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 I will report on my progress, joint with David Reutter, to construct and analyze the algebraic closure of nVec – in other words, the universal n-category of framed nD TQFTs. The invertibles are Pontryagin dual to the stable homotopy groups of spheres. The Galois group is almost, but not quite, the stable PL group. An invertible TQFT can be condensed from the vacuum if and only if it trivializes on (possibly-exceptional) spheres.
 

For quantum gravity states associated to open spin network graphs, we study how the boundary (the set of open edges, which carries spin degrees of freedom) is affected by the bulk, specifically by its combinatorial structure and by the quantum correlations among the intertwiners. In particular, we determine under which conditions certain classes of quantum gravity states map bulk degrees of freedom into boundary ones isometrically (which is a necessary condition for holography). We then look at the entanglement entropy of the boundary and recover, for slightly entangled intertwiners, the Ryu-Takayanagi formula with corrections induced by the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound, a mechanism which thus leads to the rise of a black hole-like region in the bulk.

Zoom Link: https://pitp.zoom.us/j/96356007543?pwd=U2VrRlhyOThMODdMYllDMnB6VjlZQT09

The era of multi-messenger astronomy is well and truly upon us, with 90 compact binaries observed since the Advanced LIGO detectors saw first light in 2015. Despite our very own cosmic backyard, the Milky Way, being ripe with prospective sources for ground-based gravitational wave detectors, the closest source detected thus far (GW170817, the famed binary neutron star merger) was at a distance of 40 Mpc. In this talk, I will outline a number of prospective Galactic multi-messenger sources, and discuss several ways in which their detection over the next twenty years can be improved through both experimental and analytical techniques. 

Zoom Link: https://pitp.zoom.us/j/93664322641?pwd=VUoxbmFGZE1KczJ1RU1MR09TQ05Ldz09

Conformal field theories (CFTs) are ubiquitous in theoretical physics as fixed points of renormalization, descriptions of critical systems and more. In these theories the conformal symmetry is a powerful tool in the computation of correlation functions, especially in 2 dimensions where the conformal algebra is infinite. Discretization of field theories is another powerful tool, where the theory on the lattice is both mathematically well-defined and easy to put on a computer. In this talk I will outline how these are combined using a discrete version of the 2d conformal algebra that acts in lattice models. I will also discuss recent work on convergence of this discretization, as well as on applications to non-unitary CFTs that appear in descriptions of problems of interest in condensed matter physics such as polymers, percolation and disordered systems.

Zoom Link: https://pitp.zoom.us/j/95048143778?pwd=N1hhVHlsZThVYzBWTy9CNlBTUHIydz09

Logarithmic Sobolev inequalities (LSI) were first introduced by Gross in the 1970s as an equivalent formulation of hypercontractivity. LSI have been well studied in the past few decades and found applications to information theory, optimal transport, and graph theory. Recently matrix-valued LSI have been an active area of research. Matrix-valued LSI of Lindblad operators are closely related to decoherence of open quantum systems.  In this talk, I will present recent results on matrix-valued LSI, in particular a geometric approach to matrix-valued LSI of Lindblad operators. This talk is based on joint work with Li Gao, Marius Junge, and Nicholas LaRacuente.

Understanding IP ownership and ensuring that commercialization of research provides broad societal and economic benefit both in Canada and abroad is extremely important.  Perimeter Institute is also acutely aware that entrepreneurial oriented faculty and graduate students want to engage in commercial enterprise (i.e., through contract research and licensing opportunities with industry or independently with their own research outcomes).  In this colloquium you will learn the basics about the different types of IP protection available and some of the most common pitfalls to avoid.  Hear how IP is used to commercialize technology through licensing or start-up creation. 

