E = energy eigenvalue.

For a single simple system, analytical solutions may exist. For realistic many-electron systems, however, computational approximations become essential.

AI introduces another computational layer:

Quantum system → mathematical representation → numerical simulation → data → AI model → prediction/acceleration/design

This creates a new scientific paradigm in which quantum mechanics supplies physical constraints and AI supplies flexible computational representations.

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2. The Computational Quantum Mechanics Problem

The central computational problem is the representation and calculation of quantum states.

A system containing many interacting particles has a state space whose dimensionality can grow extremely rapidly.

This creates several fundamental challenges:

1. Many-body interactions
2. Electron correlation
3. Exchange effects
4. Large configuration spaces
5. Expensive eigenvalue problems
6. Difficult wavefunction representations
7. Expensive molecular dynamics
8. High-dimensional potential-energy surfaces
9. Sampling problems
10. Numerical convergence requirements.

Traditional computational quantum mechanics therefore relies heavily on controlled approximations.

Important approaches include:

• Hartree–Fock
• Density Functional Theory
• Configuration Interaction
• Coupled-Cluster methods
• Quantum Monte Carlo
• Perturbation theory
• Green’s-function methods
• Tight-binding methods
• Semiempirical quantum chemistry.

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3. Where Artificial Intelligence Enters the Quantum Pipeline

AI can interact with quantum simulations at several different levels.

Level 1 — Data analysis

AI analyzes results generated by conventional quantum calculations.

Level 2 — Property prediction

AI predicts quantities such as:

• energy
• forces
• band gaps
• molecular properties
• electron density
• magnetic properties
• reaction energies.

Level 3 — Surrogate simulation

An AI model approximates an expensive quantum calculation.

Level 4 — Algorithm acceleration

AI identifies computational shortcuts or predicts intermediate quantities needed by an existing solver.

Level 5 — Method improvement

Machine learning can be incorporated directly into components of quantum-mechanical methods.

For example, modern research investigates machine-learning representations of density-functional-theory exchange-correlation functionals.

Level 6 — Direct quantum-state representation

Neural networks can be used as mathematical representations of many-body wavefunctions.

Neural-network quantum Monte Carlo is an important example.

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4. Machine Learning Fundamentals

The principal machine-learning categories relevant to computational quantum mechanics include:

4.1 Supervised learning

The model learns from pairs:

input → known quantum result

Examples include:

molecular structure → energy

atomic configuration → force

material structure → band gap

Common algorithms include:

• Linear regression
• Kernel methods
• Gaussian processes
• Random forests
• Support-vector machines
• Neural networks
• Graph neural networks.

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5. Neural Networks

Neural networks can approximate complicated mathematical mappings.

A basic network consists of:

Input layer → hidden layers → output layer

For quantum applications, the input might represent:

• atomic coordinates
• atomic numbers
• molecular graphs
• electron density
• orbitals
• quantum-state parameters.

The output might represent:

• total energy
• force
• potential energy
• density
• wavefunction parameters.

Deep neural networks are particularly attractive because they can learn nonlinear relationships in high-dimensional data.

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6. Graph Neural Networks

Molecules and materials naturally form graph structures.

Atoms can be represented as nodes.

Chemical interactions can be represented as edges.

Thus:

Molecule = graph

A graph neural network can learn representations such as:

atomic species + geometry + interactions → molecular property

This makes graph-based AI particularly relevant to computational chemistry and materials science.

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7. AI Potential-Energy Surfaces

One of the most important applications is learning potential-energy surfaces.

A conventional quantum calculation may calculate:

R → E(R)

where:

• R = nuclear configuration
• E(R) = quantum-mechanical energy.

A machine-learning model can learn an approximation:

E_AI(R) ≈ E_QM(R)

Once trained, the AI model may evaluate new configurations much faster than repeatedly performing expensive quantum calculations.

This approach supports molecular dynamics and exploration of chemical configuration spaces. Machine learning has been extensively investigated for predicting quantum-mechanical energies and forces.

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8. AI and Density Functional Theory

Density Functional Theory is one of the most important computational methods in electronic-structure physics.

Instead of directly representing the complete many-electron wavefunction, DFT works primarily with electron density.

The central challenge includes determining the exchange-correlation contribution.

AI can therefore be applied to:

1. Predict exchange-correlation energies
2. Predict exchange-correlation potentials
3. Improve kinetic-energy functionals
4. Predict electron densities
5. Accelerate self-consistent calculations
6. Construct surrogate DFT models.

Research published in 2026 has investigated neural-network self-consistent fields for DFT, reflecting continuing efforts to accelerate electronic-structure calculations with machine learning.

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9. Machine-Learning Exchange-Correlation Functionals

Traditional DFT depends upon approximations to the exchange-correlation functional.

