Physics

In this first of two lectures, intended to be a pedagogical introduction, I will review the quantum field theory origin of anomalies starting with the more familiar example of the axial anomaly in QED, emphasizing the infrared effects and the appearance of a two-particle massless state, similar to a Cooper pairing in superconductor, associated with both the axial and conformal anomalies in two and four dimensions. In both cases the effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a bosonic field, which one can verify becomes a bona fide propagating quantum field in its own right. At finite chiral chemical potential this boson is a chiral density wave, a gapless pseudo-scalar collective excitation of the Fermi surface of a dissipationless chiral superfluid, analogous to the Goldstone-Nambu boson of spontaneous symmetry breaking. In the limit of vanishing chiral background the boson is a chiral collective mode of the Dirac vacuum itself, which therefore supports an axion-like boson excitation with a two-photon coupling, arising directly from the axial anomaly.

 

While the term “wide-field telescope” might sound like an oxymoron, a strong argument can be made that wide-field instruments lie behind much of the success of Canadian astronomy. Furthermore, despite the large size of the optical-IR community in Canada, this success has been made possible by considering multiple wavelength windows, from gamma to radio, and access to a suite of facilities. Over the past two decades, through a pair of 10-year Long Range Plans, Canadian astronomy has carefully structured its facility access, to ensure, as best as can be reasonably hoped, that the community maintains access to world-leading facilities. I’ll summarize the progression of the community vision on wide-field astronomy, highlighting successes and some missteps. As we head towards the creation of the 3rd Canadian Long Range Plan for astronomy, I’ll also present some personal views on what scientific leadership means and the challenges that it presents for a smaller country (at least in the G7 sense!) like Canada.

Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the  "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist. In this talk, I will introduce the measure of quantum chaoticity  – a so-called out-of-time-ordered four-point correlator (whose semiclassical limit reproduces classical Lyapunov growth), and use it to describe quantum chaotic dynamics and its eventual disappearance in the standard models of classical and quantum chaos – Bunimovich stadium billiard and standard map or kicked rotor [1]. I will describe our recent results on the quantum Lyapunov exponent in these single-particle models as well as results in interacting many-body systems, such as disordered metals [2]. The latter many-body model exhibits an interaction-induced transition from quantum chaotic to non-chaotic dynamics, which may manifest itself in a sharp change of the distribution of energy levels from Wigner-Dyson to Poisson statistics. I will conclude by formulating a many-body analogue of the Bohigas-Giannoni-Schmit conjecture.
References:
[1] "Lyapunov exponent and out-of-time-ordered correlator's growth rate in a chaotic system,"  E. Rozenbaum, S. Ganeshan, and V. Galitski, Physical Review Letters 118, 086801 (2017)
[2] "Non-linear sigma model approach to many-body quantum chaos," Y. Liao and and V. Galitski, arXiv:1807.09799

Recently there have been several proposals of low-energy precision experiments that can search for new particles, new forces, and the Dark Matter of the Universe in a way that is complementary to collider searches. In this talk, I will present some examples involving atomic clocks, nuclear magnetic resonance, and astrophysical black holes accessible to LIGO.

Simplicial complexes naturally describe discrete topological spaces. When their links are assigned a length they describe discrete geometries. As such simplicial complexes have been widely used in quantum gravity approaches that involve a discretization of spacetime. Recently they are becoming increasingly popular to describe complex interacting systems such a brain networks or social networks. In this talk we present non-equilibrium statistical mechanics approaches to model large simplicial complexes. We propose the simplicial complex model of Network Geometry with Flavor (NGF), we explore the hyperbolic nature of its emergent geometry and their relation with Tree Tensor Networks. Finally we reveal the rich interplay between Network Geometry with Flavor and dynamics. We investigate the percolation properties of NGF using the renormalization group finding KTP and discontinuous phase transitions depending on the dimensionality simplex. We also comment on the synchronization properties of NGF and the emergence of frustrated synchronization.

