Machine Learning for Quantum Many-Body Systems

Jun 12, 2023, 8:15 a.m. → Jun 16, 2023, 5:00 p.m. America/Toronto

PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

Juan Felipe Carrasquilla Álvarez (Vector Institute & University of Toronto), Lauren Hayward (Perimeter Institute), Miles Stoudenmire (Flatiron Institute), Roger Melko (Perimeter Institute & University of Waterloo), Stefanie Czischek (University of Ottawa)

Machine learning techniques are rapidly being adopted into the field of quantum many-body physics, including condensed matter theory, experiment, and quantum information science. The steady increase in data being produced by highly-controlled quantum experiments brings the potential of machine learning algorithms to the forefront of scientific advancement. Particularly exciting is the prospect of using machine learning for the discovery and design of molecules, quantum materials, synthetic matter, and computers. In order to make progress, the field must address a number of fundamental questions related to the challenges of studying many-body quantum mechanics using classical computing algorithms and hardware.

The goal of this conference is to bring together experts in computational physics, machine learning, and quantum information, to make headway on a number of related topics, including:
- Data-drive quantum state reconstruction
- Machine learning strategies for quantum error correction and quantum control
- Neural-network inspired wavefunctions
- Near-term prospects for data from quantum devices
- Machine learning for quantum algorithm discovery

pirsa.org/C23002

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Monday, June 12

9:00 a.m. → 9:55 a.m. Registration

9:55 a.m. → 10:00 a.m. Welcome and Opening Remarks

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

Speaker: Roger Melko (Perimeter Institute & University of Waterloo)

10:00 a.m. → 10:45 a.m. [Virtual] Exploring Quantum Science with Machine Learning

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

Speaker: Di Luo (Massachusetts Institute of Technology)

10:45 a.m. → 11:15 a.m. Coffee Break

11:15 a.m. → 12:00 p.m. 2D quantum matter with neural quantum states

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

Neural quantum states (NQSs) have emerged as a novel promising numerical method to solve the quantum many-body problem. However, it has remained a central challenge to train modern large-scale deep network architectures to desired quantum state accuracy, which would be vital in
utilizing the full power of NQSs and making them competitive or superior to conventional numerical approaches. Here, we propose a minimum-step stochastic reconfiguration (MinSR) method that reduces the optimization complexity by orders of magnitude while keeping similar accuracy as compared to conventional stochastic reconfiguration. MinSR allows for accurate training on unprecedentedly deep NQS with up to 64 layers and more than 105 parameters in the spin-1/2 Heisenberg J1-J2 models on the square lattice. We find that this approach yields better variational energies as compared to existing numerical results and we further observe that the accuracy of our ground state calculations approaches different levels of machine precision on modern GPU and TPU hardware. The MinSR method opens up the potential to make NQS superior as compared to conventional computational methods with the capability to address yet inaccessible regimes for two-dimensional quantum matter in the future.

Speaker: Markus Heyl (Max Planck Institute for the Physics of Complex Systems)

12:00 p.m. → 2:00 p.m. Lunch

2:00 p.m. → 2:45 p.m. Near Term Distributed Quantum Computation using Optimal Auxiliary Encoding

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

Speaker: Abigail McClain Gomez (Harvard University)

2:45 p.m. → 3:15 p.m. Coffee Break

3:15 p.m. → 3:45 p.m. Dimension reduction of the Functional Renormalization Group

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

In this work, we use data-driven methods to reduce the dimensionality of the vertex function for the Hubbard model and spin liquid model. By employing a deep learning architecture based on the autoencoder, we show that the functional renormalization group (FRG) dynamics can be efficiently learned. Our approach is compared with other methods, including principal component analysis and dynamic mode decomposition. Our results demonstrate the effectiveness of our proposed approach for understanding the FRG flow in these models.

