Physics

A quantum computer is a new type of computer based on quantum physics. When it comes to certain computational objectives, the computational ability of quantum computers is much stronger than that of the familiar digital computers, and their construction will enable us to factor large integers and to break most of the current cryptosystems.

The question of whether quantum computation is possible is one of the fascinating clear-cut open scientific questions of our time. In my lecture I will explain theoretical discoveries from the 1990s that suggested that quantum computation is possible and present my theory as to why quantum computation is nevertheless impossible.

At the crux of the matter is the study of noisy intermediate scale quantum (NISQ) computers. Based on the mathematical notions of "noise sensitivity vs noise stability" (Benjamini, Kalai, and Schramm 1999, Kalai and Kindler 2014), we identify the inherent noise sensitivity of probability distributions arising from NISQ computers. This leads to a very low complexity class of probability distributions that can be robustly described by such quantum computers; consequently, NISQ computers will not allow good-quality quantum error-correction which are the necessary building blocks for larger quantum computers.

The lecture will be self-contained and will start with a gentle explanation of some basic notions about computation, and quantum computers.

Zoom link:  https://pitp.zoom.us/j/93847236670?pwd=T2Z2emZ5ZExaZTVYcTNCdU1FNkxOdz09

Amalia Madden, Perimeter Institute & University of Waterloo

New searches for the QCD axion with piezoelectric materials

The QCD axion is one of the best motivated extensions to the Standard Model, providing a solution to the strong CP problem as well as being an excellent dark matter candidate. In this talk I will describe two new observables, the “piezoaxionic” and “ferroaxionic” effects, that could be used to search for the QCD axion over many orders of magnitude of unexplored parameter space. Both of these observables rely on the interaction between the QCD axion and a class of materials known as piezoelectrics. I will then discuss our current progress in designing new experiments that could measure these observables. This talk will be based on 2112.11466 and unpublished work.

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

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

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