Zoom Link: https://pitp.zoom.us/j/99022008403?pwd=NmEzdFJkNlJiRzUvY0VDVERuY3FlUT09

Sampling from classical probability distributions is an important task with applications in a wide range of fields, including computational science, statistical physics, and machine learning. In this seminar, I will present a general strategy of solving sampling problems on a quantum computer. The entire probability distribution is encoded in a quantum state such that a measurement of the state yields an unbiased sample. I will discuss the complexity of preparing such states in the context of several toy models, where a polynomial quantum speedup is achieved. The speedup can be understood in terms of the properties of classical and quantum phase transitions, which establishes a connection between computational complexity and phases of matter. To conclude, I will comment on the prospects of applying this approach to challenging, real-world tasks.

I will present a class of recently computed holographic correlators between half-BPS operators in a vast array of SCFTs with non-maximal superconformal symmetry in dimensions d=3,4,5,6. Via AdS/CFT, these four-point functions are dual to gluon scattering amplitudes in AdS. Exploiting the notion of MRV limit I will show that, at tree level, all such correlators are completely fixed by symmetries and consistency conditions. Our results encode a wealth of novel CFT data and exhibit various emergent structures, including Parisi-Sourlas supersymmetry, hidden conformal symmetry and color-kinematics duality. This talk will be based on https://arxiv.org/pdf/2103.15830.pdf.

A generic low-energy prediction of string theory is the existence of a large collection of axions, commonly known as a string axiverse. String axions can be distributed over many orders of magnitude in mass, and are expected to interact with one another through their joint potential. In this talk, I will show how non-linearities in this potential lead to a new type of resonant energy transfer between axions with nearby masses. This resonance generically transfers energy from axions with larger decay constants to those with smaller decay constants, leading to a multitude of signatures. These include enhanced direct detection prospects for a resonant pair comprising even a small subcomponent of dark matter, and boosted small-scale structure if the pair is the majority of DM. Near-future iterations of experiments such as ADMX and DM Radio will be sensitive to this scenario, as will astrophysical probes of DM substructure.

There exist various scenarios for the very early universe that could potentially be the explanation for the observed properties of the cosmic microwave background. The current paradigm -- inflationary cosmology -- has rightfully received much attention, but it is not the only theoretically viable explanation. Indeed, several alternative scenarios exist, for example a contracting universe prior to a bounce or a slowly expanding emerging universe. It thus bares the question: how can we discriminate between the various theories, both from a theoretical and an observational point of view? A few pathways to answering this question are discussed in this talk.

I will introduce the notion of Pivot Hamiltonians, a special class of Hamiltonians that can be used to "generate" both entanglement and symmetry. On the entanglement side, pivot Hamiltonians can be used to generate unitary operators that prepare symmetry-protected topological (SPT) phases by "rotating" the trivial phase into the SPT phase. This process can be iterated: the SPT can itself be used as a pivot to generate more SPTs, giving a rich web of dualities. Furthermore, a full rotation can have a trivial action in the bulk, but pump lower dimensional SPTs to the boundary, allowing the practical application of scalably preparing cluster states as SPT phases for measurement-based quantum computation. On the symmetry side, pivot Hamiltonians can naturally generate U(1) symmetries at the transition between the aforementioned trivial and SPT phases. The sign-problem free nature of the construction gives a systematic approach to realize quantum critical points between SPT phases in higher dimensions that can be numerically studied. As an example, I will discuss a quantum Monte Carlo study of a 2D lattice model where we find evidence of a direct transition consistent with a deconfined quantum critical point with emergent SO(5) symmetry.

This talk is based on arXiv:2107.04019, 2110.07599, 2110.09512

Trotter-Suzuki formula is a practical and efficient algorithm for Hamiltonian simulation. It has been widely used in quantum chemistry, quantum field theory and condensed matter physics. Usually, its error is quantified by the operator norm distance between the ideal evolution operator and the digital evolution operator. However, recently more and more papers discovered that, even in large Trotter step region, the quantity of interest can still be accurately simulated. These robustness phenomena imply a different approach of analyzing Trotter-Suzuki formulas. In our previous paper, by analyzing the spectral analysis of the effective Hamiltonian, we successfully established refined estimations of digital errors, and thus improved the circuit complexity of quantum phase estimation and digital adiabatic simulation.