Machine Learning Initiative

In this talk, I will present two recent works on electronic lattice models, both of which utilize novel numerical algorithms to achieve a deeper understanding of the many-electron problem. Competing and intertwined orders including inhomogeneous patterns of spin and charge are observed in many correlated electron materials, such as high-temperature superconductors. In arXiv:2202.11741, we introduce a new development of constrained-path auxiliary-field quantum Monte Carlo (AFMQC) method and study the interplay between thermal and quantum fluctuations in the two-dimensional Hubbard model. We identify a finite-temperature phase transition below which charge ordering sets in. Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems.  However, discerning phases with off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. In the second work arXiv:2209.10565, we study the one-dimensional extended Hubbard model using the variational uniform matrix product states algorithm. We show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors.

Zoom link:  https://pitp.zoom.us/j/97325001971?pwd=QXNmU2I0L3BxQVErMEZWSDF2bGZ0QT09

A well-established approach to solving interacting quantum systems is variational Monte Carlo. There is a lot of renewed interest in it since the introduction of neural networks as a highly expressive and unbiased variational ansatz. Similar to more traditional ansätze, neural networks struggle with solving frustrated quantum systems. A conjecture has been made that the cause of these difficulties lies in the sign structures of the ground state wavefunctions. Here, we will discuss these sign structures in more detail and try to analyze how complex they really are by establishing a connection to classical Ising models.

Zoom link:  https://pitp.zoom.us/j/99087954160?pwd=Vm5zWWRFbHBwVFR1RHZMc3ptem03QT09

The XXZ model on the three-dimensional frustrated pyrochlore lattice describes a family of rare-earth materials showing signatures of fractionalization and no sign of ordering in the neutron-scattering experiments. The phase diagram of such XXZ model is believed to host several spin-liquid states with fascinating properties, such as emergent U(1) electrodynamics with emergent photon and possible confinement-deconfinement transition. Unfortunately, numerical studies of such lattice are hindered by three-dimensional geometry and absence of obvious small parameters.
In this talk, I will present my work [Phys. Rev. X 11, 041021] on the variational study of the pyrochlore XXZ model using the RVB-inspired and Neural-Network-inspired ansätze. They yield energies better than known results of DMRG at finite bond dimension. With these wave functions, we study the properties of frustrated phase at the Heisenberg point, and observe signatures of long-range dimer correlations.

Lastly, I will sketch the prospects of using the Programmable Rydberg Simulator platform for the study of these spin-liquid states. I will construct two possible embeddings of the pyrochlore XXZ model onto the Rydberg atoms simulator, employing the notion of spin ice and perturbative hexagon flip processes.

Zoom link:  https://pitp.zoom.us/j/99480889764?pwd=cnY2RHBjeDZvRkM2K3FlYU9OWjgxUT09

Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized. In particular, for certain parameters, we will show that these neural network states can look typical in their entanglement profile while still being distinguishable from a typical state by their fractal dimensions. The obtained phase diagrams may help inform the initialization of neural network ansatzes for future computational tasks.

Zoom link:  https://pitp.zoom.us/j/94316902357?pwd=RGxWYm9EWGtGYzBvUzM5ZWdwVTB5dz09

Variational methods have proven to be excellent tools to approximate the ground states of complex many-body Hamiltonians. Generic tools such as neural networks are extremely powerful, but their parameters are not necessarily physically motivated. Thus, an efficient parametrization of the wave function can become challenging. In this talk I will introduce a neural-network-based variational ansatz that retains the flexibility of these generic methods while allowing for a tunability with respect to the relevant correlations governing the physics of the system. I will illustrate the ansatz on a model exhibiting topological phase transitions: The toric code in the presence of magnetic fields. Additionally, I will talk about the use of variational wave functions to gain physical insights beyond lattice models, in particular for the real use-case of two-dimensional materials.

The past decade has witnessed tremendous advancements in the size, coherence and control accuracy of qubits across various material platforms. In the case of superconducting qubits fabricated from Josephson junctions, quantum systems with over 50 qubits and >99% gate fidelities can now be reliably fabricated. In this talk, I will introduce the basics of superconducting qubits, with a particular focus on the implementation and calibration of two-qubit gates. I will then describe an experiment demonstrating quantum computational advantage on a specific task, namely sampling from random quantum circuits comprising 53 qubits [1]. The success of this experiment hinges on the chaotic dynamics underlying the random circuits, which generates sufficiently large entanglement to challenge classical simulation within the coherence times of the qubits. To systematically study the physics of quantum chaos, we perform a second experiment which investigates the “fingerprints” of chaos on local quantum observables [2]. We demonstrate how the two fundamental mechanisms of quantum chaos, operator spreading and operator entanglement, may be diagnosed by reversing the flow of time and measuring the so-called out-of-time-order correlators (OTOCs). Additionally, we find that with proper error-mitigation strategies, even local quantum observables such as OTOCs may be measured up to accuracies requiring non-trivial classical computational resources to simulate. These works pave a critical path toward using quantum computers for scientific discovery in the NISQ era.

