Talks

Zero-knowledge proofs are one of the cornerstones of modern cryptography. It is well known that any language in NP admits a zero-knowledge proof. In the quantum setting, it is possible to go beyond NP. Zero-knowledge proofs for QMA have first been studied in a work of Broadbent et al (FOCS'16). There, the authors show that any language in QMA has an (interactive) zero-knowledge proof. In this talk, I will describe an idea, based on quantum teleportation, to remove interaction at the cost of adding an instance-independent preprocessing step. Assuming the Learning With Errors problem is hard for quantum computers, the resulting protocol is a non-interactive zero-knowledge argument for QMA, with a preprocessing step that consists of (i) the generation of a Common Reference String and (ii) a single (instance-independent) quantum message from the verifier to the prover.

This is joint work with Thomas Vidick and Tina Zhang

One of the major themes of the modern condensed matter physics is the study of materials with nontrivial electronic structure topology. Particularly significant progress in this field has happened within the last decade, due to the discovery of topologically nontrivial states of matter, that have a gap in their energy spectrum, namely Topological Insulators and Topological Superconductors. In this talk I will describe the most recent work, partly my own, extending the notions of the nontrivial electronic structure topology to gapless states of matter as well, namely to semimetals and even metals. I will discuss both the theoretical concepts, and the recent experimental work, realizing these novel states of condensed matter.

Current and forthcoming observing runs at ground-based laser interferometry detectors are starting to uncover gravitational waves from binary black hole (BBH) mergers at cosmological distances, and a fraction of them are expected to be gravitationally lensed by intervening galaxy or cluster lenses with multiple images. Such strongly lensed events, if discovered, may offer a precious opportunity to localize BBH host galaxies and probe global and small-scale property of the lens mass profile. We investigate multiple BBH events showing parameter coincidence in the LIGO/Virgo O2 run, and search for additional sub-threshold signals that may be fainter lensed images. For the first time, we factor in the effect of the Morse phase shift in the analysis, and demonstrate how to measure the relative Morse phase via joint parameter inference. We confirm curiously high level of intrinsic and extrinsic parameter coincidence between GW170814 and GW170104, and uncover a third sub-threshold candidate lensed image, GWC170620, in a single-template search, which amounts to an estimated 10^-4 overall chance of statistical fluke. The measured relative Morse phases among the three events, although consistent with ray-optics lensing, point toward a complicated and unexpected image topology with a magnified image at a local maximum of the Fermat potential, which however casts doubt on the lensing hypothesis. The long time delays on the order of months necessarily require a massive lens of galaxy cluster scale. If a genuine set of multiple lensed images, we localize the source to ~ 16 deg^2 on the sky and suggest a range 0.4 < z < 0.7 for its redshift. Optical follow-up observations are encouraged to collect any additional information that may further shed light on the case. 
 

In this talk, we review an approach to describing cosmological physics using ordinary AdS/CFT, where the cosmological physics is the effective description of an end-of-the-world brane which cuts off the second asymptotic region of a two-sided black hole. The worldvolume geometry of the brane is an FRW big-bang/big-crunch spacetime. Infavorable circumstances, the brane acts as a Randall-Sundrum Planck brane so that gravity localizes. We describe a microscopic construction for such an end-of-the-world brane with localized gravity in AdS/CFT, starting from N=4 SYM theory. We suggest specific microscopic states of N=4 SYM theory that may encode the physics in a four-dimensional cosmological spacetime.

The interplay between topology, strong correlations, and kinetic energy presents a new challenge for the theory of quantum matter. In this talk I will describe some recent progress on understanding a simple class of problems where these effects can all be analytically handled. I will first present results on a microscopic lowest Landau theory of the composite fermi liquid state of bosons at filling 1.  Building on work from the 1990s I will derive an effective field theory for this system that takes the form of a non-commutative field theory. I will show that an approximate mapping of this theory to a commutative field theory yield the familiar Halperin-Lee-Read action but with parameters correctly described by the interaction strength. I will describe the effect of a finite bandwidth  introduced to the Landau Level and describe the evolution between the composite Fermi liquid and a boson superfluid. Time permitting, I will describe some generalizations that will include the evolution between a Quantum Anomalous Hall state and a Landau Fermi liquid that may be experimentally accessible in moire graphene systems.

