Quantum Information and Quantum Matter

Conference

WHEN May 22-26, 2023
WHERE A3-001, West Administration Building WHO NYUAD Center for Quantum and Topological Systems By Invitation Interested scholars please contact nyuad.cqts.info@nyu.edu

The conference Quantum Information and Quantum Matter aims at gathering active researchers at the forefront of the science of quantum information and quantum matter, in order to foster the incubation of new ideas and collaborations at the forefront of quantum algorithms, emerging perspectives on quantum matter and novel generations of quantum communication protocols, quantum sensing and quantum simulation.

Topics include recent developments in quantum computing, quantum simulation of exotic states of matter, quantum software and algorithms, theory of quantum materials, topological quantum matter, and topological quantum processes.

The event is motivated by aimed at contributing to the strong interaction between the two fields of quantum information and quantum matter, and talks are intended to reflect the interdisciplinary nature between and within these fields.

For instance, key phenomena in condensed matter theory, such as the characterization and detection of topologically ordered ground states, are increasingly understood by quantum information theoretic quantifications of entropy and/or entanglement. In the other direction, topologically ordered ground states are of course the substrate on which topological quantum computation is going to be realized, and recent insights into physically possible anyonic topological phases is leading to new perspectives on topological quantum protocols in particular. Even with the dramatic recent activity in quantum sciences, it seems clear that we are only at the beginning of fully grasping the

Interaction of quantum information with quantum matter. We intend this meeting to initiate an annual series in the subject to both reflect and propel the development of the emerging deepening of the field of quantum science.

Host	Title and Affiliation
Hisham Sati	Professor of Mathematics, NYU Abu Dhabi
Urs Schreiber	Research Scientist, NYU Abu Dhabi

Speakers and Abstracts

Luigi Amico, Technology Innovation Institute, Abu Dhabi

Title: Coherence of confined matter in lattice gauge theories at the mesoscopic scales

Abstract: Atomtronics is the emerging quantum technology of matter-wave circuits which coherently guide propagating ultra-cold atoms. The field benefits from the remarkable progress in micro optics, allowing to control the coherent matter with enhanced flexibility on the micron spatial scale. This way, both fundamental studies in quantum science and technological applica:ons can be carried out. I will sketch recent progress in matter-wave circuitry and atomtronics-based quantum technology. In particular, I will focus on a specific scheme simulating lattice gauge theories and analyze confined matter at the mesoscopic spatial scale.
Leandro Aolita, Technology Innovation Institute, Abu Dhabi

Title: Exploring large-scale combinatoric optimization on NISQ devices

Abstract: Combinatorial optimizations is a major promise of quantum computation, with proven quadratic speed-ups for fault-tolerant machines. Heuristic solvers exist for NISQ hardware too; but their impact in practice is unclear. We present two novel approaches that reduce the requirements of NISQ solvers. In the first part, we show that, by encoding binary variables into non-commuting observables, one can drastically reduce the number of qubits required for Quadratic Unconstraint Binary Optimizations (QUBOs). In particular, variational algorithms using a number of qubits quadratically smaller than the number variables produces approximate solutions with qualities comparable to those of state-of-the-art classical solvers. We further report on a trapped-ion implementation, where instances of several hundreds of variables are deployed using only 19 qubits. More generally, solving constrained optimizations requires first reducing them to QUBOs. For this, constraints are lifted to penalization terms of an objective function. The weight of these terms — denoted as M — has to be sufficiently large. However, too large values slow down the runtime. For standard NISQ solvers, this ‘big-M problem’ is specially daunting, since M affects the spectral gap of the Hamiltonian. In the second part, we thus present a simple classical algorithm for choosing M based on SDP relaxations. For different constrained problems, including portfolio optimization, the quantum runtime using the novel reformulation is orders of magnitude smaller than with existing approaches. This is also relevant to quantum-inspired solvers. Both works aim at NISQ explorations of problem sizes practical relevance.
Ajit Balram, Institute of Mathematical Sciences, Chennai

Title: Very high energy collective modes in fractional quantum Hall fluids: Rise of the parton