Speaker: Jiawei Zang (Columbia University)

3:45 p.m. → 4:15 p.m. Neural quantum states for simulating strongly interacting fermions in continuous space

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09

We introduce a novel neural quantum state architecture for the accurate simulation of extended, strongly interacting fermions in continuous space. The variational state is parameterized via permutation equivariant message passing neural networks to transform single-particle coordinates to highly correlated quasi-particle coordinates. We show the versatility and accuracy of this Ansatz by simulating the ground-state of the 3D homogeneous electron gas at different densities and system sizes. Our model respects basic symmetries of the Hamiltonian, such as continuous translation symmetries. We compare our ground-state energies to results obtained by different state-of-the-art NQS Ansaetze for continuous space, as well as to different quantum chemistry methods. We obtain better or comparable ground-state energies, while using orders of magnitudes less variational parameters and optimization steps. We investigate its capability of identifying and representing different phases of matter without imposing any structural bias toward a given phase. We scale up to system sizes of N=128 particles, opening the door for future work on finite-size extrapolations to the thermodynamic limit.

Speaker: Jannes Nys ( École Polytechnique Fédérale de Lausanne)

4:15 p.m. → 5:15 p.m. Self-organized Discussions

Tuesday, June 13

10:00 a.m. → 10:45 a.m. Automated Characterization of Engineered Quantum Materials

Speaker: Eliška Greplová (Delft University)

10:45 a.m. → 11:15 a.m. Coffee Break

11:15 a.m. → 12:00 p.m. Learning Feynman Diagrams with Tensor Trains

Speaker: Xavier Waintal (CEA Grenoble)

12:00 p.m. → 1:30 p.m. Lunch

1:30 p.m. → 2:15 p.m. Data-centric learning of Quantum Many-body States with Classical Machines

Speaker: Eun-Ah Kim (Cornell University)

2:15 p.m. → 2:45 p.m. Coffee Break

2:45 p.m. → 3:15 p.m. Quantum and Classical Dynamics from a Time Dependent Variational Principle

Speaker: Moritz Reh (Heidelberg University)

3:15 p.m. → 3:45 p.m. A QMC study of the Rydberg phase diagram

Speaker: Anna Knörr (Perimeter Institute)

3:45 p.m. → 4:00 p.m. Break

4:00 p.m. → 5:30 p.m. Colloquium

Speaker: Neil Turok (University of Edinburgh)

Wednesday, June 14

10:00 a.m. → 11:00 a.m. [VIRTUAL] A deep variational free energy approach to dense hydrogen

Dense hydrogen, the most abundant matter in the visible universe, exhibits a range of fascinating physical phenomena such as metallization and high-temperature superconductivity, with significant implications for planetary physics and nuclear fusion research. Accurate prediction of the equations of state and phase diagram of dense hydrogen has long been a challenge for computational methods. In this talk, we present a deep generative model-based variational free energy approach to tackle the problem of dense hydrogen, overcoming the limitations of traditional computational methods. Our approach employs a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wavefunction at given proton positions. The joint optimization of these two neural networks leads to a comparable variational free energy to previous coupled electron-ion Monte Carlo calculations. Our results suggest that hydrogen in planetary conditions is even denser than previously estimated using Monte Carlo and ab initio molecular dynamics methods. Having reliable computation of the equation of state for dense hydrogen, and in particular, direct access to its entropy and free energy, opens new opportunities in planetary modeling and high-pressure physics research.

