Physics

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

A fundamental aspect of a random walk is determining when it reaches a specified threshold position for the first time.  This first-passage time, and more generally, the distribution of first passage times underlies many non-equilibrium phenomena, such as the triggering of integrate and fire neurons, the statistics of cell division, and the execution of stock options.  The computation of the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory.  I will present some aspects of these fundamentals and then discuss applications of first-passage ideas to diverse phenomena, including stochastic search processes and a toy model of wealth sharing.

Zoom link:  https://pitp.zoom.us/j/98293478936?pwd=NTR3dWZoNElWRmd2NVJ1bzk5aC9ZQT09

In order for quantum computing devices to accomplish preparation of quantum states, or simulation of other quantum systems, exceptional control of experimental parameters is required. The optimal parameters, such as time dependent magnetic fields for nuclear magnetic resonance, are found via classical simulation and optimization. Such idealized parameterized quantum systems have been shown to exhibit different phases of learning during optimization, such as overparameterization and lazy training, where global optima may potentially be reached exponentially quickly, while parameters negligibly change when the system is evolved for sufficient time (Larocca et al., arXiv:2109.11676, 2021). Here, we study the effects of imposing constraints related to experimental feasibility on the controls, such as bounding or sharing parameters across operators, and relevant noise channels are added after each time step. We observe overparameterization being robust to parameter constraints, however fidelities converge to zero past a critical simulation duration, due to catastrophic accumulation of noise. Compromises arise between numerical and experimental feasibility, suggesting limitations of variational ansatz to account for noise.

Zoom link:  https://pitp.zoom.us/j/98649931693?pwd=Z2s1MlZvSmFVNEFqdjk2dlZNRm9PQT09

Trapped Rydberg ions are a novel approach for quantum information processing [1,2]. This idea joins the advanced quantum computing toolbox of trapped ions with strong dipolar interaction between Rydberg atoms. For trapped ions, this method can speed up entangling interactions and enables such fast operations in larger ion crystals. In this presentation, I will first introduce the quantum computing platform of trapped ions, and present the novel experimental platform of trapped Rydberg ions [2]. I will describe the specific physics involved when exciting ions into Rydberg states, the effects on the trapping potential due to the strong polarizability of Rydberg ions, and the controllable strong interaction between ion and motion. Moreover, I will summarize methods and results in speeding up trapped ion entanglement operations via the strong dipolar Rydberg interaction [3].ReferencesM. Müller, L. Liang, I. Lesanovsky, and P. Zoller, Trapped Rydberg Ions: From Spin Chains to Fast Quantum Gates, New J. Phys. 10, 093009 (2008).A. Mokhberi, M. Hennrich, and F. Schmidt-Kaler, Trapped Rydberg Ions: A New Platform for Quantum Information Processing, in Advances In Atomic, Molecular, and Optical Physics, Vol. 69 (Elsevier, 2020), pp. 233–306.C. Zhang, F. Pokorny, W. Li, G. Higgins, A. Pöschl, I. Lesanovsky, and M. Hennrich, Submicrosecond Entangling Gate between Trapped Ions via Rydberg Interaction, Nature 580, 345 (2020).