Abstract: The low-energy physics of fractional quantum Hall (FQH) states --a paradigm of strongly correlated topological phases of matter -- to a large extent is captured by weakly interacting quasiparticles known as composite fermions. In this talk, I will demonstrate that some high-energy states in the FQH spectra necessitate a different description based on parton quasiparticles. The Jain states at filling factor \nu = n/(2pn \pm 1) with integers n, p \ge 2 support two kinds of collective modes: In addition to the well-known Girvin-MacDonald-Platzman (GMP) mode, they host a high-energy collective mode, which we interpret as the GMP mode of partons. I will elucidate observable signatures of the parton mode in the dynamics following a geometric quench. I will also present a microscopic wave function for the parton mode and demonstrate agreement between its variational energy and exact diagonalization. These results point to partons being ``real" quasiparticles which, in a way reminiscent of quarks, become observable only at sufficiently high energies.
Subhro Bhattacharjee, International Centre for Theoretical Sciences, Bengaluru

Title: Spin-orbit coupled Dirac fermions on a Honeycomb lattice

Abstract: One of the central quests of present condensed matter research is to find new phases of quantum matter. In this regard, a crucial ingredient is the emergence of novel implementation of symmetries. In this talk, I shall discuss how new and enhanced symmetries may arise at low energies in a two dimensional honeycomb system due to spin-orbit coupling in certain heavier transition metal compounds. The resultant Dirac semimetal phases, as I shall discuss, act as parent phases for several unconventional topological phases and associated phase transitions.
Leron Borsten, University of Hertfordshire, UK

Title: Colour—Kinematics duality, homotopy algebras and quantum matter: an invitation

Abstract: Symmetry, in the guise of groups and Lie algebras, has been a guiding principle of XX-century physics. However, recent decades have witnessed growing applications of generalized notions of symmetry. In this talk I will review two a priori distinct instances of this phenomenon: colour-kinematics duality in scattering amplitudes and homotopy Lie algebras in quantum field theory. I will then describe their relation and suggest how these features may arise in quantum matter. You are invited to consider the possible implications. In particular, colour-kinematics duality implies the double copy: graviton scattering amplitudes are “square” of gluon amplitudes. Given Yang-Mills, Einstein comes for free! What would the double copy mean in condensed matter?
Adrien Bouhon, Cambridge University

Title: Non-Abelian and Euler multi-gap topological phases in crystalline materials

Abstract: Multi-gap Euler and non-Abelian topological phases in crystalline systems constitute a new and uncharted venue in topological materials. Indicated by topological invariants that are not entirely reducible to Wilson loops, these phases lie beyond the existing schemes of classification based on irreducible representations of crystallographic symmetries. I will first review the quantization of multi-gap non-Abelian topological charges of band crossings in "real" band structures. These charges characterize the nodal (semimetallic) phases lying at the transition between inequivalent 2D Euler insulating phases. Inversely, a change of Euler topology is obtained via the conversion of non-Abelian charges induced by the braiding of nodal points formed by adjacent energy bands. I will then address subtleties of the associated one-dimensional non-Abelian insulating phases, both in intrinsic one-dimensional lattices and in 1D Brillouin paths of higher dimensional lattices. I show that only under strict conditions one retrieves meaningful 1D quantization of the multi-gap non-Abelian charges. These results thus pave the way to the finding and the design of such phases in material contexts.
Nadia Boutabba | Institute of Applied Technology, Fatima College of Health Sciences

Title: Quantum Control of atomic systems by the spontaneously generated coherence

Abstract: In this work, we investigate the coherent control of the Casimir force (CF) in a four-level atomic system under electromagnetically induced chirality. Therefore, we consider two parallel slabs of finite length in a quantum vacuum composed of ensembles of cesium vapor atoms in a four-level double A-type atomic configuration. By the use of the quantum interference (QI) effect which arises from the cross-coupling between the different spontaneous emission pathways, we demonstrate that it is possible to fully control the CF in the system via the spontaneously generated coherence (SGC) and the relative phase between the electromagnetic fields. In fact, we first show that the chirality in the atomic system can be induced by the SGC and the probe detuning, satisfying the passivity conditions. Next, we manipulate and control the QI in the system by changing the angle between the dipole moments, as the SGC is sensitive to their relative orientations. Besides, we explore the dependence of the Casimir interaction energy on the relative phase of the control fields. Finally, we observe that the Casimir interaction energy can be switched from negative to positive for a specific given phase value.
Tim Byrnes, NYU, Shanghai
ChunJun Cao, Caltech/Virginia Tech