Conceptually:

electron density → exchange-correlation functional → energy

Machine learning attempts to learn this relationship from high-quality reference calculations.

The objective is:

F_AI[n] → approximation to F_exact[n]

Potential advantages include:

• improved accuracy
• better transferability
• reduced computational cost
• systematic data-driven development.

However, physical constraints remain essential. An AI functional must not merely fit a dataset; it should behave correctly outside the exact configurations represented in its training data.

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10. AI and Quantum Monte Carlo

Quantum Monte Carlo uses statistical sampling to investigate quantum systems.

AI can enter through the representation of trial wavefunctions.

A neural network can be constructed as:

Ψ_AI(R₁,R₂,…,Rₙ)

and optimized according to physical objectives such as energy minimization.

Neural-network wavefunctions have demonstrated the possibility of approaching highly accurate solutions for small systems and have been extended toward larger molecular and condensed-matter problems.

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11. Neural-Network Wavefunctions

A major conceptual development is the attempt to make the neural network itself part of the quantum-state representation.

Instead of:

Quantum calculation → data → AI prediction

the architecture becomes:

Quantum Hamiltonian → neural representation of Ψ → optimization → physical observables

This is fundamentally different from simply training an AI model to reproduce a dataset.

The neural network becomes part of the computational representation of the quantum state.

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12. AI for Strongly Correlated Systems

One of the major difficulties in computational quantum physics is strong electron correlation.

Examples include:

• transition-metal compounds
• magnetic systems
• correlated solids
• superconducting materials
• complex molecular states.

Standard approximations can struggle in these regimes.

Recent research continues to investigate neural-network quantum Monte Carlo and related methods for treating electron correlation beyond conventional DFT.

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13. AI for Molecular Dynamics

Traditional molecular dynamics repeatedly evaluates forces:

coordinates → quantum calculation → forces → motion

This can be computationally expensive.

An AI potential changes the workflow:

quantum calculations → training dataset → AI potential → rapid force prediction → molecular dynamics

This permits much larger numbers of force evaluations.

Applications include:

• chemical reactions
• liquids
• materials
• catalysis
• interfaces
• biological molecules.

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14. Active Learning

A major challenge is generating training data.

Calculating millions of quantum-mechanical configurations can defeat the purpose of acceleration.

Active learning addresses this problem.

The process becomes:

Initial quantum dataset

↓

Train AI

↓

Search unexplored configurations

↓

Detect uncertain configurations

↓

Perform expensive quantum calculation only there

↓

Add new data

↓

Retrain

↓

Repeat

This creates an adaptive computational loop.

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15. AI and Quantum Chemistry

AI-assisted quantum chemistry can accelerate the exploration of chemical compound space.

The basic concept is:

chemical structure → AI representation → predicted quantum properties

followed by:

candidate selection → high-accuracy quantum calculation → experimental validation

This can dramatically reduce the number of expensive calculations required during molecular discovery.

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16. AI for Materials Discovery

The same architecture applies to materials.

Possible inputs include:

• crystal structure
• elemental composition
• atomic positions
• symmetry
• electronic configuration.

Possible predictions include:

• formation energy
• band gap
• stability
• magnetic properties
• conductivity-related properties
• mechanical properties.

The computational discovery cycle becomes:

Generate → predict → filter → calculate → validate → synthesize

AI therefore becomes a search engine for materials space.

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17. Inverse Quantum Design

Traditional scientific computation asks:

Given structure, what are its properties?

AI enables the inverse problem:

Given desired properties, what structure might produce them?

For example:

Desired band gap + stability + conductivity

↓

AI search

↓

candidate structures

↓

quantum-mechanical verification

↓

experimental synthesis

This represents a major transformation from simulation toward computational design.

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18. Generative AI for Quantum Systems

Generative models can potentially generate:

• molecular structures
• crystal structures
• quantum states
• candidate materials
• reaction pathways.

The architecture becomes:

Specification → generative model → candidate → quantum verification

The important principle is that AI-generated candidates must ultimately be checked against physical laws and high-quality computational or experimental evidence.

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19. Physics-Informed Machine Learning

Pure data-driven AI can produce physically unreasonable predictions.

Physics-informed machine learning attempts to incorporate physical constraints directly.

Possible constraints include:

• conservation of energy
• conservation of momentum
• symmetry
• translational invariance
• rotational invariance
• particle exchange symmetry
• boundary conditions
• known mathematical relationships.

The general philosophy is:

Data + physics → physically constrained AI

rather than:

Data alone → prediction

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20. Symmetry-Aware AI

Quantum systems contain powerful symmetry information.

Examples include:

• rotational symmetry
• translational symmetry
• permutation symmetry
• crystal symmetry
• spin symmetry.

