Scientific Series

Most people are familiar with periodic tessellations and lattices; from the floor in the PI Bistro to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their applications to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.

Zoom Link: https://pitp.zoom.us/j/91876287518?pwd=NGNLOXZHa1h1cmdnMzJxQzVMVFJJdz09

Canonical transformations play fundamental roles in simplifying and solving physical systems. However, their design and implementation can be challenging in the many-particle setting. Viewing canonical transformations from the angle of learnable diffeomorphism reveals a fruitful connection to normalizing flows in machine learning. The key issue is then how to impose physical constraints such as symplecticity, unitarity, and permutation equivariance in the flow transformations. In this talk, I will present the design and application of neural canonical transformations for several physical problems. Symplectic flow identifies independent and nonlinear modes of classical Hamiltonians and natural datasets. Fermi flow variationally solves ab initio many-electron problems at finite temperatures.
Refs:
[1] Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, and Lei Wang, Phys. Rev. X 10, 021020 (2020)
[2]  Hao Xie, Linfeng Zhang, and Lei Wang, J. Mach. Learn. , 1, 38 (2022)

Zoom link:  https://pitp.zoom.us/j/98830940500?pwd=WjdydGY5aS9QQzk5SnI0TE1xMkwrdz09

Kronecker coefficients appear in representation of the symmetric group in the decomposition of tensor products of irreducible representations. They are notoriously difficult to compute and it is a long standing problem to find a combinatorial expression for them. 

We study the problem of computing Kronecker coefficients from quantum computational perspective. First, we show that the coefficients can be expressed as a dimension of a subspace given by intersection of two commuting, efficiently implementable projectors and relate their computation to the recently introduced quantum approximate counting class (QAPC). Using similar construction, we show that deciding positivity of Kronecker coefficients is contained in QMA. We give similar results for a related problem of approximating row sums in a character table of the symmetric group and show that its decision variant is in QMA. We then discuss two quantum algorithms - one that samples a distribution over squared characters and another one that approximates normalized Kronecker coefficients to inverse-polynomial additive error. We show that under a conjecture about average-case hardness of computing Kronecker coefficients, the resulting distribution is hard to sample from classically. 

Our work explores new structures for quantum algorithms and improved characterization of the quantum approximate counting.

Joint work with David Gossett, Sergey Bravyi, Anirban Chowdhury and Guanyu Zhu 

Zoom link:  https://pitp.zoom.us/j/95976938016?pwd=eDV3TXZReHo5UHdvZ0hIbkhXOFcxQT09

The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. I will discuss a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra. However, at loop level new poles are generated, the simplest of which are described the 1-loop effective graviton vertex. These quantum corrections violate associativity of the operator product. I will argue that this failure can be traced to an anomaly in the twistor uplift of self-dual gravity. Associativity can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.

Zoom link:  https://pitp.zoom.us/j/91979544537?pwd=Ykw4Q3lRK2ZicVhCMDhlNUxFaHhlUT09

In this talk I’ll highlight the existence of gaps in the spectrum of GWs poorly explored by current observations and that may contain information about BSM physics or primordial cosmology. I’ll focus on the muHz gap, and explain how to use the resonance absorption of GWs by binary systems (as the Earth-Moon system or binary pulsars) to access this band. I’ll also highlight the potential of high frequency (\omega > kHz) GWs. The focus of this second part will be the use of cavities to detect these signals, together with a brief discussion of sources and what can be learned from them.

Zoom Link:  https://pitp.zoom.us/j/94501758748?pwd=amFsTjV5Z1c5SHJrVVBCanVCRHRMUT09

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. I will introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator.  I will show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. I will provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

Zoom link:  https://pitp.zoom.us/j/99584743899?pwd=aHl1cVlpK29ZVDkrdFZyM01GemJJdz09

In this talk, I will present two recent works on electronic lattice models, both of which utilize novel numerical algorithms to achieve a deeper understanding of the many-electron problem. Competing and intertwined orders including inhomogeneous patterns of spin and charge are observed in many correlated electron materials, such as high-temperature superconductors. In arXiv:2202.11741, we introduce a new development of constrained-path auxiliary-field quantum Monte Carlo (AFMQC) method and study the interplay between thermal and quantum fluctuations in the two-dimensional Hubbard model. We identify a finite-temperature phase transition below which charge ordering sets in. Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems.  However, discerning phases with off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. In the second work arXiv:2209.10565, we study the one-dimensional extended Hubbard model using the variational uniform matrix product states algorithm. We show that a multi-scale complexity measure can pinpoint the transition to and from the bond ordered wave phase with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors.

Zoom link:  https://pitp.zoom.us/j/97325001971?pwd=QXNmU2I0L3BxQVErMEZWSDF2bGZ0QT09

Nonclassicality, as witnessed by the incapacity of Classical Causal Theory (CCT) of explaining a system's behavior given its causal structure, come to be one of the hottest topics in Quantum Foundations over the last decades, a movement that was motivated both by its vast range of practical applications and by the powerful insights it provides about the rules of the quantum world. Among the many attempts at understanding/quantifying this phenomenon, we highlight the idea of inquiring how further would it be necessary to relax the causal structure associated with a given system in order to have its nonclassical behavior explained by CCT. More recently, we showed that the relaxation demanded to explain the behavior of a subset of variables in a given experiment may not be allowed by the embedding causal structure when considering the behavior of the remaining variables, which led to a new way of witnessing nonclassicality. In this seminar, we discuss a new way of quantifying this incompatibility and possible generalizations of this approach to different scenarios.