Speaker: Lei Wang (Chinese Academy of Sciences)

11:00 a.m. → 11:30 a.m. Coffee Break

11:30 a.m. → 12:15 p.m. Quantum-enhanced reinforcement learning

The field of artificial intelligence (AI) has experienced major developments over the last decade. Within AI, of particular interest is the paradigm of reinforcement learning (RL), where autonomous agents learn to accomplish a given task via feedback exchange with the world they are placed in, called an environment. Thanks to impressive advances in quantum technologies, the idea of using quantum physics to boost the performance of RL agents has been recently drawing the attention of many scientists. In my talk I will focus on the bridge between RL and quantum mechanics, and show how RL has proven amenable to quantum enhancements. I will provide an overview of the most recent results — for example, the development of agents deciding faster on their next move [1]— and I will then focus on how the learning time of an agent can be reduced using quantum physics. I will show that such a reduction can be achieved and quantified only if the agent and the environment can also interact quantumly, that is, if they can communicate via a quantum channel [2]. This idea has been implemented on a quantum platform that makes use of single photons as information carriers. The achieved speed-up in the agent’s learning time, compared to the fully classical picture, confirms the potential of quantum technologies for future RL applications.

[1] Sriarunothai, T. et al. Quantum Science and Technology 4, 015014 (2018).
[2] Saggio, V. et al. Nature 591, 229–233 (2021).

Speaker: Valeria Saggio (Massachusetts Institute of Technology)

12:15 p.m. → 2:00 p.m. Lunch

2:00 p.m. → 2:30 p.m. Unsupervised detection of quantum phases and their order parameters from projective measurements

Recently, machine learning has become a powerful tool for detecting quantum phases. While the sole information about the presence of transition is valuable, the lack of interpretability and knowledge on the detected order parameter prevents this tool from becoming a customary element of a physicist's toolbox. Here, we report designing a special convolutional neural network with adaptive kernels, which allows for fully interpretable and unsupervised detection of local order parameters out of spin configurations measured in arbitrary bases. With the proposed architecture, we detect relevant and simplest order parameters for the one-dimensional transverse-field Ising model from any combination of projective measurements in the x, y, or z basis. Moreover, we successfully tackle the bilinear-biquadratic spin-1 model with a nontrivial nematic order. We also consider extending the proposed approach to detecting topological order parameters. This work can lead to integrating machine learning methods with quantum simulators studying new exotic phases of matter.

Speaker: Anna Dawid (Flatiron Institute)

2:30 p.m. → 3:00 p.m. Investigating Topological Order with Recurrent Neural Network Wave Functions

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. In this talk, we will illustrate how to use 2D RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we will demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. Overall, we will show that RNN wave functions constitute a powerful tool for studying phases of matter beyond Landau's symmetry-breaking paradigm.

Speaker: Mohamed Hibat Allah (Vector Institute)

3:00 p.m. → 3:30 p.m. Coffee Break

3:30 p.m. → 4:15 p.m. Ethics PROBES: Artificial Intelligence, Machine Learning, & Quantum Computing

Speaker: Gus Skorburg (University of Guelph)

4:15 p.m. → 5:30 p.m. Discussion Session: The Ethics of Quantum and AI

Speaker: Gus Skorburg (University of Guelph)

5:30 p.m. → 7:00 p.m. Poster Session and Social

Thursday, June 15

10:00 a.m. → 10:45 a.m. [VIRTUAL] Emergent Classicality from Information Bottleneck

Our universe is quantum, but our everyday experience is classical. Where is the boundary between quantum and classical worlds? How does classical reality emerge in quantum many-body systems? Does the collapse of the quantum states involve intelligence? These are fundamental questions that have puzzled physicists and philosophers for centuries. The recent development of quantum information science and artificial intelligence offers new opportunities to investigate these old problems. In this talk, we present our preliminary research on using a transformer-based language model to process randomized measurement data collected from Schrödinger’s cat quantum state. We show that the classical reality emerges in the language model due to the information bottleneck: although our training data contains the full quantum information of Schrödinger’s cat, a weak language model can only learn the classical reality of the cat from the data. Our study opens up a new avenue for using the big data generated on noisy intermediate-scale quantum (NISQ) devices to train generative models for representation learning of quantum operators, which might be a step toward our ultimate goal of creating an artificial intelligence quantum physicist.

