Physics

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

The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three 'purely even' examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups on Z/2-graded Hilbert spaces. We explain this classification, its connection to Clifford algebras, and some of its implications.

Zoom Link: https://pitp.zoom.us/j/96451287888?pwd=dlp2eVhKVTU0L2hqN2UxMy95V21SQT09

We investigate the ground states of spin-S Kitaev ladders using exact analytical solutions (for S=1/2), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer S, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer S, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer S we find a transition between two distinct SPT orders, and for integer S we find unnecessary first order phase transitions within a trivial phase

Zoom link:  https://pitp.zoom.us/j/96692976298?pwd=d3dieERwTHJ2MEh5NFF2bFpnS3hOUT09

I will introduce asymptotically safe quantum gravity, which is based on the quantum realization of scale invariance, as one candidate theory to describe nature at all scales. I will discuss the concept of an asymptotically safe fixed point, and how the realization of scale invariance at high energies might provide a predictive and UV-complete description of nature. In particular, I will focus on the interplay of gravity and matter, and highlight mechanisms how this interplay might lead to constraints and predictions of asymptotically safe gravity-matter systems.

Zoom Link: https://pitp.zoom.us/j/99056179498?pwd=SzlXK1R5dExNckFMM1pMS3IvS1VyQT09

Quantum algorithms have been found which are able to solve important problems exponentially faster than any known classical algorithm. The most well known example is Shor's algorithm which would be able to break all RSA encryption if fault tolerant quantum computers existed for it to be run on. It is currently not believed that quantum computers will be able to efficiently solve NP-Complete problems, but the answer is still unknown. I present a novel quantum algorithm which is able to solve 3-SAT along with numerical simulations to see how it performs on small instances, but new methods of analyzing the complexity of quantum algorithms will need to be developed before we can say exactly how it performs. This will be the goal of my PSI essay.

Zoom Link: https://pitp.zoom.us/j/95795655548?pwd=aU5jNFhFZHEzUWpLK1FvWjd2Q1c2Zz09

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

I will introduce the QAOA and discuss some recent developments. These might include the application of the QAOA to the Sherrington-Kirkpatrick model, landscape independence, and the odd behavior when starting in a good place.

Zoom link:  https://pitp.zoom.us/j/94804346887?pwd=c1hkRHBZZmRHS1RpM1BqU0R6TCtEdz09

Sofia Gonzalez Garcia, Perimeter Institute & University of Waterloo

Tensor Networks in a Nutshell

This seminar will be an introductory 'class' to Tensor Networks, so I will assume no previous knowledge on the subject. I aim to provide motivation for this powerful ansatz as well as some of its applications. I will introduce the main architectures (MPS, PEPS and MERA) and their characteristics. Throughout the seminar I will try to include part of the material I have produced for a 2017 PSI course taught by Guifre Vidal. 

If time permits I will also briefly introduce my research on the subject, which is on 2D tensor networks contraction and its accuracy convergence.