Zoom link:  https://pitp.zoom.us/j/96051313203?pwd=bFNhOEhkSVhXWk8yd1hVZWVVa0U4UT09

In this talk, I present the latest works on anyonic information theory and how it is linked to aspects of quantum foundations. First, the theory of 2+1 D non-abelian anyons will be introduced. The newly discovered notion of anyonic creation operators will be presented, as well as their use as local elements of reality within the Deutsch-Hayden interpretation of quantum mechanics. Lastly, I will show strange properties of anyonic entanglement that appear due to the lack of a tensor product structure, such as the different spectra of marginals in bipartite systems. This property makes the Von Neumann entropy a bad entanglement measure. I will explain the challenges of defining entanglement measures for anyonic systems and current approaches. 

Zoom link:  https://pitp.zoom.us/j/99863263804?pwd=MUhkYTBzcUlwTmJ0Z3F4aFo3Rkt6QT09

Extensions of asymptotic phase spaces and their corresponding asymptotic symmetry groups have become a topic of increasing interest in recent years, due to results that connect them with a wide spectrum of areas, such as symmetries of the S-matrix, soft theorems, corner symmetries, double copy maps and celestial holography. The study of these extensions aims to characterize the degrees of freedom of the physical theories at the classical level, gathering information on how their symmetries can be upgraded to the quantum theories. In this talk, I will describe extensions of phase spaces at null infinity for gravity and gauge theories, such that the charges are consistent with tree-level soft (graviton, gluon or photon) theorems and act canonically. First, as motivation, I will show how the Geroch group for cylindrically symmetric general relativity can be upgraded as a quantum symmetry, exploiting the integrability of the system (arXiv:1906.04856 [gr-qc]). Second, I will review the construction of an extended phase space where the generalized BMS symmetry group acts canonically (arXiv:2002.06691 [gr-qc]). I will show that this construction is consistent with the extended corner symmetry approach (via the embedding maps). Finally, I will show that a similar approach can be done in Yang Mills, by extending the phase space with "Goldstone modes" that transform inhomogeneously under linearized O(r) symmetries (arXiv:2111.00973 [hep-th]). Some preliminary results regarding the extension to higher order O(r^n) will be discussed (arXiv:2211.12991 [hep-th]).

Zoom link:  https://pitp.zoom.us/j/95866794894?pwd=UEtQYlBpV0NCM3cyeWpDcTI2WVp6UT09

The Event Horizon Telescope has released total intensity images of the Messier 87* and Sagittarius A* accretion flows; polarized images have been released for M 87*, and are imminent for Sgr A*. These images are a rich source of theoretical constraints on the black hole accretion flow system, but a trustworthy measurement of either black hole's spin remains elusive. Spin nonetheless remains a high priority, as the black hole angular momentum is deeply linked to mechanisms of energy extraction and galactic co-evolution. In my talk, I will discuss my work on providing theoretical traction on supermassive black hole spin, and will review the state of spin measurements using existing and future EHT data, including measurements of the black hole photon ring, inference of near-horizon magnetic field structure, and next-generation spacetime/emissivity inference codes.

Zoom:  https://pitp.zoom.us/j/95355525128?pwd=blczM1ZUMGs5RmNxMVNCV3hlRDA4UT09

In spite of its immense importance in the present-day information technology, the foundational aspects of quantum theory (QT) remain still elusive. In particular, there is no such set of physically motivated axioms which can answer why Hilbert space formalism is the only natural choice to describe the microscopic world. Hence, to shed light on the unique formalism of QT, two different operational frameworks will be described in the primitive of various convex operational theories. The first one refers to a kinematical symmetry principle which would be proposed from the perspective of single copy state discrimination and it would be shown that this symmetry holds for both classical and QT – two successful descriptions of the physical world. On the other hand, studying a wide range of convex operational theories, namely the General Probabilistic Theories (GPTs) with polygonal state spaces, we observe the absence of such symmetry. Thus, the principle deserves its own importance to mark a sharp distinction between the physical and unphysical theories. Thereafter, a distributed computing scenario will be introduced for which the other convex theories except the QT turn out to be equivalent to the classical one even though the theories possess more exotic state and effect spaces. We have coined this particular operational framework as ‘Distributed computation with limited communication’ (DCLC). Furthermore, it will be shown that the distributed computational strength of quantum communication will be justified in terms of a stronger version of this task, namely the ‘Delayed choice distributed computation with limited communication’ (DC2LC). The proposed task thus provides a new approach to operationally single out quantum theory in the theory-space and hence promises a novel perspective towards the axiomatic derivation of Hilbert space quantum mechanics.

References:
Phys. Rev. A (Rapid)100, 060101 (2019)
Ann. Phys.(Berlin)2020,532, 2000334 (2020)
arXiv:2012.05781 [quant-ph](2020)

Zoom link:  https://pitp.zoom.us/j/92924188227?pwd=ODJYQXVoaUtzZmZIdFlmcUNIV3Rmdz09