Source-linked AI summary
Machine Learning for Quantum Matter
Juan Carrasquilla
TL;DR
Quantum matter research faces difficult many-body problems, while machine learning offers methods suited to related high-dimensional computational tasks. This review surveys machine-learning applications spanning neural-network quantum states, Monte Carlo, quantum-state reconstruction, control, circuits, and quantum-physics-inspired learning. It highlights opportunities for more accurate and scalable simulations, while noting that sampling neural-network quantum states can be computationally intractable.
Problem
Research in quantum matter and strongly correlated systems requires computationally demanding methods for many-body states, simulations, tomography, and control.
Method
The paper reviews and adapts machine-learning approaches across quantum-state representations, Monte Carlo simulations, quantum tomography, quantum control, circuits, and tensor-network-inspired learning.
Results
The reviewed applications include reduced simulation complexity, retained accuracy for important correlation functions, improved quantum-control performance, and accelerated quantum-circuit parameter searches.
Takeaways & Limitations
Machine learning may help predict novel phenomena rapidly, improve Monte Carlo simulations, and extend accessible many-body simulation regimes.
Takeaways & Limitations
Sampling families of neural-network quantum states, particularly restricted Boltzmann machines, is computationally intractable despite heuristic algorithms.
Abstract
from arXiv · showhide
Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials science, statistical mechanics, quantum information, quantum gravity, and large-scale numerical simulations. Recently, researchers interested quantum matter and strongly correlated quantum systems have turned their attention to the algorithms underlying modern machine learning with an eye on making progress in their fields. Here we provide a short review on the recent development and adaptation of machine learning ideas for the purpose advancing research in quantum matter, including ideas ranging from algorithms that recognize conventional and topological states of matter in synthetic an experimental data, to representations of quantum states in terms of neural networks and their applications to the simulation and control of quantum systems. We discuss the outlook for future developments in areas at the intersection between machine learning and quantum many-body physics.
1. Introduction
Machine learning has drawn interest in quantum matter because many-body and machine-learning problems share challenging high-dimensional structures. The review surveys adaptations of machine-learning methods across quantum matter, strongly correlated systems, and related areas.
- Many-body state spaces grow exponentially with particle number, paralleling machine learning’s curse of dimensionality.
- Modern machine-learning architectures may therefore provide scalable tools for tasks in quantum matter, strongly correlated systems, quantum information, and statistical physics.
- It also discusses machine-learning speed-ups, machine learning for quantum technology, and quantum generalizations of statistical learning concepts.
- The review covers machine learning for fermion simulations, phase identification, neural-network quantum states, Monte Carlo acceleration, quantum control, and quantum-physics-inspired machine learning.
2. Machine learning
Machine learning includes supervised, unsupervised, semi-supervised, and reinforcement-learning settings distinguished by their data, objectives, and training procedures. These frameworks cover prediction, structure discovery, learning from limited labels, and reward-driven action selection.
- Supervised Learning: Supervised learning infers predictions from input vectors paired with target outputs, including discrete classification and continuous regression.
- Learning-task categories: Figure 1 distinguishes classification, regression, clustering, and semi-supervised classification by their targets, grouping structure, and labelled-data availability.
- Unsupervised learning: Unsupervised learning discovers hidden structure from unlabelled inputs, including clusters, probability distributions, and low-dimensional representations.
- Semi-supervised learning: Semi-supervised learning combines a small amount of labelled data with a large amount of unlabelled data for classification.
- Reinforcement learning: Reinforcement learning discovers actions that maximize numerical rewards through trial and error rather than direct exposure to optimal actions.
3. Machine learning in simulations of strongly correlated fermions
Machine learning has been applied to molecular and strongly correlated simulations to reduce computational costs while preserving useful physical outputs. Reported approaches include accelerated density-functional-theory emulation and kernel-based impurity-model calculations.
- Supervised machine learning accurately modeled molecular atomization energies using energies computed with hybrid density-functional theory.
- Machine-learning approaches bypassing Kohn–Sham equations reduce density-functional-theory cost to linear system-size scaling while emulating exact Kohn–Sham DFT with high fidelity.
- Kernel methods were applied in dynamical mean-field theory to find the Green’s function of the Anderson impurity model.