Title: Quantum Legos and Expansion Pack

Abstract: Inspired by quantum code toy models of AdS/CFT, we propose the quantum legos framework for crafting novel quantum error correcting codes. This universal framework generalizes code concatenation, and is able to create any quantum code by combining a few types of simple lego blocks. For codes with a suitable quantum lego construction, we provide the current best algorithm for computing quantum weight enumerators using tensor network methods. As a corollary, it offers a more efficient way for finding quantum code distances that is up to exponentially faster than existing ones. The enumerator also provides an analytical expression for error probabilities, thereby inducing the optimal decoder when the code is subject to any i.i.d. single qubit/qudit error.
Andrew Forbes, University of the Witwatersrand, South Africa

Title: Tailoring photonic quantum landscapes

Abstract: Structured light is an exploding topic, giving rise to new applications from classical to quantum. The structuring can be done with single photons and entangled states for tailored photonic quantum landscapes, offering access to the infinite alphabet of patterns of light for high-dimension quantum information processing. In this talk I will review the recent progress in quantum entanglement of photons in their spatial degree of freedom. I will explain how to create high-dimensional quantum states in the laboratory, how to measure them, and what the present state of the art is in terms of applications. I will outline the progress in using such entangled states as a means to encode information for secure quantum communication and will consider the preservation of entanglement through noisy channels by tailored quantum wave functions.
Pedro Gomes, State University of Londrina, BR

Title: Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description

Abstract: In this talk, we will discuss the derivation of low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global $U(1)$ symmetry. We couple this symmetry with a background gauge field and compute the effective action by integrating out the gapped fermions. In spite of the fact that the corresponding Dirac operator governing the dynamics of the original fermions is nonrelativistic, the leading contribution in the effective action is a usual Abelian $U(1)$ Chern-Simons term. The proximity to a conventional superconductor induces a pairing potential in the quantum Hall state, favoring the formation of Cooper pairs. When the pairing is strong enough, it drives the system to a topological superconducting phase, hosting Majorana fermions. Even though the continuum $U(1)$ symmetry is broken down to a $\mathbb{Z}_2$ one, we can forge fictitious $U(1)$ symmetries that enable us to derive the effective action for the topological superconducting phase, also given by a Chern-Simons theory. To eliminate spurious states coming from the artificial symmetry enlargement, we demand that the fields in the effective action are $O(2)$ instead of $U(1)$ gauge fields. In the $O(2)$ case we have to sum over the $\mathbb{Z}_2$ bundles in the partition function, which projects out the states that are not $\mathbb{Z}_2$ invariants. The corresponding edge theory is the $U(1)/\mathbb{Z}_2$ orbifold, which contains Majorana fermions in its operator content.
Alioscia Hamma, Università di Napoli Federico II and INFN

Title: The Universe is Universal

Abstract: Quantum computers that are capable of universal quantum computation have an advantage over classical computers. This universality is reflected in the enormously greater complexity of quantum systems compared to classical ones. However, not all quantum computers are universal: some quantum computers can even be effectively simulated on a classical computer. In this talk we try to answer these two questions: (i) what makes quantum mechanics complex and quantum computers universal? and (ii) consider the classical, deterministic world. One could argue that stochastic classical systems arise from the underlying quantum mechanical essential nature of fundamental physics. However, after measurement or decoherence, classical systems are yes stochastic, but just classical. Then one can ask: are the observed classical probabilities that one observes in Nature due to an underlying universal quantum computer or something simpler can do? We shall see that quantum complexity arises from the conspiration of two different, purely quantum, characteristics: entanglement and the so-called non-stabilizerness. We show that both these quantities are different kinds of entropic quantities and that both these resources are necessary to attain universal quantum computation. Finally, we show that even typical classical probabilities like those given by the Boltzmann distribution necessitate both resources. If the theory of the Universe is that of quantum mechanics, the Universe must be an universal quantum computer.
Philipp Andres Hoehn, Okinawa Institute of Science and Technology in Okinawa, Japan

Title: Quantum frame covariance and subsystem relativity

Abstract: How does one extend the relativity principle into the quantum realm? To answer this question, one has to go beyond the usual background role assigned to reference frames, according to which they define a description of the physical scenario at hand, but are external to it. Such an idealization indeed does not account for gravity where external frames do not exist or for situations in quantum information and foundations when access to them is not available. Under such circumstances, it is necessary to take serious that reference frames are physical systems themselves that need to be included in the description. Being subject to the laws of quantum theory, they become internal quantum reference frames. A naturally arising question is then how descriptions relative to different quantum reference frame choices are related, especially given that they can now be in relative superposition. I will discuss recent developments answering this question and argue that they can be viewed as a quantum extension of classical relativity principles. This leads to a quantum frame dependence of the very notion of subsystem and thereby to a quantum relativity of correlations, superpositions and thermal properties. Time permitting, I will comment on how these observations extend to gauge theories and gravity where quantum reference frames appear, for example, in the form of edge modes.
Chang-Tse Hsieh, National Taiwan University

