Neural Quantum States for Time Evolution - Challenges and OpportunitiesIn-Person Event

18 Nov 2024, 14:00 → 20 Nov 2024, 12:00 Europe/Berlin

The complexity of simulating quantum many-body systems grows exponentially with the number of particles, making it infeasible to study anything but the smallest systems using conventionally exact methods. Approximation schemes like the density-matrix renormalization group (DMRG) have been highly effective in one-dimensional systems, providing essential insights into out-of-equilibrium dynamics. Despite these successes, simulating systems in two and three dimensions remains challenging. Interest in these higher-dimensional systems is growing, driven by the unprecedented capabilities of emerging quantum hardware.

To address the need for theoretical methods capable of accurately simulating the dynamics of higher-dimensional quantum systems, Time-Dependent Variational Principles (TDVP) have emerged as a promising approach. TDVP combines the power of variational techniques with advanced neural network representations (NQS) to efficiently approximate the complex wave functions of quantum states. While TDVP has shown significant potential to revolutionise our understanding of quantum many-body systems it introduces not only opportunities, but also challenges that require thorough discussion and investigation. In this symposium we bring together leading experts on the topic of TDVP and NQS to discuss the state of the field and future directions. Our goal is to join the force of the community in order to address the greatest challenges of the method. We seek to foster a collaborative effort to overcome these challenges to make TDVP with NQS the new gold-standard for time evolution of quantum many-body systems. See below for the list of invited speakers and the booklet with all contributions.

We invite qualified postgraduate students and researchers to register for participation. A contribution in the form of a poster is expected from anyone who seeks attandence. If financial support is required by a potential attendee we can provide that upon reasonable request in the sign up form.

Invited speakers:

Filippo Vicentini	Ecole Polytechnique
Markus Heyl	University of Augsburg
Anabelle Bohrdt	University of Regensburg
Gianluca Lagnese	Institut Jožef Stefan
Jannes Nys	École Polytechnique Fédérale de Lausanne
Juan Carrasquilla	ETH Zürich
Martin Gärttner	Friedrich Schiller University Jena
Marin Bukov	Max Planck Institute for the Physics of Complex Systems
Matija Medvidović	Columbia University
Zakari Denis	École Polytechnique Fédérale de Lausanne
Johannes Zeiher	Max-Planck Institute of Quantum Optics

 

We are grateful for the funding provided by Young Excellent Scientist Program at Forschungszentrum Jülich GmbH.

Booklet.pdf

Monday 18 November

14:00 → 14:45 Variational dynamics of continuous-variable quantum rotor models

Time-dependent variational Monte Carlo (t-VMC) has emerged as a powerful method of simulating real-time dynamics of correlated quantum systems in the recent years. With wider adoption of variational states based on neural networks, these methods have started to reach experimentally relevant time scales. However, despite rapid progress and growing interest, the t-VMC method is still relatively difficult to control and implement in high-parameter regimes of interest. After introducing the method, in this talk I will outline open problems in the field on a specific example of the quantum rotor model where the method has been successfully applied to a problem with continuous degrees of freedom.

Speaker: Matija Medvidović

14:45 → 15:30 Solving quantum and classical dissipative dynamics with artificial neural networks

We develop a variational approach to simulating the dynamics of open quantum and classical many-body systems using artificial neural networks. The parameters of a compressed representation of a probability distribution are adapted dynamically according to the Lindblad master equation or Fokker Planck equation, respectively, by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg model in one and two dimensions for up to 40 spins and by applying it to the simulation of confinement dynamics in the presence of dissipation. Also, we use normalizing flows to variationally solve diffusive classical dynamics in high dimensions.

Speaker: Marti Gärttner

15:30 → 16:15 Coffee

16:15 → 17:00 Reinforcement learning for quantum error correction

TBA

Speaker: Marín Bukov

17:00 → 17:45 Diving beyond t-VMC with state compression and tailored integration schemes

TBA

Speaker: Filippo Vicentini

17:45 → 18:00 Coffee

Tuesday 19 November

08:45 → 09:30 Fermions in Motion: A New Approach to Quantum Dynamics

Describing the real-time evolution of many-electron quantum systems is crucial for understanding the dynamical properties of condensed matter, molecular systems in quantum chemistry, and the behaviors of complex materials. However, the real-time evolution of non-equilibrium quantum electronic systems poses a significant challenge for theoretical and computational approaches. This work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by capturing many-body correlations. Our methodology introduces a parameterization of the time-evolving quantum state, enabling an accurate approximation of its evolution. We utilize the time-dependent variational Monte Carlo technique to efficiently compute optimal time-dependent parameters. Additionally, we introduce a new time-evolution method based on Taylor-root expansions of the propagator, enhancing the accuracy and efficiency of our simulations. The results showcase the ability of our variational approach to accurately capture the time evolution of quantum states, providing insight into the quantum dynamics of interacting electronic systems, beyond the capabilities of mean-field.