The Raychaudhuri equation predicts the convergence of geodesics and gives rise to the singularity theorems. The quantum Raychaudhuri equation (QRE), on the other hand, shows that quantal trajectories, the quantum equivalent of the geodesics, do not converge and are not associated with any singularity theorems. Furthermore, the QRE gives rise to the quantum corrected Friedmann equation. The quantum correction is dependent on the wavefunction of the perfect fluid whose pressure and density enter the Friedmann equation. We show that for a suitable choice of the wavefunction this term can be interpreted as a small positive cosmological constant.

The statement that general relativity is deterministic finds its mathematical formulation in the celebrated ‘Strong Cosmic Censorship Conjecture’ due to Roger Penrose. I will present my recent results on this conjecture in the case of negative cosmological constant and in the context of black holes. It turns out that this is intimately tied to Diophantine properties of a suitable ratio of mass and angular momentum of the black hole.

We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied question in machine learning and statistics. In this work, we give the first sample-efficient algorithm for the quantum Hamiltonian learning problem. In particular, we prove that polynomially many samples in the number of particles (qudits) are necessary and sufficient for learning the parameters of a spatially local Hamiltonian in l_2-norm.
Our main contribution is in establishing the strong convexity of the log-partition function of quantum many-body systems, which along with the maximum entropy estimation yields our sample-efficient algorithm. Classically, the strong convexity for partition functions follows from the Markov property of Gibbs distributions. This is, however, known to be violated in its exact form in the quantum case. We introduce several new ideas to obtain an unconditional result that avoids relying on the Markov property of quantum systems, at the cost of a slightly weaker bound. In particular, we prove a lower bound on the variance of quasi-local operators with respect to the Gibbs state, which might be of independent interest.

Joint work with Srinivasan Arunachalam, Tomotaka Kuwahara, Mehdi Soleimanifar

In most materials, electrons fill bands, starting from the lowest kinetic energy states. The Fermi level is the boundary between filled states below and empty states above. This is the basis for our very successful understanding of how metals and semiconductors work. But what if all the electrons within a band had the same kinetic energy (this situation is called a "flat band")? Then electrons could arrange themselves so as to minimize their Coulomb repulsion, giving rise to a wide variety of possible states including superconductors and magnets. Until recently, flat bands were achieved only by applying large magnetic fields perpendicular to a 2D electron system; in this context they are known as Landau levels. Fractional quantum hall effects result from Coulomb-driven electron arrangement within a Landau level. Recently, Pablo Jarillo-Herrero of MIT and coworkers demonstrated flat minibands in graphene-based superlattices, discovering correlated insulators and superconductors at different fillings of these minibands. We have now discovered dramatic magnetic states in such superlattice systems. Specifically, in magic-angle twisted bilayer graphene which is also aligned with a hexagonal boron nitride (hBN) cladding layer, we observe a giant anomalous Hall effect as large as 10.4 kΩ, and signs of chiral edge states. This all occurs at zero magnetic field, in a narrow density range around an apparent insulating state at 3 electrons (1 hole) per moiré cell in the conduction miniband [1]. Remarkably, the magnetization of the sample can be reversed by applying a small DC current. Although the anomalous Hall resistance is not quantized, and dissipation is significant, we suggest that the system is essentially a "Chern insulator", a type of topological insulator similar to an integer quantum Hall state. In a quite different superlattice system, ABC-trilayer graphene aligned with hBN, again near 3 electrons (1 hole) per moiré cell a Chern insulator emerges [2]. This time the flat band is a valence miniband, and a magnetic field of order 100 mT is needed to quantize the anomalous hall signal. This trilayer system can be tuned in-situ to display superconductivity instead of magnetism [3]. We will discuss possible magnetic states, complementary probes to examine which state actually emerges as the ground state in each system, and what one might do with such states.

[1] A.L. Sharpe et al., “Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene”, Science 365, 6453 (2019).
[2] G. Chen et al., “Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moire Superlattice”, Nature 579, 56 (2020)
[3] G. Chen et al., “Signatures of tunable superconductivity in a trilayer graphene moiré superlattice”, Nature 572, 215 (2019).