Title: Generalized Lieb-Schultz-Mattis theorem for 1d quantum magnets

Abstract: The Lieb-Schultz-Mattis (LSM) theorem is a fundamental result in condensed matter physics that relates symmetries to the ground state properties of quantum many-body systems. The conventional LSM theorem states that a 1d antiferromagnetic spin chain with spin-rotation and lattice-translation symmetries cannot have a unique gapped ground state if the spin per unit cell is half-integral. In this talk, I will present extensions of the LSM theorem for 1d quantum magnets with certain combinations of spin-rotation, spatial, and time-reversal symmetries. Our results can be applied to a wider range of systems with spin interactions beyond the Heisenberg exchange interaction, such as Dzyaloshinskii-Moriya and chiral three-spin interactions.
Po-Shen Hsin, University of California, Los Angeles
Yongguan Ke, School of physics and astronomy, Sun Yat-sen University

Title: Topological photonic scattering in waveguide quantum electrodynamics

Abstract: Light-matter interaction plays a crucial role in both science and technologies such as Laser, LED, solar cells. Recently, the interplay between topological phase and light-matter interaction has attracted intense attention and broad interest. In this talk, I will introduce characterization and detection of topological phase in a waveguide QED with inversion symmetry. For the first time, we put forward topological inverse band theory, with which we find unexpected rich topological phase diagram, breakdown of bulk-edge correspondence, dark Wannier states supported by flat band, and scale-free localization. We propose to use quantum walks of excitation to detect the topological phase. The scattering of photon is affected by both the topological phase and even-odd effect. At last, I will give a brief summary and discussion about the potential direction.
Liang Kong, SUSTech, Southern University of Science and Technology, China

Title: Topological orders and higher categories

Abstract: I will explain why topological defects in an n+1D topological order form a fusion n-category with a trivial E_1-center. I will present some basic results on separable n-categories, E_m-monoidal fusion n-categories, E_n-centers and their physical applications obtained in arXiv:2011.02859 and arXiv:2107.03858.
Chaohong Lee, Shenzhen University

Title: Quantum lock-in amplifier with cold atoms

Abstract: High-precision measurement of weak alternating signals in noise background is important for both fundamental science and practical technology. Generally, the target signal is submerged in noise background and is hard to be detected. To obtain a high signal-to-noise ratio, one can decreasing the effect of noise and enhancing the response to the target signal. In metrology, conventional lock-in amplifiers can extract time-dependent alternating signals from an extreme noisy background and have been applied in various fields. Beyond the conventional protocol, it is challenging to enhance lock-in amplifiers via using quantum resources. However, all existing studies of quantum lock-in amplifiers concentrate on single-particle systems [1-4]. It’s unclear that how quantum entanglement can improve the measurement precision in a quantum lock-in amplifier. Meanwhile, as the target signal usually has an unknown initial phase, it is a challenge to extract the complete information of the target signal (amplitude, frequency and phase).

In this talk, we present a general protocol for achieving a many-body quantum lock-in amplifier via quantum interferometry under a periodic multipulse sequence and employ entanglement to improve its measurement precision [5]. Further, we present a general protocol for achieving a quantum double lock-in amplifier via two quantum interferometry with two orthogonal periodic multi-pulse sequences to extract the complete information of the target signal [6]. We also discuss the experimental feasibility of our two protocols in cold atoms. Our study opens an avenue for extracting an alternating signal within strong noise background, which is beneficial for developing practical quantum sensing technologies.

References

[1] J. R. Maze, et al., Nanoscale magnetic sensing with an individual electronic spin in diamond, Nature 455, 644 (2008).

[2] G. de Lange, et al., Single-spin magnetometry with multipulse sensing Sequences, Phys. Rev. Lett 106, 080802 (2011).

[3] S. Kotler, et al., Single-ion quantum lock-in amplifier, Nature 473, 61 (2011).

[4] R. Shaniv, et al., Quantum lock-in force sensing using optical clock doppler velocimetry, Nat. Commun. 8, 14157 (2017).

[5] M. Zhuang, et al., Many-Body Quantum Lock-In Amplifier, PRX Quantum 2, 040317 (2021).