Speaker: Jannes Nys

09:30 → 10:15 Real-time quantum dynamics of thermal states with neural thermofields

Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal density matrices, 1D systems, and/or zero-temperature states. In this work, we propose a method to study the real-time dynamics of thermal states in two dimensions, based on thermofield dynamics, variational Monte Carlo, and neural-network quantum states. To this aim, we introduce two novel tools: (i) a procedure to accurately simulate the cooling down of arbitrary quantum variational states from infinite temperature, and (ii) a generic thermal (autoregressive) recurrent neural-network (ARNNO) Ansatz that allows for direct sampling from the density matrix using thermofield basis rotations. We apply our technique to the transverse-field Ising model subject to an additional longitudinal field and demonstrate that the time-dependent observables, including correlation operators, can be accurately reproduced for a 4×4 spin lattice. We provide predictions of the real-time dynamics on a 6×6 lattice that lies outside the reach of exact simulations.

Speaker: Zakari Denis

10:15 → 11:00 Coffee

11:00 → 11:45 Dynamics of quantum matter with classical networks and neural quantum states

Neural quantum states have emerged as a novel promising numerical
method to solve the quantum many-body problem both in and out of equilibrium.
In this talk I will discuss recent developments and challenges. I will also
highlight potential ways to solve for some of these challenges.

Speaker: Markus Heyl

12:30 → 14:00 Lunch

14:00 → 14:45 Solving the (time-dependent) Schrödinger equation

Simulating the time evolution of interacting quantum systems is in general a very hard problem. Quantum simulation experiments, such as cold atoms in optical lattices, are naturally well suited to study closed system dynamics. A bottleneck for these setups are slow data taking rates, which enable experimentalists typically only to get a limited number of projective measurements at a limited number of time steps. In this talk, I will (i) demonstrate how limited, noisy, experimental data can be useful in a hybrid approach for ground state searches using neural quantum states (NQS); and (ii) introduce a new NQS based method to simulate the time evolution of interacting quantum many-body systems.

Speaker: Annabelle Bohrdt

14:45 → 15:30 Quantum-gas microscopy of Hubbard systems

Neutral atoms trapped in optical lattices are a versatile platform to study many-body physics in and out of equilibrium.
Quantum gas microscopes provide an excellent toolbox to prepare, control and detect such systems at the level of individual atoms.
First, I will present our recent work on realizing long-range interacting Ising and Hubbard models for Rubidium atoms in optical lattices. Using off-resonant coupling from ground to Rydberg states, we induce tunable interactions via the excitation light. We probe interactions in different experiments on frozen spin systems and the itinerant regime, where they stabilize initial out-of-equilibrium states. In particular, we also observe the buildup of density-density correlations when probing a one-dimensional extended Hubbard system near equilibrium.
Second, I will introduce a new strontium setup that combines large-scale optical lattices with local control achieved through tweezer arrays. I will present our efforts on loading, cooling, and imaging individual strontium atoms in optical tweezers and lattices, where we obtain high-fidelity and low-loss imaging performance using repulsive Sisyphus-cooling. Combining optical tweezer arrays with lattices opens new perspectives to scale tweezer-based quantum simulators to larger system sizes and offers an alternative preparation route of assembled Hubbard systems in optical lattices with the prospect of combining analog and digital quantum simulation capabilities.

Speaker: Johannes Zeiher

15:30 → 16:15 Coffee

16:15 → 18:00 Posters + Discussion

20:00 → 20:45 Positive Operator Valued Measures Neural Networks for simulation of light-matter coupled systems

TBA

Speaker: Gianluca Lagnese

Wednesday 20 November

08:45 → 09:30 TBA

TBA

Speaker: Jonas Rigo

09:30 → 10:15 Neural network simulation of a spin glass dynamics transition

I will explain a recent experiment about the simulation of nonequilibrium dynamics of a magnetic spin system quenched through a quantum glass phase transition and our attempt at using neural networks to simulate the dynamics seen in the experiment.

Speaker: Juan Carrasquilla

10:15 → 11:00 Coffee

11:00 → 12:00 Discussion