Speaker: Yi-Zhuang You (University of California, San Diego)

10:45 a.m. → 11:15 a.m. Coffee Break

11:15 a.m. → 12:00 p.m. Talk - tbc

Speaker: Stefanie Czischek (University of Ottawa)

12:00 p.m. → 2:00 p.m. Lunch

2:00 p.m. → 3:30 p.m. Panel Discussion

Speakers: Edwin Miles Stoudenmire ( Flatiron Institute Center for Computational Quantum Physics), Eliška Greplová (Delft University), Juan Felipe Carrasquilla (Vector Institute), Mykola Maksymenko (Haiqu)

3:30 p.m. → 4:00 p.m. Coffee Break and group photo

4:00 p.m. → 4:45 p.m. Machine Learning of Conserved Quantities and Symmetry Invariants

Speaker: Sebastian Wetzel (University of Waterloo)

4:45 p.m. → 5:30 p.m. Solving 2D quantum matter with neural quantum states

Neural quantum states (NQSs) have emerged as a novel promising numerical method to solve the quantum many-body problem. However, it has remained a central challenge to train modern large-scale deep network architectures to desired quantum state accuracy, which would be vital in utilizing the full power of NQSs and making them competitive or superior to conventional numerical approaches. Here, we propose a minimum-step stochastic reconfiguration (MinSR) method that reduces the optimization complexity by orders of magnitude while keeping similar accuracy as compared to conventional stochastic reconfiguration. MinSR allows for accurate training on unprecedentedly deep NQS with up to 64 layers and more than 105 parameters in the spin-1/2 Heisenberg J1-J2 models on the square lattice. We find that this approach yields better variational energies as compared to existing numerical results and we further observe that the accuracy of our ground state calculations approaches different levels of machine precision on modern GPU and TPU hardware. The MinSR method opens up the potential to make NQS superior as compared to conventional computational methods with the capability to address yet inaccessible regimes for two-dimensional quantum matter in the future.

Speaker: Markus Heyl (Max Planck Institute for the Physics of Complex Systems)

5:30 p.m. → 7:30 p.m. BBQ and PI Community Night

Friday, June 16

10:00 a.m. → 10:45 a.m. The Quantum Cartpole

How do you control something you can not look at? For controlling quantum systems, information on the system’s state could come through weak measurements. Such measurements provide some information, but will inevitably also perturb the system, meaning there is noise both in the state estimation as well as in the measurement. We study a simple single particle quantum setup (the quantum equivalent of the instability problem known as the cartpole problem) and investigate several control methods including reinforcement learning, and compare their performance.

Speaker: Evert van Nieuwenburg (Leiden University)

10:45 a.m. → 11:15 a.m. Coffee Break

11:15 a.m. → 12:00 p.m. Quantum HyperNetworks: Training Binary Neural Networks in Quantum Superposition

Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However, their training, architectural design, and hyperparameter tuning remain challenging as these involve multiple computationally expensive combinatorial optimization problems. Here we introduce quantum hypernetworks as a mechanism to train binary neural networks on quantum computers, which unify the search over parameters, hyperparameters, and architectures in a single optimization loop. Through classical simulations, we demonstrate that of our approach effectively finds optimal parameters, hyperparameters and architectural choices with high probability on classification problems including a two-dimensional Gaussian dataset and a scaled-down version of the MNIST handwritten digits. We represent our quantum hypernetworks as variational quantum circuits, and find that an optimal circuit depth maximizes the probability of finding performant binary neural networks. Our unified approach provides an immense scope for other applications in the field of machine learning.

Speaker: Estelle Inack (Perimeter Institute)

12:10 p.m. → 12:15 p.m. Closing Remarks

Speaker: Roger Melko (Perimeter Institute & University of Waterloo)

12:30 p.m. → 2:00 p.m. Lunch

2:00 p.m. → 4:00 p.m. Self-organized Discussions

4:00 p.m. → 5:00 p.m. Friday Social