4. Machine learning phases of matter in synthetic and experimental data
Machine learning is used to characterize phases and hidden order in both simulated and experimental quantum-matter data. Experimental applications address noisy measurements and can identify predictive theories, phase transitions, and electronic ordering.
- Machine learning has been applied to glasses and other complex amorphous systems for automatic characterization of natural structures.
- Quantum-gas-microscope data show that machine learning can distill microscopic mechanisms and hidden order from noisy experimental measurements.
- Machine learning applied to experimental snapshots helped identify the most predictive theory among competing theories of quantum many-body states.
- Artificial neural networks identified quantum phase transitions from single-shot momentum-space density images with greater accuracy than conventional methods.
5. Renormalization group and its relation to machine learning
Renormalization-group ideas have been connected to deep learning through structural analogies and exact mappings. Machine-learning-based RG schemes can learn coarse-graining procedures and relevant degrees of freedom from data.
- RG studies how physical systems change across length scales and underpins the understanding of phase transitions and critical phenomena.
- Deep neural networks and RG have been linked because both extract increasingly higher-level structure through layered transformations.
- A specific deep architecture based on stacked RBMs has an exact mapping to variational RG.
- Training stacked RBMs on two-dimensional Ising-model data approximately implements coarse-graining similar to Kadanoff’s block renormalization.
- Mutual-information maximization can identify relevant degrees of freedom for RG decimation without prior system knowledge.
6. Neural-network quantum states and their applications
Neural-network quantum states represent many-body wavefunctions with flexible neural architectures, addressing the exponential complexity of quantum-state specification. Applications include exact representations, variational simulation, and alternative sampling strategies, while sampling remains computationally intractable for important model families.
- Neural-network quantum states represent quantum states by using neural-network function approximators for their wavefunctions.
- Early neural-network applications represented single-particle wavefunctions with fully connected networks optimized to solve Schrödinger equations in several systems.
- Convolutional architectures can encode toric-code constraints and represent computational-basis wavefunction amplitudes for spin configurations.
- RBMs provide variational quantum-state representations and have yielded exact representations for several symmetry-protected and topologically ordered states.
- Sampling families of neural-network quantum states, particularly RBMs, is computationally intractable despite heuristic sampling and normalization methods.
- Autoregressive quantum-state representations allow uncorrelated sampling, avoiding the Markov-chain costs and potential biases of traditional variational Monte Carlo.
7. Machine learning acceleration of Monte Carlo simulations
Machine learning is used to accelerate Monte Carlo simulations, whose convergence can become slow for large systems near critical points. Learned update schemes, effective models, and neural solvers improve computational efficiency across several quantum and statistical-physics settings.
- Monte Carlo methods study ground-state, excited-state, finite-temperature, and nonequilibrium properties of quantum many-body systems.
- Near critical points, large-system Monte Carlo simulations suffer slow convergence because general efficient update algorithms are lacking.
- Self-learning Monte Carlo learns efficient updates from trial configurations and achieved a 10 to 20 times speedup at a phase transition.
- In the Holstein model, incorporating physical Z2 symmetry reduced computational complexity from O(L11) to O(L7) and improved transition-temperature accuracy by an order of magnitude.
- A convolutional autoencoder reduced DMFT computational complexity while retaining accuracy relative to exact impurity-solver comparisons.
- Flow-based generative models systematically improve Markov-chain autocorrelation times in φ4-theory simulations.
8. Quantum information, quantum control, and quantum computation
Machine learning is applied across quantum measurement, state reconstruction, error correction, and control, addressing scaling and noise challenges in quantum technologies. Reviewed studies report accurate estimation, scalable reconstruction, improved decoding, and enhanced quantum-control performance.
- Quantum measurement: Particle-swarm policies achieve optimal precision scaling for single-shot interferometric phase estimation.The setup estimates an unknown phase difference between the arms of a Mach-Zehnder interferometer.
- Quantum measurement: Neural networks estimate coherent and incoherent process rates from discretized time records without characterizing quantum or classical noise.The estimation task is formulated as regression for simulated quantum systems.