[6] S. Chen, et al., arXiv:2303.07559 (2023).
Netanel Lindner, Technion
Marwa Mannai, NYU Abu Dhabi

Title: Two dimensional topological models: role of strain, disorder, stacking and twist.
Markus Müller | RWTH Aachen University and Forschungszentrum Jülich, Germany

Title: Fault-Tolerant Topological Quantum Computing: From Concepts to Experiments

To date, the construction of scalable fault-tolerant quantum computers remains a fundamental scientific and technological challenge, due to the influence of unavoidable noise. In my talk, I will first introduce basic concepts of topological quantum error correction codes, which allow one to protect quantum information during storage and processing. I will discuss recent theory work, perspectives and recent collaborative experimental breakthroughs towards fault-tolerant quantum error correction on various physical quantum computing platforms. This includes the first realisation of repeated high-performance quantum error-correction cycles on a topological surface code with superconducting qubits [1], and the first demonstration of a universal and fault-tolerant logical gate set with trapped ions [2]. Furthermore, I will present new fundamental connections between topological quantum error correction and classical statistical mechanics models, in the context of the correction of qubit loss [3,4] and the determination of fundamental error thresholds for circuit noise [5].

[1] S. Krinner et al., Realizing repeated quantum error correction in a distance-three surface code, Nature 605, 669 (2022)

[2] L. Postler et al., Demonstration of fault-tolerant universal quantum gate operations, Nature 605, 675 (2022)

[3] D. Vodola, et al., Twins Percolation for Qubit Losses in Topological Color Codes, Phys. Rev. Lett. 121, 060501 (2018)

[4] R. Stricker et al., Deterministic correction of qubit loss, Nature 585, 207 (2020)

[5] D. Vodola et al., Fundamental thresholds of realistic quantum error correction circuits from classical spin models, Quantum 6, 618 (2022)
Felix von Oppen | Freie Universität Berlin, Germany

Title: Edge modes in the random Floquet quantum Ising model

Abstract: Motivated by a recent experiment on a superconducting quantum processor [Mi et al., Science 378, 785 (2022)], we study the stability of edge modes in the random-field Floquet quantum Ising model and its ramifications for temporal boundary spin-spin correlations. The edge modes induce pairings in the many-body Floquet spectrum with splittings exponentially close to zero (Majorana zero mode or MZM phase) or π (Majorana π phase or MPM phase). We find that random transverse fields induce a log-normal distribution of both types of splittings. In contrast, random longitudinal fields affect the zero and π splittings in drastically different ways. While the random longitudinal field rapidly lifts the zero pairings, it strengthens the π pairing, with concomitant differences in the boundary spin-spin correlations. We explain our result within a low-order Floquet perturbation theory. The strengthening of π pairings by random longitudinal fields may have applications in quantum information processing.
Daniele Oriti, Ludwig-Maximilians University, Munich

Title: Quantum information structure of spacetime: tensor network tools, entanglement and holographic properties in quantum gravity states

Abstract: Quantum information concepts and tools play an important and natural role in quantum gravity models based on spin network states. In particular, random tensor network techniques have found several interesting applications, recently, in the study of their entanglement properties and in identifying conditions for holographic behaviour. The talk will survey such developments and other indications that quantum information could be the appropriate language for reconstructing geometry and spacetime from more fundamental quantum constituents.
Pramod Padmanabhan, Indian Institute of Technology Bhubaneswar

Title: Topological quantum computation on susy spin chains and beyond

Abstract: A promising route for fault-tolerant quantum computing is by using the fusion spaces of anyons as they support representations of the braid group. Quantum gates built out of the corresponding braid group elements are naturally insensitive to perturbations making the entire setup desirable for quantum computing. However, anyons that can provide universal gates have still been elusive in experiments prompting the need to look for alternate sources. In this talk I will show that the zero modes of SUSY spin chains can mimic the effects of anyons and thus providing an alternative for realizing a quantum computer on magnetic systems. Furthermore I will explain how this route can be generalized also to non-SUSY spin chains. I will illustrate how to obtain these features on spin chains made out of the Fredkin moves that support Dyck walks as eigenstates.