[1] Google Quantum AI, Nature 574, 505 (2019).

[2] X. Mi et al., Science 374, 1479 (2021).

Zoom Link: https://pitp.zoom.us/j/93446337538?pwd=UXpsUFZ4M0tDSDd6bnA0VFBsazNPQT09

Recent advances in quantum simulation experiments have paved the way for a new perspective on strongly correlated quantum many-body systems. Digital as well as analog quantum simulation platforms are capable of preparing desired quantum states, and various experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. State-of-the art quantum simulators provide single-site resolved quantum projective measurements of the state. Depending on the platform, measurements in different local bases are possible. The question emerges which observables are best suited to study such quantum many-body systems.

In this talk, I will cover two different approaches to make the most use of these possibilities. In the first part, I will discuss the use of machine learning techniques to study the thermalization behavior of an interacting quantum system. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We apply this method to numerically simulated data, as well experimental snapshots of ultracold atoms taken with a quantum gas microscope. 

In the second part of this talk, I will present a scheme to perform adaptive quantum state tomography using active learning. Based on an initial, small set of measurements, the active learning algorithm iteratively proposes the basis configurations which will yield the maximum information gain. We apply this scheme to GHZ states of a few qubits as well as ground states of one-dimensional lattice gauge theories and show an improvement in accuracy over random basis configurations.

The vast and growing number of publications in all disciplines of science cannot be comprehended by a single human researcher. As a consequence, researchers have to specialize in narrow subdisciplines, which makes it challenging to uncover scientific connections beyond the own field of research.

In my talk, I will present a possible solution: I demonstrate the development of a semantic network for quantum physics (SemNet), using 750,000 scientific papers and knowledge from books and Wikipedia. I use it in conjunction with an artificial neural network for predicting future research directions. Finally, I show first indications how individual scientists can use SemNet for suggesting and inspiring personalized, out-of-the-box ideas.

I believe that computer-inspired scientific ideas will play a significant role in accelerating scientific progress, and am looking forward hearing your thoughts and ideas about this crucial question.

References
[1] Mario Krenn, Anton Zeilinger, Predicting research trends with semantic and neural networks with an application in quantum physics, PNAS 117(4) 1910-1916 (2020).
[2] IEEE BigData 2021 competition: Science4Cast: https://github.com/iarai/science4cast

Zoom Link: https://pitp.zoom.us/j/92240839439?pwd=LytUTHlMWE9ycjlsUXJkdHRta2c1UT09

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

Majorana zero modes have attracted much interest in recent years because of their promising properties for topological quantum computation. A key question in this regard is how fast two Majoranas can be exchanged giving rise to a unitary gate operation. In this presentation I will first explain that the transport of Majoranas in one-dimensional topological superconductors can be formulated as a “simple” optimal control optimization problem for which we propose several different control regimes. Next I will discuss the optimization methods, Differential Programming and Natural Evolution Strategies, that were applied to the Majorana control problem and came up with a counter-intuitive transport strategy. This strategy, which we dubbed jump-move-jump, will form the focus of the last part of the presentation in which I explain the key underlying mechanisms behind the strategy by reformulating the motion of Majoranas in a moving frame. I will conclude by arguing that these results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behaviour of many interesting models, most notably the Hubbard model. Research aimed at solving the sign problem, via various clever manipulations, has been thriving for a long time with various recent exciting results. The complementary question, of whether some phases of matter forbid the existence of any sign-free microscopic model, has received attention only recently. In this talk, I’ll review recent progress and discuss a novel and quite general criteria we obtained for when a topological quantum field theory has no sign-free microscopic model. I’ll also point out relations to sign problems in frustrated magnets and to the notion of quantum supremacy.

Neural networks (NNs) normally do not allow any insight into the reasoning behind their predictions. We demonstrate how influence functions can unravel the black box of NN when trained to predict the phases of the one-dimensional extended spinless Fermi-Hubbard model at half-filling. Results provide strong evidence that the NN correctly learns an order parameter describing the quantum transition. Moreover, we demonstrate that influence functions not only allow to check that the network, trained to recognize known quantum phases, can predict new unknown ones but even guide physicists in understanding patterns responsible for the phase transition. This method requires no a priori knowledge on the order parameter, the system itself, or even the architecture of the ML model.