AI architectures can be designed to respect these symmetries.

This can improve:

• data efficiency
• accuracy
• generalization
• computational efficiency.

It also helps prevent the model from learning relationships that violate known physical properties.

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21. Hybrid Quantum-Classical AI

A second major research direction combines classical AI with quantum computing.

A simplified architecture is:

Classical computer

↓

data encoding

↓

quantum circuit

↓

measurement

↓

classical AI optimizer

↓

updated quantum circuit

This creates a feedback loop between classical and quantum computation.

Quantum algorithms have been extensively investigated for electronic structure, quantum dynamics and quantum statistical-mechanics problems, although practical quantum advantage remains problem- and hardware-dependent.

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22. Quantum Machine Learning

Quantum machine learning reverses part of the relationship:

Instead of using classical AI to solve quantum problems, quantum computers themselves can execute machine-learning algorithms.

Important categories include:

• Quantum neural networks
• Quantum kernels
• Variational quantum algorithms
• Quantum generative models
• Quantum classifiers
• Hybrid quantum-classical models.

QML remains an emerging field, with important unresolved issues involving scalability, state preparation, noise and meaningful benchmarking against classical methods.

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23. Classical AI vs Quantum AI

Dimension	Classical AI for Quantum Mechanics	Quantum Machine Learning
Primary hardware	CPU/GPU/accelerator	Quantum processor + classical computer
Main role	Approximate/accelerate quantum simulation	Use quantum computation for ML
Current maturity	Relatively mature	Emerging
Training data	Often quantum calculations	Classical or quantum data
Main advantage	Speed and scalability of surrogate models	Potential future quantum computational advantage
Major limitation	Training-data quality and extrapolation	Hardware noise and scalability

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24. AI + HPC

Large-scale quantum simulation requires substantial computing infrastructure.

A modern system can combine:

CPU

GPU

high-speed memory

parallel storage

high-speed interconnect

quantum chemistry software

AI frameworks

machine-learning models

This creates an integrated scientific-computing environment.

AI therefore does not eliminate conventional computational physics. Instead, it increasingly becomes another layer in the scientific-computing stack.

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25. The Complete AI–Quantum Computational Pipeline

A complete workflow can be represented as:

Physical system

↓

Hamiltonian

↓

Mathematical representation

↓

Quantum solver

↓

Reference dataset

↓

Data cleaning

↓

Feature/representation generation

↓

AI model

↓

Training

↓

Validation

↓

Uncertainty estimation

↓

AI prediction

↓

Quantum verification

↓

Scientific interpretation

↓

Experimental validation

This closed loop is one of the most important architectures for AI-assisted computational physics.

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26. The Training Dataset Problem

AI is only as reliable as the data and assumptions behind it.

Quantum datasets may contain:

• atomic coordinates
• energies
• forces
• electron densities
• wavefunctions
• orbital information
• transition states
• excitation energies.

Important dataset problems include:

• insufficient coverage
• biased sampling
• inaccurate reference calculations
• inconsistent computational methods
• duplicate configurations
• unphysical structures
• poor representation of rare events.

Therefore, dataset engineering is a scientific problem rather than merely a software problem.

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27. Accuracy, Generalization and Extrapolation

An AI model can achieve excellent accuracy inside its training distribution while failing dramatically outside it.

This creates a critical distinction:

Interpolation ≠ extrapolation

For example, an AI trained on one class of molecular structures may perform poorly on a chemically different class.

Consequently, quantum verification remains essential.

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28. Uncertainty Quantification

A trustworthy AI quantum simulator should ideally answer two questions:

What does the model predict?

and

How confident is the model?

Uncertainty estimation can identify configurations requiring additional quantum calculations.

This makes uncertainty a component of the active-learning loop.

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29. Explainability

Scientific AI should ideally provide more than predictions.

Researchers need to understand:

• why the model predicts a particular property
• which structural features matter
• whether the prediction respects physical constraints
• whether the result is inside the training distribution.

This motivates research into interpretable and physics-aware AI.

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30. Major Applications

AI-driven computational quantum mechanics has potential applications across:

Chemistry

• reaction prediction
• molecular energetics
• catalysis
• spectroscopy
• drug discovery.

Materials science

• semiconductor materials
• batteries
• catalysts
• magnetic materials
• superconductors
• nanomaterials.

Physics

• many-body systems
• quantum dynamics
• condensed matter
• statistical mechanics.

Energy

• photovoltaics
• batteries
• hydrogen technologies
• fuel cells.

Nanotechnology

• quantum dots
• nanoscale devices
• molecular electronics.

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31. The Semiconductor Connection

The relationship between AI and quantum mechanics is particularly important to semiconductor technology.