- Quantum state reconstruction: Machine-learning quantum state tomography scales beyond small systems but assumes the state has structure amenable to the chosen architecture.Exact tomography requires exponentially scaling measurements, analysis time, and storage, whereas neural networks reconstructed entangled states with more than a hundred qubits.
- Quantum state reconstruction: Experimental Rydberg-atom data enabled reconstruction of quantum many-body states from eight and nine atoms using one measurement basis and regularization for measurement errors.The reconstruction used data from a programmable quantum simulator.
- Quantum error correction: Neural belief-propagation decoders improve quantum low-density parity-check decoding accuracy by orders of magnitude across three code families.The reported codes are the toric, quantum bicycle, and quantum hypergraph product codes.
- Quantum error correction: Machine-learning decoders combined with quantum-error-correction domain knowledge can perform on par with hand-made algorithms.The review identifies this combination as a viable route toward decoding schemes for broader error models and codes.
- Quantum control: Reinforcement learning improves quantum-control speed and fidelity against leakage and stochastic control errors for broad families of two-qubit gates.One reviewed framework reports a two-order-of-magnitude improvement in average gate error over stochastic gradient descent and up to one order of magnitude in gate time over optimal synthesis counterparts.
- Quantum circuits and gates: Meta-learning supplies initialization heuristics that accelerate parameterized-circuit optimization by several orders of magnitude and can yield superior optima.Policy-gradient reinforcement learning is also reported as noise-robust for QAOA parameter optimization and effective in quantum state transfer.
9. Quantum physics inspired machine learning
Quantum physics has inspired classical and quantum machine-learning methods, especially tensor networks and parameterized quantum circuits. These approaches support supervised learning, generative modeling, and other data-driven tasks, while quantum circuits may offer quantum speedups.
- Tensor networks: Tensor networks, developed to represent entanglement in many-body physics, have been adapted for supervised learning through matrix product states.The approach uses nonlinear kernel learning for multiclass classification.
- Tensor networks: Tensor networks have also been applied to dimensionality reduction, unsupervised learning, generative modeling, representation learning, sequence-to-sequence learning, language modeling, and Bayesian inference.The reviewed literature includes matrix product states, multiscale tensor networks, and matrix product operators.
- Quantum machine learning: Parameterized quantum circuits are studied for supervised learning and generative modeling, with potential quantum speedups in machine-learning implementations.The review notes experimental demonstrations of parameterized quantum models.
- Quantum machine learning: Quantum circuit Born machines treat circuit-produced wavefunctions as generative models for sampling low-energy Ising distributions.Related work includes a low-depth variational algorithm and numerical simulations of quantum-circuit generative modeling.
10. Conclusions and outlook
The review finds expanding opportunities at the intersection of machine learning and quantum many-body physics, while identifying accurate, physics-informed models as a near-term goal. It anticipates applications to difficult simulations, Monte Carlo, nonequilibrium dynamics, and the limits of classical simulation.
- Conclusions: Recent work demonstrates opportunities for machine learning techniques, ideas, and research culture in quantum many-body physics.The review describes machine learning as spreading through quantum matter and strongly correlated-systems research.
- Outlook: A near-term goal is combining quantum many-body physics with machine learning to predict novel phenomena at modern machine-learning speed and necessary accuracy.The stated goal is prospective rather than a reported achieved result.
- Outlook: Future applications may improve approximations for frustrated magnetism and fermionic matter, reduce critical slowing down in Monte Carlo, and extend nonequilibrium simulation.The review also connects these developments to identifying when classical simulation ceases to suffice.
- Outlook: Physics may continue contributing new machine-learning models and training strategies, including tensor networks and quantum Boltzmann and Helmholtz machines.The outlook includes studying their expressive power and characterization.
- Outlook: The field is described as being at an early stage of sustained collaboration among condensed-matter, quantum-information, and atomic, molecular, and optical physics researchers.The review anticipates further results from continued work at this intersection.
Funding
The acknowledgments state that J.C. received support from several Canadian research organizations and a Google Quantum Research Award.
- Funding: J.C. acknowledges support from NSERC, SHARCNET, Compute Canada, a Google Quantum Research Award, and CIFAR’s AI chair program.These are the funding and infrastructure sources listed in the acknowledgments.