Science and engineering
Machine learning for quantum matter
Researchers use neural networks as variational wavefunctions to find ground states of many-body spin and electron systems, and use classifiers to detect phase transitions from simulated or measured data. Results are checked against exact solutions on small systems.
How machine learning is used for quantum matter
Neural networks as wavefunctions
A neural network can represent the amplitude of a many-body wavefunction for each configuration. Its parameters are optimised to minimise energy, giving a flexible variational method for ground states and dynamics.
Real exampleNeural-network quantum states (Carleo and Troyer, 2016)Introduced a variational representation of quantum states based on neural networks and applied it to ground states and time evolution of interacting spin models in one and two dimensions.
Detecting phases and transitions
Classifiers trained on sampled configurations can tell phases apart, and where they become uncertain points to the transition. Unsupervised methods can find structure without labels.
Real exampleMachine learning phases of matter (Carrasquilla and Melko, 2016)Trained a standard feed-forward neural network to detect phases and order parameters directly from raw configurations sampled with Monte Carlo.
Solving for many-electron ground states
Deep wavefunction models built to respect the antisymmetry of electrons can approach very accurate energies for atoms and molecules from first principles.
Real exampleFermiNet (Pfau et al., 2019)Introduced the Fermionic Neural Network, a deep learning wavefunction ansatz for solving the many-electron Schrödinger equation.
Analysing experimental snapshots
Quantum gas microscopes record real-space snapshots of atoms in optical lattices. Classifiers can compare these snapshots with competing theories to see which one fits the data better.
Real exampleClassifying snapshots of the doped Hubbard model (Bohrdt et al., 2018)Used machine learning to classify experimental quantum gas microscope snapshots of the two-dimensional Fermi-Hubbard model and compare them with two theoretical approaches.
Can you learn machine learning for quantum many-body physics?
Yes, if you have or build the physics background. This field sits at graduate level: you need quantum mechanics and many-body methods, plus Python, Monte Carlo statistics and neural networks. The machine learning side is usually the easier half.
- PythonWrite simulation and analysis code; NetKet and similar libraries are Python-based.Learn it in Python
- Linear algebraHamiltonians, eigenstates and tensor operations are linear algebra at scale.Learn it in Maths
- Monte Carlo and statisticsVariational Monte Carlo relies on sampling, and every estimate carries a statistical error.Learn it in Statistics
- Neural networksFeed-forward, convolutional and transformer networks used as wavefunctions and classifiers.Learn it in Deep Learning
- Many-body reference methodsExact diagonalisation, quantum Monte Carlo and tensor networks give the results that learned methods are checked against.
Moving into machine learning for quantum matter
If you already work in the field
Condensed-matter physicists already know the models, the methods and the reference results to check against. Add PyTorch or JAX and try NetKet on a spin model where exact results exist. Most of this work is academic, with some roles in quantum technology and materials companies.
If you come from data science or ML
Machine learning practitioners need quantum mechanics, second quantisation and the standard lattice models such as the Ising, Heisenberg and Hubbard models. A graduate course or textbook in many-body physics is the realistic route.
Roles that do this workPostdoctoral researcher, condensed matter theoryComputational physicistResearch scientist, quantum simulationResearch software engineer
Tools you will use
| Tool | What you use it for |
|---|---|
| NetKet | Train neural quantum states with variational Monte Carlo. |
| JAX | Write custom neural wavefunctions and differentiate through them. |
| TeNPy | Compute tensor-network reference results such as DMRG ground states. |
| QuSpin | Run exact diagonalisation of spin, fermion and boson models for small-system references. |
Public data to practise on
- PennyLane quantum spin systems: Ising, Heisenberg and Hubbard spin-system datasets from PennyLane across a range of model parameters.
- V-score variational benchmark: Published variational ground-state energies for many lattice models to compare your own results against.
Your first project
Download transverse-field Ising data from PennyLane's spin-system datasets, fit a restricted Boltzmann machine ansatz in NetKet, and compare its energy with the dataset's reference values and a mean-field ansatz using relative error.
Common questions
What is a neural-network quantum state?
It is a neural network that outputs the amplitude of a many-body wavefunction for each configuration. Its parameters are optimised variationally to minimise energy, like other variational methods.
Can machine learning detect phase transitions?
Yes. Supervised and unsupervised methods can identify phases from sampled configurations or experimental snapshots, although interpreting what the model learned still needs physics.
Is machine learning better than tensor networks or quantum Monte Carlo?
Not universally. Each method has regimes where it works best; neural states are promising in two dimensions and for fermions, and are checked against established methods wherever those apply.
Do I need a PhD for this area?
Most of the work happens in research groups, so a PhD in physics or chemistry is the usual route. The skills transfer well to industry machine learning roles later.
Courses for these skills
- Deep Learning with PyTorchStudy neural fitting and loss design.Syllabus available · lessons open as produced
- Maths for Machine LearningConnect derivatives, vectors and physical objectives.26 published lessons · all planned lessons open
- Statistics and Probability for Machine LearningDistinguish confidence, prediction uncertainty and calibration.41 published lessons · all planned lessons open
- Practical Machine Learning in PythonCompare losses and models for continuous outcomes.51 published lessons · more lessons in production
New to programming or maths? Start with Python, or follow the machine learning path in order. Published lessons are free to read; compare Free and Pro.