Quantum calculations can investigate:

• electronic band structures
• defects
• interfaces
• carrier behavior
• crystal structures
• semiconductor materials.

AI can then accelerate the exploration of enormous materials spaces.

This creates a pathway:

Quantum physics → materials simulation → AI prediction → semiconductor design → manufacturing

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32. The Drug-Discovery Connection

Molecular quantum mechanics provides information about:

• molecular energies
• electron distribution
• molecular interactions
• reaction pathways
• binding-related properties.

AI can use quantum-generated information to search enormous chemical spaces more efficiently.

The resulting architecture is:

quantum chemistry + AI + molecular generation + experimental testing

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33. AI as a Scientific Accelerator

The most realistic near-term role of AI is not necessarily replacing quantum mechanics.

It is acting as an accelerator.

Instead of performing:

1,000,000 expensive quantum calculations

one might perform:

10,000 carefully selected quantum calculations

and use AI to approximate or prioritize the remaining search space.

This changes computational science from brute-force calculation toward intelligent sampling.

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34. AI as a Quantum Solver

A more ambitious direction is to use AI inside the solution process itself.

The architecture becomes:

Hamiltonian

↓

AI representation

↓

optimization

↓

wavefunction/density

↓

energy

↓

self-consistency

This is considerably more fundamental than using AI merely as a post-processing tool.

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35. The Emerging Scientific Architecture

The future computational architecture can be represented as:

Quantum Mechanics

↕

Numerical Methods

↕

High-Performance Computing

↕

Machine Learning

↕

Generative AI

↕

Quantum Computing

↕

Experimental Science

These technologies are increasingly becoming interconnected rather than independent disciplines.

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36. Major Limitations

Important limitations remain.

36.1 Data requirements

High-quality quantum data can be expensive.

36.2 Transferability

A model trained for one chemical or physical domain may fail elsewhere.

36.3 Physical consistency

AI predictions can violate known physical constraints unless these are incorporated.

36.4 Computational cost

Training very large models can itself require substantial computing resources.

36.5 Interpretability

A highly accurate model may still provide limited physical insight.

36.6 Benchmarking

Claims of AI advantage require comparison against strong conventional computational methods.

36.7 Quantum hardware limitations

Quantum-machine-learning approaches face additional challenges involving noise, scalability, state preparation and measurement.

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37. Future Research Directions

Major research directions include:

1. Neural-network wavefunctions
2. AI-enhanced DFT
3. Machine-learned exchange-correlation functionals
4. Machine-learned kinetic-energy functionals
5. AI quantum Monte Carlo
6. Neural interatomic potentials
7. Active-learning quantum simulations
8. Generative molecular design
9. AI materials discovery
10. Physics-informed neural networks
11. Symmetry-preserving architectures
12. Quantum machine learning
13. Hybrid quantum-classical algorithms
14. AI-assisted quantum error mitigation
15. AI-controlled scientific experiments.

Recent work on machine-learning-enhanced orbital-free DFT illustrates another direction: using ML to improve kinetic-energy functionals, pseudopotentials and electron-density prediction for very large simulations.

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38. The Long-Term Vision

The ultimate objective is an autonomous scientific discovery system.

A possible future architecture is:

Scientific question

↓

AI interprets problem

↓

Generates candidate hypotheses

↓

Constructs computational model

↓

Runs quantum simulation

↓

Analyzes results

↓

Identifies uncertainty

↓

Requests additional calculations

↓

Generates improved hypotheses

↓

Designs candidate molecule/material

↓

Quantum verification

↓

Experimental verification

↓

AI learns from experiment

↓

Next scientific cycle

This represents a transition from conventional computer-assisted science toward increasingly autonomous computational discovery.

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39. Conclusion

AI algorithms are becoming an important computational layer for quantum mechanics.

Their role ranges from relatively straightforward prediction of quantum-mechanical properties to much more ambitious attempts to represent wavefunctions, improve density-functional approximations and participate directly in quantum-state optimization.

The most important principle is that AI does not make quantum mechanics unnecessary. Rather, AI provides new ways of representing, approximating, accelerating and exploring quantum-mechanical calculations.

The emerging field can therefore be summarized as:

Quantum mechanics provides the physical laws.

Numerical methods provide the computational machinery.

High-performance computing provides the computational scale.

AI provides adaptive approximation and pattern discovery.

Quantum computing may eventually provide new computational capabilities.

Experiment provides physical validation.

Together these technologies create a new computational paradigm for chemistry, physics, materials science, nanotechnology, energy research and scientific discovery.

The central scientific challenge for the coming decades will be to build AI systems that are not merely statistically accurate, but physically consistent, mathematically controlled, computationally scalable, uncertainty-aware and capable of discovering genuinely new quantum phenomena.