The talk will partly be based on https://arxiv.org/abs/2209.03822.
Nicolas Regnault, Ecole Normale Superieure and CNRS, Paris, France

Title: Ideal bands as Landau levels in curved space, and magic in twisted TMDs

Abstract: The advent of moiré materials has boosted the search for topological bands strictly equivalent to generalized Landau levels and thus leading to fractional quantum Hall phases. In this talk, we will show that all the criteria proposed in the literature to identify Chern bands hosting fractional Chern insulating ground states, in fact, describe an equivalence with lowest Landau levels defined in curved space. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may posses interesting phases beyond Landau level physics. Finally, we will describe why such ideal bands may appear in the moire transition metal dichalcogenide heterostructures, and highlight experimental consequences on the possibility of observing fractional Chern insulators at zero field.
Title: Interacting quantum matter: Perspectives from topology and high energy physics

Abstract: Sophisticated topological techniques have consistently shown to be impactful in high energy physics, including in field theory and string theory. I will explain how such techniques when applied to condensed matter/topological phases lead to a systematic and systematic and novel description of interacting quantum topological matter. In particular, it naturally enhances the classification of free topological phases to interacting anyonic phases via twisted equivariant differential (TED) K-theory.

The connection to high energy physics goes beyond analogies. The construction is dual to certain M-brane configurations in M-theory, OK thereby providing a natural embedding in microscopic theory via hypothesis H.

This is joint work with Urs Schreiber.
Frank Schindler, Princeton University

Title: Hermitian Bulk -- Non-Hermitian Boundary Correspondence

Abstract: Non-Hermitian topology offers a fresh perspective on open quantum systems, but identifying suitable physical realizations remains a challenge. In my talk, I will demonstrate that the lossless edge states of Hermitian topological insulators acquire nontrivial non-Hermitian topological invariants upon exposure to minor perturbations. This discovery expands the range of potential materials for non-Hermitian topology to encompass all known topological insulators. I will provide a comprehensive characterization of the emergent higher-order non-Hermitian skin effects and edge states, which act as distinctive experimental signatures for the correspondence between Hermitian and non-Hermitian topology.
Herbert Schoeller, RWTH Aachen

Title: Supersymmetry protected topological states and realization of periodic Witten models in two dimensional second-order topological insulators

Abstract: For a generic two-dimensional topological insulator with band inversion and spin-orbit coupling, we propose the generation of topological zero-energy bound states via the application of an in-plane Zeeman field breaking rotational invariance. The Zeeman field induces a surface gap and generates the topological states via a second-order mechanism generically at the surface positions where the normal component of the Zeeman field vanishes. Via the application of an additional half-integer Aharonov-Bohm flux through a hole of the system, we show that the topological states are protected by supersymmetry. For smooth surfaces, we derive an effective surface Hamiltonian in the form of a periodic Witten model and propose how the surface bound states of the supersymmetric spectrum can be calculated via a trapping mechanism in effective surface potentials. We study the whole phase diagram of the model together with its stability and discuss the high tunability of the topological states.
Title: Entanglement of Sections: The pushout of entangled and parameterized
quantum information

Abstract: Recently Freedman & Hastings asked [arXiv:2304.01072] for a
mathematical theory that would unify quantum
entanglement/tensor-structure with parameterized/bundle-structure via
their amalgamation (a hypothetical “pushout”) along bare quantum
(information) theory — a question motivated by the role of vector
bundles of spaces of quantum states in the K-theory classification of
topological phases of matter (there: parameterized over the Brillouin
torus).

In reply to this question, first we make precise a form of the
relevant pushout-diagram in monoidal category theory. Then we prove
that it produces what is known as the "external" tensor product on
vector bundles/K-classes, or rather on flat such bundles (flat
K-theory), i.e. those equipped with monodromy encoding topological
Berry phases. This external tensor product was recently highlighted in
discussion of topological phases of matter by B. Mera (2020) but has
not otherwise found due attention in quantum theory yet.

The bulk of our result is a further homotopy theoretic enhancement of
the situation to the derived category of flat infinity-vector bundles
(“infinity-local systems”) equipped with the “derived functor” of the
external tensor product. We explain how this serves as categorical
semantics for the multiplicative fragment of the homotopically typed
quantum programming language LHoTT. This is the generality in which we
recently showed [arXiv:2303.02382] that topological anyonic braid
quantum gates are native objects in the LHoTT-quantum programming
language (in which case the parameterization is over the configuration
space of defect anyons in the Brillouin zone).

