Machine Learning Initiative

This talk will consider a stochastic multiple-timescale dynamical system modeling a biological neuron. With this model, we will separately uncover the mechanisms underlying two different ways biological neurons encode information with stochastic perturbations: self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR). We will then show that in the same weak noise limit, SISR and ISR are related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the model’s critical manifold.  This mathematical result could explain the experimental observation where neurons with identical morphological features sometimes encode different information with identical synaptic input. Finally, if time permits, we shall discuss the plausible applications of this result in neuro-biologically inspired machine learning algorithms, particularly reservoir computing based on liquid-state machines.

Zoom link:  https://pitp.zoom.us/j/94345141890?pwd=aTRFM3M0a0xCOEM3aXZjY2hFYzVrQT09

This talk is motivated by the question: why do we put so much effort and investment into quantum computing? A short answer is that we expect quantum advantages for practical problems. To achieve this goal, it is essential to reexamine existing experiments and propose new protocols for future quantum advantage experiments. In 2019, Google published a paper in Nature claiming to have achieved quantum computational advantage, also known as quantum supremacy. In this talk, I will explain how they arrived at their claim and its implications. I will also discuss recent theoretical and numerical developments that challenge this claim and reveal fundamental limitations in their approach. Due to these new developments, it is imperative to design the next generation of experiments. I will briefly mention three potential approaches: efficient verifiable quantum advantage, hardware-efficient fault-tolerance, and quantum algorithms on analog devices, including machine learning and combinatorial optimization.

Zoom Link: https://pitp.zoom.us/j/96945612624?pwd=ckRKMFJqZ0Q0dGtFOU91c1hnMzIzZz09

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realize and investigate topological quantum spin liquids (QSLs) phase. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases. In this talk, I will discuss how to construct Z2 QSLs states as the ground state of a static Hamiltonian with only local two-qubit interactions and a transverse field, and demonstrate its realization in the classical limit at the endpoint of quantum annealing protocol, using D-Wave DW-2000Q machine . I will also demonstrate how to probe signatures of Z2 QSLs fractional statistics in quantum simulators via quasiparticle interferometry. At the end, I will show the robustness of this probe against disorders and dephasing -- effects that are generally pervasive in quantum devices nowadays.

Zoom Link: https://pitp.zoom.us/j/99207971920?pwd=N3R3YUJtWXJWVjFQWlRoZ3hYSDlMZz09

We present an approach for representing fermionic quantum many-body states using tensor networks, by introducing a change of basis with local unitary gates obtained via compressing fermionic Gaussian states into quantum circuits. These fermionic Gaussian circuits enable efficient disentangling of low-energy states and entanglement renormalization in matrix product states/operators, significantly reducing bond dimension and improving computational efficiency. As a demonstration, we apply this approach to the 1D single impurity Anderson model through suppression of entanglement in both ground states and time-evolved low-lying excited states. We also explore the use of hierarchical compression to generate Gaussian multi-scale entanglement renormalization ansatz (GMERA) circuits and study their emergent coarse-grained physical models in terms of entanglement properties and suitability for time evolution.

Zoom link:  https://pitp.zoom.us/j/99677586832?pwd=ZGdIVGpac3pWcnhJYjlkNU16Wmlndz09

Canonical transformations play fundamental roles in simplifying and solving physical systems. However, their design and implementation can be challenging in the many-particle setting. Viewing canonical transformations from the angle of learnable diffeomorphism reveals a fruitful connection to normalizing flows in machine learning. The key issue is then how to impose physical constraints such as symplecticity, unitarity, and permutation equivariance in the flow transformations. In this talk, I will present the design and application of neural canonical transformations for several physical problems. Symplectic flow identifies independent and nonlinear modes of classical Hamiltonians and natural datasets. Fermi flow variationally solves ab initio many-electron problems at finite temperatures.
Refs:
[1] Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, and Lei Wang, Phys. Rev. X 10, 021020 (2020)
[2]  Hao Xie, Linfeng Zhang, and Lei Wang, J. Mach. Learn. , 1, 38 (2022)

Zoom link:  https://pitp.zoom.us/j/98830940500?pwd=WjdydGY5aS9QQzk5SnI0TE1xMkwrdz09

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.