Schur-Weyl duality, arising from tensor-power representations of the unitary group, is a big useful hammer in the quantum information toolbox. This is especially the case for problems which have a full unitary invariance, say, estimating the spectrum of a quantum state from a few copies. Many problems in quantum computing have a smaller symmetry group: the Clifford group. This talk will show how to decompose tensor-power Clifford representations through a Schur-Weyl type construction. Our results...

Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum...

I will overview recent results on the defect CFT corresponding to Wilson loop operators in N=4 SYM theory. In particular, I will review the calculation of defect correlators at strong coupling using the AdS2 string worldsheet, and I will present exact results for correlation functions in a subsector of the defect CFT using localization. I will also discuss a defect RG flow from the BPS to the ordinary Wilson loop, which can be used to...

General relativity does not distinguish a preferred reference frame, and conservatively one ought to expect that its quantization does not necessitate such background structure. However, this desire stands in contrast to orthodox formulations of quantum theory which rely on a background time parameter external to the theory, and in the case of quantum field theory a spacetime foliation. Such considerations have led to the development of the Page-Wootters formalism, which seeks to describe motion relative...

Over the past decades, the asymptotic safety scenario has matured into a viable contender for a consistent theory of quantum gravity. However, the pressing question of unitarity is far from being settled. I will present important steps towards tackling this issue and show the first direct computation of the graviton spectral function in asymptotically safe quantum gravity with a novel Lorentzian renormalisation group approach. We find a positive graviton spectral function, showing a massless one-graviton...

In thermal equilibrium, 1d bosonic systems (e.g. spin- or qubit- chains) cannot support intrinsically topological phases without symmetry protection. For example, the edge states of the Haldane spin chain are fragile to magnetic fields, in contrast to the absolutely stable Majorana edge states of a topological superconducting wire of fermionic electrons. This fragility is a serious drawback to harnessing topological edge states as protected quantum memories in existing AMO and qubit platforms...

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...

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....

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...

Perturbative QFT calculations in de Sitter are plagued by a variety of divergences. One particular kind, the secular growth terms, cause the naive perturbation expansion to break down at late times. Such contributions often arise from loop integrals, which are notoriously hard to compute in dS. We discuss an approach to evaluate such loop integrals, for a scalar field theory in a fixed de Sitter background. Our method is based on the Mellin-Barnes representation of...

Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediate-scale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Here we show that, for the crucial case of estimating...

Despite years of research into dark matter, little has been done to explore models which are heavier than most WIMPs and lighter than most primordial black hole models, "blobs".  This parameter space is particularly difficult to probe, due to low number densities and low masses.  This talk will present a new model-independent mechanism that can be used to probe this difficult to reach region of dark matter parameter space.  Blobs form binaries which spin down...

Type IIB string theory has a duality symmetry given by the pin+ cover of GL(2, Z). In joint work with Markus Dierigl, Jonathan J. Heckman, and Miguel Montero, we show that this symmetry is anomalous, and describe how to cancel the anomaly, up to a few calculations we were unable to determine, by adding a Chern-Simons term. I will talk about the setup of the problem in terms of computing the partition function of an invertible...

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a...

Tensor network algorithms are numerical tools widely used in physical research. But traditionally they are only applied to lattice systems with specific structure. In this talk, tensor network algorithms to deal with physical systems with arbitrary topology will be discussed. Theoretical framework will firstly be constructed to analyze the difficulty of contracting an arbitrary tensor network. Then both approximate and exact contraction approaches will be involved according to computational tasks of interest. Finally two applications,...

Consider a polynomial differential operator in one variable, depending on a small parameter (Planck constant). Under appropriate conditions, the low-energy spectrum admits an asymptotic expansion in hbar.
I will present a way to calculate such a series via a purely "commutative problem", a mixture of variations of Hodge structures and of the Stirling formula. This result came from discussions with A.Soibelman. It seems that we obtain an explanation of an old observation by J.Zinn-Justin...

Recent studies revealed that wormhole geometries play a central role in understanding quantum gravity. After disorder-averaging over random couplings, Sachdev-Ye-Kitaev (SYK) model has a collective field description of wormhole saddles. A recent paper by Saad, Shenker, Stanford, and Yao studied the SYK model with fixed couplings and found that the wormhole saddles persist, but that new saddles called “half-wormholes” also appear in the path-integral. 

In this talk, we introduce a “partially disorder-averaged...

Primordial black holes are a fascinating candidate for the dark matter in the universe. We discuss about their formation in the early universe and evolution across the cosmic history, and focus on their possible detectability at present and future gravitational wave experiments.

Nakajima’s quiver varieties play important roles in mathematical physics and representation theory. They are defined as symplectic reduction of the space of representations of the doubled quivers, and they are equipped with natural scheme structures. It is not known in general whether this scheme is reduced or not, and the reducedness issue does show up in certain scenario, for example the integration formula of the K-theoretic Nekrasov’s partition function. In this talk I will show...

Cosmic inflation is an important paradigm of the early Universe which is so far developed in two equivalent ways, either by geometrical modification of Einstein's general relativity (GR) or by introducing new forms of matter beyond the standard model of particle physics. Starobinsky's R+R^2 inflation based on a geometric modification of GR is one of the most observationally favorable models of cosmic inflation based on a geometric modification of GR. In this talk, I will...

 3d mirror symmetry relates the geometry of dual pairs of algebraic symplectic stack and has served in as a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only part of the subject has been mathematically accessible. In this talk, I will explain joint work with Ben Gammage and Aaron Mazel-Gee on formulation of abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from...

Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is stable against perturbations. In this talk, I will review the pseudospectrum, a mathematical tool which can shed light on the spectral stability of quasinormal modes, and discuss its novel...