Talk notes are available at: ncatlab.org/schreiber/show/Entanglement+of+Sections
Javad Shabani, New York University
Shun-Qing Shen, The University of Hong Kong

Title: Half Quantum Hall Effect in Metal

Abstract: The quantum Hall effects refer to a series of peculiar quantum states of matter in the two-dimensional electron systems in a strong magnetic field at a very low temperature. Similar phenomena in quasi-two-dimensional materials in the absence of a magnetic field are named the quantum anomalous Hall effect. So far all the quantum Hall effects occur in insulating phases and are characterized by an integer or rational fraction. These quantum Hall effects occur when the Fermi level lies in the energy gap of the Landau levels or the band gap, and are characterized by the TKNN number or Chern number for the band structure as a topological invariant. The longitudinal conductivity is zero and either the Hall resistivity or conductivity is quantized. The bulk-edge correspondence illustrates that the number corresponds to the number of the localized edge modes around the system boundary, which carries the dissipationless chiral charge current.

Here we report a half-quantized Hall effect in a metal or semimetal. The Hall conductance is half quantized and the longitudinal conductance is nonzero, but the Hall resistivity is not quantized. The half quantization occurs when the Fermi surface is invariant under the parity symmetry while the symmetry is broken in the whole system. A recent experiment reports the observation of the half-quantized Hall conductance in a magnetically-doped topological insulator. We discover that a single gapless Dirac cone exists in the band structure and has half-quantized conductance when the Fermi level intercepts the gapless surface states in which the parity symmetry is respected for in a finite regime in the Brillouin zone. As there are no localized chiral edge states in the gapless and metallic system, we find that the chiral edge current is carried by the gapless surface states. The current density peaks at the edge and decays in a power law rather than the exponential decay in the quantum anomalous Hall effect. We term the unexpected and nontrivial quantum phase as “parity anomalous semimetal.” The work opens the door to exploring novel topological states of matter with fractional topological invariants.
Steven Simon, Oxford University

Title: nu=1/2+1/2 quantum Hall bilayers: Do we finally understand it.

Abstract: The quantum Hall bilayer at total filling nu=1 is a problem that has been studied heavily, both experimentally and theoretically, for almost thirty years. If the filling in the two layers is equal (nu=1/2+1/2) when the two layers are moved apart the system transitions from an exciton superfluid to a system of two uncoupled composite fermion liquids. The nature of the transition between these limits, perhaps the simplest question one can ask, has been debated extensively. We believe we have finally come to a detailed understanding of how this transition occurs and we are able to support our picture in several complementary languages.
Thais Silva, Technology Innovation Institute, Abu Dhabi
Robert-Jan Slager , Cambridge University

Title: Multi-gap topological physics: geometrical notions, physical phases and novel responses

Abstract: In this talk I will review recent work on multi-gap topological states. These phases are characterized by topological structures that cannot be captured by advances in more conventional symmetry-based topological classifications schemes. Upon utilizing new insights into connections with general geometric identities I will elucidate the structure of these phases and highlight physical signatures in both equilibrium and out-of-equilibrium settings. As a highlight I will address how this understanding vice versa also relates to new takes on formulating quantum geometrical notions that can be probed by physical responses.
Juven Wang, Harvard University

Title: Ultra Unification, and Categorical Symmetry of the Standard Model from Gravitational Anomaly

Abstract: In the Standard Model, the total "sterile right-handed" neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.14765, 2204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Ultra Unification would combine the Standard Model and grand unification, particularly for the models with 15 Weyl fermions per family, without the necessity of right-handed sterile neutrinos, by adding new gapped topological phase sectors (in 4d or 5d) or new gapless interacting conformal sectors (in 4d) consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the mixed gauge-gravitational anomaly, such as a ℤ_{16} class anomaly, associated with the baryon minus lepton number B−L and the electroweak hypercharge Y).

Moreover, for the Standard Mode alone, the invertible B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons, hypothetically pertinent for leptogenesis in the very early universe. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we construct noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ_{16} respectively. For this construction, we utilize the anomaly inflow concept, the 4d Pontryagin class and the gravitational Chern-Simons 3-form, the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory with a framing anomaly corresponding to a 2d rational conformal field theory with an appropriate chiral central charge, and the 4d Z_4^{TF}-time-reversal symmetric topological superconductor with 3d boundary topological order ([2302.14862], URL1, and URL2).
Guanyu Zhu | IBM T.J. Watson Research Center

Title: Defects, higher symmetries and fault-tolerant logical gates in (3+1)D topological phases

Abstract: (3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3. Understanding these defects and the corresponding emergent symmetries plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error correcting codes. In particular, sweeping a codimension-(k+1) invertible defects gives rise to a k-form emergent symmetry, which equivalently implements a fault-tolerant logical gate supported on a codimension-k submanifold.