We propose to generalise classical maximum likelihood learning to density matrices. As the objective function, we propose a quantum likelihood that is related to the cross entropy between density matrices. We apply this learning criterion to the quantum Boltzmann machine (QBM), previously proposed by Amin et al. We demonstrate for the first time learning a quantum Hamiltonian from quantum statistics using this approach. For the anti-ferromagnetic Heisenberg and XYZ model we recover the true ground state wave function and Hamiltonian. The second contribution is to apply quantum learning to learn from classical data. Quantum learning uses in addition to the classical statistics also quantum statistics for learning. These statistics may violate the Bell inequality, as in the quantum case. Maximizing the quantum likelihood yields results that are significantly more accurate than the classical maximum likelihood approach in several cases. We give an example how the QBM can learn a strongly non-linear problem such as the parity problem. The solution shows entanglement, quantified by the entanglement entropy.

Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning inspired approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap Tr(rho*sigma) between two quantum states rho and sigma. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to rho=sigma, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate alphabets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error - compared to the Swap Test - on these computers.

The general purpose computer can run any program we can express in
symbolic logic; that makes it the go-to tool for accomplishing any task
that can be reduced to a computable function, and that's why software is
eating the world and cars and colliders and airplanes and pacemakers and
toasters are all just turning into computers in fancy cases.

That also means that every policy problem we can imagine will eventually
involve a computer -- and thus involve a lawmaker insisting that it must
be possible to make a computer that can run every program except for
some program that creates a problem in the world.

We don't know how to make that computer, but we can approximate it by
creating a computer with some spyware-like program running on it that
checks to see whether you're running a "naughty" program and shuts it down.

That's a spider we swallow to catch a fly. Here's the bird we swallow to
catch the spider: laws like Canada's C-11 make it a crime to
investigate, circumvent, or point out defects in systems that have these
spyware-like processes.

Companies have noticed that this offers some real upsides for them: they
can use these spyware-like processes to prevent users their customers
from using their own consumables (e.g. printer ink), parts, service
depots, apps -- anything that the company can command a high margin on,
provided that it's illegal for a customer to choose someone else's products.

What a deadly combination: companies are rapidly expanding the
constellation of devices that are locked in this way, and once a device
is locked in this way, it can't be investigated, its defects can't be
disclosed, and it can't be modified to improve it, mitigate its flaws,
and protects its owner from cybersecurity risk.

Peer review exists out of recognition that there is no way to know if
you're right until you let your enemies try to prove you wrong; in
creating a monopolistic right to control the use of products after they
were sold, Parliament also created the right for companies to enjoin the
most fundamental task of scientific knowledge creation: finding mistakes
and pointing them out.

This is urgent: our world is made of computers, those computers are
designed to treat their owners as their enemies, and security
researchers can't audit those computers without risking civil and
criminal reprisals. That's a catastrophe in the making.

Can computers think? They can certainly calculate - with staggering speed and ever-increasing power - and they have driven scientific and technological advances that would have been impossible without them. Even so, we would like to believe that, for some puzzles, there's no substitute for old-fashioned human intuition. But this view may be changing.

A new breed of machine learning algorithms have begun knocking down cognitive milestones that, until recently, scientists believed were still decades away. Major advances are being made in computer vision, language translation, autonomous robotic action, and other complex applications. At the same time, these new algorithms are helping scientists accelerate discovery in physics.

This stunning progress poses as many questions as answers: What are the fundamental possibilities and limits of machine learning? Can we create true human-level artificial intelligence, and how might its thoughts differ from our own? What new breeds of computer will fuel artificial intelligence and, conversely, how will artificial intelligence enable new forms of computing?

In his public lecture at Perimeter Institute, Roger Melko will explore how computers have helped humanity solve increasingly complex puzzles, and ask which challenges, if any, only human intuition is equipped to tackle.