In this talk, I will focus on a class of invertible codimension-2 topological defects, which is referred to as twist strings. I will present two general constructions for twist strings, in terms of gauging lower dimensional invertible phases and layer constructions. I will discuss some special examples in the context ℤ 2 ×ℤ 2 gauge theory, and also in non-Abelian discrete gauge theories based on dihedral (Dn) and alternating (A6) groups, including the corresponding logical gates in these cases. In addition, I will present an exotic boundary which condenses the combination of flux string and twist string and how to use it to perform fault-tolerant non-Clifford logical gates.

References:

1. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn,

Guanyu Zhu

2. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua

Day One: Monday, May 22, 2023

Time	Details
9:00-9:05am	Hisham Sati – Welcome & Opening Remarks
9:05-9:40am	Luigi Amico (Technology Innovation Institute)
9:45-10:20am	Po-Shen Hsin (University of California)
10:50-11:25am	Tim Byrnes (NYU, Shanghai)
11:30-12:05am	Herbert Schoeller (RWTH Aachen)
12:10-1:10pm	Lunch
1:10-1:45pm	Netanel Lindner (Technion)
1:50-2:25pm	Adrien Bouhon (Cambridge University)
2:55-3:30pm	Frank Schindler (Princeton University)
3:35-4:10pm	Marwa Mannai (NYU, Abu Dhabi)

Day Two: Tuesday, May 23, 2023

Time	Details
9:00-9:35am	Nicolas Regnault (Ecole Normale Superieure and CNRS, Paris, France)
9:40-10:15am	Chang-Tse Hsieh (National Taiwan University)
10:45-11:20am	Felix von Oppen (Freie Universität Berlin, Germany)
11:25-12:00pm	Subhro Bhattacharjee (International Centre for Theoretical Sciences)
12:00-1:00pm	Lunch
1:00-1:35pm	Ajit Balram (Institute of Mathematical Sciences, Chennai)
1:40-2:15pm	Shun-Qing Shen (The University of Hong Kong)
2:45-3:20pm	Pedro Gomes (State University of Londrina, BR)

Day Three: Wednesday, May 24, 2023

Time	Details
9:00-9:35am	Daniele Oriti (Ludwig-Maximilians University, Munich)
9:40-10:15am	Alioscia Hamma (Università di Napoli Federico II and INFN)
10:45-11:20am	Philipp Andres Hoehn (Okinawa Institute of Science and Technology in Okinawa, Japan)
11:25-12:00pm	Leron Borsten (University of Hertfordshire, UK)
12:05-12:40pm	Steven Simon (Oxford University)
12:45-1:45pm	Lunch

Day Four: Thursday, May 25, 2023

Time	Details
9:00-9:35am	Andrew Forbes (University of the Witwatersrand, South Africa)
9:40-10:15am	Yongguan Ke (School of physics and astronomy, Sun Yat-sen University)
10:45-11:20am	Leandro Aolita (Technology Innovation Institute, Abu Dhabi)
11:25-12:00pm	Thais de Lima Silva (Technology Innovation Institute, Abu Dhabi)
12:00-1:00pm	Lunch
1:00-1:35pm	Nadia Boutabba (Institute of Applied Technology, Fatima College of Health Sciences)
1:40-2:15pm	Chaohong Lee (Shenzhen University)
2:45-3:20pm	ChunJun Cao (Caltech/Virginia Tech)
3:25-4:00pm	Robert-Jan Slager (Cambridge University)
4:00-4:30pm	Javad Shabani (NYU)

Day Five: Friday, May 26, 2023

Time	Details
9:00-9:35am	Markus Müller (RWTH Aachen University and Forschungszentrum Jülich, Germany)
9:40-10:15am	Pramod Padmanabhan (Indian Institute of Technology Bhubaneswar)
10:45-11:20am	Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)
11:25-12:00pm	Liang Kong (SUSTech, Southern University of Science and Technology, China)
12:00-1:00pm	Lunch
1:00-1:35pm	Hisham Sati (NYU, Abu Dhabi)
1:40-2:15pm	Urs Schreiber (NYU, Abu Dhabi)
2:25-3:00pm	Juven Wang (Harvard University)

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NYUAD Center for Quantum and Topological Systems

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